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algorithm-in-python
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mbinary 2020-04-15 12:28:20 +08:00
parent 985b29ce65
commit ab86fa483a
75 changed files with 3122 additions and 2426 deletions
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10
README.md
View File

@ -6,7 +6,7 @@
[![repo-size](https://img.shields.io/github/repo-size/mbinary/algorithm.svg)]()
[![License](https://img.shields.io/badge/LICENSE-WTFPL-blue.svg)](LICENSE)
[![Language](https://img.shields.io/badge/language-python3-orange.svg)]()
[![codebeat badge](https://codebeat.co/badges/d52dd17d-a437-4dee-a6ec-cb532e8135bd)](https://codebeat.co/projects/github-com-mbinary-algorithm-master)
[![codebeat badge](https://codebeat.co/badges/4ef725b5-405a-4390-a860-a86deefab3f8)](https://codebeat.co/projects/github-com-mbinary-algorithm-master)
>Notes and codes for learning algorithm and data structures :smiley:
@ -17,12 +17,10 @@ Some pictures and ideas are from `<<Introduction to Algotithm>>`
* [.](.)
* [LICENSE](./LICENSE)
* [README.md](./README.md)
* [backtracking](./backtracking)
* [dataStructure](./dataStructure)
* [LRU](./dataStructure/LRU)
* [bTree.py](./dataStructure/bTree.py)
* [binaryHeap.py](./dataStructure/binaryHeap.py)
* [binaryHeap1.py](./dataStructure/binaryHeap1.py)
* [binaryTree.py](./dataStructure/binaryTree.py)
* [circularQueue.py](./dataStructure/circularQueue.py)
* [graph](./dataStructure/graph)
@ -32,7 +30,6 @@ Some pictures and ideas are from `<<Introduction to Algotithm>>`
* [intervalTree.py](./dataStructure/intervalTree.py)
* [leftHeap.py](./dataStructure/leftHeap.py)
* [linkedList.py](./dataStructure/linkedList.py)
* [loserTree.py](./dataStructure/loserTree.py)
* [map.cc](./dataStructure/map.cc)
* [polynomial.cpp](./dataStructure/polynomial.cpp)
* [polynomial.py](./dataStructure/polynomial.py)
@ -40,7 +37,7 @@ Some pictures and ideas are from `<<Introduction to Algotithm>>`
* [redBlackTree0.py](./dataStructure/redBlackTree0.py)
* [splayTree.py](./dataStructure/splayTree.py)
* [trie](./dataStructure/trie)
* [unionFindSet](./dataStructure/unionFindSet)
* [unionFindSet.py](./dataStructure/unionFindSet.py)
* [winnerTree.py](./dataStructure/winnerTree.py)
* [divideAndConquer](./divideAndConquer)
* [min_distance_of_n_points.py](./divideAndConquer/min_distance_of_n_points.py)
@ -85,8 +82,9 @@ Some pictures and ideas are from `<<Introduction to Algotithm>>`
* [PL0-compiler](./parser/PL0-compiler)
* [calculator](./parser/calculator)
* [declarationParser](./parser/declarationParser)
* [poly.c](./poly.c)
* [search](./search)
* [8Astar.py](./search/8Astar.py)
* [Astar.py](./search/Astar.py)
* [BFS_knight.hs](./search/BFS_knight.hs)
* [binary_search.hs](./search/binary_search.hs)
* [bloomFilter.py](./search/bloomFilter.py)

260
dataStructure/bTree.py
View File

@ -10,213 +10,257 @@
#########################################################################
'''
class node:
def __init__(self,keys=None,isLeaf = True,children=None):
if keys is None:keys=[]
if children is None: children =[]
def __init__(self, keys=None, isLeaf=True, children=None):
if keys is None:
keys = []
if children is None:
children = []
self.keys = keys
self.isLeaf = isLeaf
self.isLeaf = isLeaf
self.children = []
def __getitem__(self,i):
def __getitem__(self, i):
return self.keys[i]
def __delitem__(self,i):
def __delitem__(self, i):
del self.keys[i]
def __setitem__(self,i,k):
def __setitem__(self, i, k):
self.keys[i] = k
def __len__(self):
return len(self.keys)
def __repr__(self):
return str(self.keys)
def __str__(self):
children = ','.join([str(nd.keys) for nd in self.children])
return f'keys: {self.keys}\nchildren: {children}\nisLeaf: {self.isLeaf}'
def getChd(self,i):
def getChd(self, i):
return self.children[i]
def delChd(self,i):
def delChd(self, i):
del self.children[i]
def setChd(self,i,chd):
def setChd(self, i, chd):
self.children[i] = chd
def getChildren(self,begin=0,end=None):
if end is None:return self.children[begin:]
def getChildren(self, begin=0, end=None):
if end is None:
return self.children[begin:]
return self.children[begin:end]
def findKey(self,key):
for i,k in enumerate(self.keys):
if k>=key:
def findKey(self, key):
for i, k in enumerate(self.keys):
if k >= key:
return i
return len(self)
def update(self,keys=None,isLeaf=None,children=None):
if keys is not None:self.keys = keys
if children is not None:self.children = children
if isLeaf is not None: self.isLeaf = isLeaf
def insert(self,i,key=None,nd=None):
if key is not None:self.keys.insert(i,key)
if not self.isLeaf and nd is not None: self.children.insert(i,nd)
def isLeafNode(self):return self.isLeaf
def split(self,prt,t):
def update(self, keys=None, isLeaf=None, children=None):
if keys is not None:
self.keys = keys
if children is not None:
self.children = children
if isLeaf is not None:
self.isLeaf = isLeaf
def insert(self, i, key=None, nd=None):
if key is not None:
self.keys.insert(i, key)
if not self.isLeaf and nd is not None:
self.children.insert(i, nd)
def isLeafNode(self): return self.isLeaf
def split(self, prt, t):
# form new two nodes
k = self[t-1]
nd1 = node()
nd2 = node()
nd1.keys,nd2.keys = self[:t-1], self[t:] # note that t is 1 bigger than key index
# note that t is 1 bigger than key index
nd1.keys, nd2.keys = self[:t-1], self[t:]
nd1.isLeaf = nd2.isLeaf = self.isLeaf
if not self.isLeaf:
if not self.isLeaf:
# note that children index is one bigger than key index, and all children included
nd1.children, nd2.children = self.children[0:t], self.children[t:]
nd1.children, nd2.children = self.children[0:t], self.children[t:]
# connect them to parent
idx = prt.findKey(k)
if prt.children !=[]: prt.children.remove(self) # remove the original node
prt.insert(idx,k,nd2)
prt.insert(idx,nd = nd1)
if prt.children != []:
prt.children.remove(self) # remove the original node
prt.insert(idx, k, nd2)
prt.insert(idx, nd=nd1)
return prt
class bTree:
def __init__(self,degree=2):
def __init__(self, degree=2):
self.root = node()
self.degree=degree
self.degree = degree
self.nodeNum = 1
self.keyNum = 0
def search(self,key,withpath=False):
def search(self, key, withpath=False):
nd = self.root
fathers = []
while True:
i = nd.findKey(key)
if i==len(nd): fathers.append((nd,i-1,i))
else: fathers.append((nd,i,i))
if i<len(nd) and nd[i]==key:
if withpath:return nd,i,fathers
else:return nd,i
if nd.isLeafNode():
if withpath:return None,None,None
else:return None,None
if i == len(nd):
fathers.append((nd, i-1, i))
else:
fathers.append((nd, i, i))
if i < len(nd) and nd[i] == key:
if withpath:
return nd, i, fathers
else:
return nd, i
if nd.isLeafNode():
if withpath:
return None, None, None
else:
return None, None
nd = nd.getChd(i)
def insert(self,key):
if len(self.root)== self.degree*2-1:
self.root = self.root.split(node(isLeaf=False),self.degree)
self.nodeNum +=2
def insert(self, key):
if len(self.root) == self.degree*2-1:
self.root = self.root.split(node(isLeaf=False), self.degree)
self.nodeNum += 2
nd = self.root
while True:
idx = nd.findKey(key)
if idx<len(nd) and nd[idx] == key:return
if idx < len(nd) and nd[idx] == key:
return
if nd.isLeafNode():
nd.insert(idx,key)
self.keyNum+=1
nd.insert(idx, key)
self.keyNum += 1
return
else:
chd = nd.getChd(idx)
if len(chd)== self.degree*2-1: #ensure its keys won't excess when its chd split and u
nd = chd.split(nd,self.degree)
self.nodeNum +=1
# ensure its keys won't excess when its chd split and u
if len(chd) == self.degree*2-1:
nd = chd.split(nd, self.degree)
self.nodeNum += 1
else:
nd = chd
def delete(self,key):#to do
def delete(self, key): # to do
'''search the key, delete it , and form down to up to rebalance it '''
nd,idx ,fathers= self.search(key,withpath=True)
if nd is None : return
nd, idx, fathers = self.search(key, withpath=True)
if nd is None:
return
del nd[idx]
self.keyNum-=1
self.keyNum -= 1
if not nd.isLeafNode():
chd = nd.getChd(idx) # find the predecessor key
while not chd.isLeafNode():
fathers.append((chd,len(chd)-1,len(chd)))
chd = nd.getChd(idx) # find the predecessor key
while not chd.isLeafNode():
fathers.append((chd, len(chd)-1, len(chd)))
chd = chd.getChd(-1)
fathers.append((chd,len(chd)-1,len(chd)))
nd.insert(idx,chd[-1])
fathers.append((chd, len(chd)-1, len(chd)))
nd.insert(idx, chd[-1])
del chd[-1]
if len(fathers)>1:self.rebalance(fathers)
def rebalance(self,fathers):
nd,keyIdx,chdIdx = fathers.pop()
while len(nd)<self.degree-1: # rebalance tree from down to up
prt,keyIdx,chdIdx = fathers[-1]
lbro = [] if chdIdx==0 else prt.getChd(chdIdx-1)
rbro = [] if chdIdx==len(prt) else prt.getChd(chdIdx+1)
if len(lbro)<self.degree and len(rbro)<self.degree: # merge two deficient nodes
beforeNode,afterNode = None,None
if lbro ==[]:
if len(fathers) > 1:
self.rebalance(fathers)
def rebalance(self, fathers):
nd, keyIdx, chdIdx = fathers.pop()
while len(nd) < self.degree-1: # rebalance tree from down to up
prt, keyIdx, chdIdx = fathers[-1]
lbro = [] if chdIdx == 0 else prt.getChd(chdIdx-1)
rbro = [] if chdIdx == len(prt) else prt.getChd(chdIdx+1)
if len(lbro) < self.degree and len(rbro) < self.degree: # merge two deficient nodes
beforeNode, afterNode = None, None
if lbro == []:
keyIdx = chdIdx
beforeNode,afterNode = nd,rbro
beforeNode, afterNode = nd, rbro
else:
beforeNode,afterNode = lbro,nd
keyIdx = chdIdx-1 # important, when choosing
beforeNode, afterNode = lbro, nd
keyIdx = chdIdx-1 # important, when choosing
keys = beforeNode[:]+[prt[keyIdx]]+afterNode[:]
children = beforeNode.getChildren() + afterNode.getChildren()
isLeaf = beforeNode.isLeafNode()
prt.delChd(keyIdx+1)
del prt[keyIdx]
nd.update(keys,isLeaf,children)
prt.children[keyIdx]=nd
self.nodeNum -=1
elif len(lbro)>=self.degree: # rotate when only one sibling is deficient
nd.update(keys, isLeaf, children)
prt.children[keyIdx] = nd
self.nodeNum -= 1
elif len(lbro) >= self.degree: # rotate when only one sibling is deficient
keyIdx = chdIdx-1
nd.insert(0,prt[keyIdx]) # rotate keys
prt[keyIdx] = lbro[-1]
nd.insert(0, prt[keyIdx]) # rotate keys
prt[keyIdx] = lbro[-1]
del lbro[-1]
if not nd.isLeafNode(): # if not leaf, move children
nd.insert(0,nd=lbro.getChd(-1))
nd.insert(0, nd=lbro.getChd(-1))
lbro.delChd(-1)
else:
keyIdx = chdIdx
nd.insert(len(nd),prt[keyIdx]) # rotate keys
prt[keyIdx] = rbro[0]
nd.insert(len(nd), prt[keyIdx]) # rotate keys
prt[keyIdx] = rbro[0]
del rbro[0]
if not nd.isLeafNode(): # if not leaf, move children
#note that insert(-1,ele) will make the ele be the last second one
nd.insert(len(nd),nd=rbro.getChd(0))
# note that insert(-1,ele) will make the ele be the last second one
nd.insert(len(nd), nd=rbro.getChd(0))
rbro.delChd(0)
if len(fathers)==1:
if len(self.root)==0:
if len(fathers) == 1:
if len(self.root) == 0:
self.root = nd
self.nodeNum -=1
self.nodeNum -= 1
break
nd,i,j = fathers.pop()
nd, i, j = fathers.pop()
def __str__(self):
head= '\n'+'-'*30+'B Tree'+'-'*30
tail= '-'*30+'the end'+'-'*30+'\n'
lst = [[head],[f'node num: {self.nodeNum}, key num: {self.keyNum}']]
head = '\n'+'-'*30+'B Tree'+'-'*30
tail = '-'*30+'the end'+'-'*30+'\n'
lst = [[head], [f'node num: {self.nodeNum}, key num: {self.keyNum}']]
cur = []
ndNum =0
ndTotal= 1
ndNum = 0
ndTotal = 1
que = [self.root]
while que!=[]:
while que != []:
nd = que.pop(0)
cur.append(repr(nd))
ndNum+=1
que+=nd.getChildren()
if ndNum==ndTotal:
ndNum += 1
que += nd.getChildren()
if ndNum == ndTotal:
lst.append(cur)
cur = []
ndNum = 0
ndTotal =len(que)
ndTotal = len(que)
lst.append([tail])
lst = [','.join(li) for li in lst]
return '\n'.join(lst)
def __iter__(self,nd = None):
if nd is None: nd = self.root
def __iter__(self, nd=None):
if nd is None:
nd = self.root
que = [nd]
while que !=[]:
while que != []:
nd = que.pop(0)
yield nd
if nd.isLeafNode():continue
if nd.isLeafNode():
continue
for i in range(len(nd)+1):
que.append(nd.getChd(i))
if __name__ =='__main__':
if __name__ == '__main__':
bt = bTree()
from random import shuffle,sample
from random import shuffle, sample
n = 20
lst = [i for i in range(n)]
shuffle(lst)
test= sample(lst,len(lst)//4)
test = sample(lst, len(lst)//4)
print(f'building b-tree with {lst}')
for i in lst:
bt.insert(i)
#print(f'inserting {i})
#print(bt)
# print(f'inserting {i})
# print(bt)
print(bt)
print(f'serching {test}')
for i in test:
nd,idx = bt.search(i)
nd, idx = bt.search(i)
print(f'node: {repr(nd)}[{idx}]== {i}')
for i in test:
print(f'deleting {i}')

149
dataStructure/binaryHeap.py
View File

@ -11,106 +11,137 @@
'''
from collections import Iterable
from collections import Iterable
class node:
def __init__(self,val,freq=1):
self.val=val
def __init__(self, val, freq=1):
self.val = val
self.freq = freq
def __eq__(self,a):
return self.val == a.val
def __lt__(self,a):
return self.val<a.val
def __le__(self,a):
return self.val<=a.val
def __gt__(self,a):
return self.val>a.val
def __ge__(self,a):
return self.val>=a.val
def __ne__(self,a):
def __eq__(self, a):
return self.val == a.val
def __lt__(self, a):
return self.val < a.val
def __le__(self, a):
return self.val <= a.val
def __gt__(self, a):
return self.val > a.val
def __ge__(self, a):
return self.val >= a.val
def __ne__(self, a):
return not self == a
class binaryHeap:
def __init__(self,s=None,sortByFrequency = False,reverse=False):
self.sortByFrequency=sortByFrequency
def __init__(self, s=None, sortByFrequency=False, reverse=False):
self.sortByFrequency = sortByFrequency
self.reverse = reverse
self.data = [node(0)] # make index begin with 1
if s==None:return
if not isinstance(s,Iterable):s = [s]
if s == None:
return
if not isinstance(s, Iterable):
s = [s]
for i in s:
self.insert(i)
def __bool__(self):
return len(self)!=1
def _cmp(self,a,b):
return len(self) != 1
def _cmp(self, a, b):
if self.sortByFrequency:
if self.reverse:return a.freq>b.freq
else:return a.freq<b.freq
if self.reverse:
return a.freq > b.freq
else:
return a.freq < b.freq
else:
if self.reverse:return a>b
else:return a<b
def insert(self,k):
if not isinstance(k,node): k = node(k)
if self.reverse:
return a > b
else:
return a < b
def insert(self, k):
if not isinstance(k, node):
k = node(k)
for j in range(self.data[0].val):
i = self.data[j+1]
if i==k:
i.freq+=1
if i == k:
i.freq += 1
if self.sortByFrequency:
idx = self.percolateDown(j+1)
self.percolateUp(idx)
return
return
self.data.append(k)
self.data[0].val += 1
self.percolateUp()
def percolateUp(self,n=None):
if n ==None:n=self.data[0].val
def percolateUp(self, n=None):
if n == None:
n = self.data[0].val
tmp = self.data[n]
while n!=1 and self._cmp(tmp,self.data[n//2]):
while n != 1 and self._cmp(tmp, self.data[n//2]):
self.data[n] = self.data[n//2]
n = n//2
self.data[n] = tmp
def deleteTop(self):
tmp = self.data[1]
i = self.percolateDown(1)
self.data[i] = self.data[-1]
self.data[0].val-= 1
self.data[0].val -= 1
del self.data[-1]
return tmp
def percolateDown(self,i):
def percolateDown(self, i):
tmp = self.data[i]
while self.data[0].val>=2*i+1:
if self._cmp(self.data[i*2],self.data[2*i+1]):
self.data[i] = self.data[2*i]
i = 2*i
else:
self.data[i] = self.data[2*i+1]
i = 2*i+1
while self.data[0].val >= 2*i+1:
if self._cmp(self.data[i*2], self.data[2*i+1]):
self.data[i] = self.data[2*i]
i = 2*i
else:
self.data[i] = self.data[2*i+1]
i = 2*i+1
self.data[i] = tmp
return i
def __len__(self):
return self.data[0].val
def Nth(self,n=1):
def Nth(self, n=1):
tmp = []
for i in range(n):
tmp.append(self.deleteTop())
for i in tmp:
self.insert(i)
return tmp[-1]
def display(self):
val =self.data[0].val+1
val = self.data[0].val+1
if self.sortByFrequency:
info='heapSort by Frequency:'
else:info = 'heapSort by Value:'
info = 'heapSort by Frequency:'
else:
info = 'heapSort by Value:'
if self.reverse:
info +=' From big to small'
else:info +=' From small to big'
info += ' From big to small'
else:
info += ' From small to big'
print('*'*15)
print(info)
print('total items:%d\nval\tfreq'%(val-1))
print('total items:%d\nval\tfreq' % (val-1))
fmt = '{}\t{}'
for i in range(1,val):
print(fmt.format(self.data[i].val,self.data[i].freq))
for i in range(1, val):
print(fmt.format(self.data[i].val, self.data[i].freq))
print('*'*15)
class Test:
def topKFrequent(self, words, k):
hp = binaryHeap(sortByFrequency = True,reverse=True)
hp = binaryHeap(sortByFrequency=True, reverse=True)
for i in words:
hp.insert(i)
hp.display()
@ -124,15 +155,19 @@ class Test:
mp[top.freq] = [top.val]
for i in mp:
mp[i].sort()
key = sorted(mp.keys(),reverse = True)
key = sorted(mp.keys(), reverse=True)
rst = []
count = 0
for i in key:
for i in key:
for j in mp[i]:
rst.append(j)
count+=1
if count == k:return rst
count += 1
if count == k:
return rst
if __name__ == '__main__':
s=["plpaboutit","jnoqzdute","sfvkdqf","mjc","nkpllqzjzp","foqqenbey","ssnanizsav","nkpllqzjzp","sfvkdqf","isnjmy","pnqsz","hhqpvvt","fvvdtpnzx","jkqonvenhx","cyxwlef","hhqpvvt","fvvdtpnzx","plpaboutit","sfvkdqf","mjc","fvvdtpnzx","bwumsj","foqqenbey","isnjmy","nkpllqzjzp","hhqpvvt","foqqenbey","fvvdtpnzx","bwumsj","hhqpvvt","fvvdtpnzx","jkqonvenhx","jnoqzdute","foqqenbey","jnoqzdute","foqqenbey","hhqpvvt","ssnanizsav","mjc","foqqenbey","bwumsj","ssnanizsav","fvvdtpnzx","nkpllqzjzp","jkqonvenhx","hhqpvvt","mjc","isnjmy","bwumsj","pnqsz","hhqpvvt","nkpllqzjzp","jnoqzdute","pnqsz","nkpllqzjzp","jnoqzdute","foqqenbey","nkpllqzjzp","hhqpvvt","fvvdtpnzx","plpaboutit","jnoqzdute","sfvkdqf","fvvdtpnzx","jkqonvenhx","jnoqzdute","nkpllqzjzp","jnoqzdute","fvvdtpnzx","jkqonvenhx","hhqpvvt","isnjmy","jkqonvenhx","ssnanizsav","jnoqzdute","jkqonvenhx","fvvdtpnzx","hhqpvvt","bwumsj","nkpllqzjzp","bwumsj","jkqonvenhx","jnoqzdute","pnqsz","foqqenbey","sfvkdqf","sfvkdqf"]
s = ["plpaboutit", "jnoqzdute", "sfvkdqf", "mjc", "nkpllqzjzp", "foqqenbey", "ssnanizsav", "nkpllqzjzp", "sfvkdqf", "isnjmy", "pnqsz", "hhqpvvt", "fvvdtpnzx", "jkqonvenhx", "cyxwlef", "hhqpvvt", "fvvdtpnzx", "plpaboutit", "sfvkdqf", "mjc", "fvvdtpnzx", "bwumsj", "foqqenbey", "isnjmy", "nkpllqzjzp", "hhqpvvt", "foqqenbey", "fvvdtpnzx", "bwumsj", "hhqpvvt", "fvvdtpnzx", "jkqonvenhx", "jnoqzdute", "foqqenbey", "jnoqzdute", "foqqenbey", "hhqpvvt", "ssnanizsav", "mjc", "foqqenbey", "bwumsj", "ssnanizsav", "fvvdtpnzx", "nkpllqzjzp",
"jkqonvenhx", "hhqpvvt", "mjc", "isnjmy", "bwumsj", "pnqsz", "hhqpvvt", "nkpllqzjzp", "jnoqzdute", "pnqsz", "nkpllqzjzp", "jnoqzdute", "foqqenbey", "nkpllqzjzp", "hhqpvvt", "fvvdtpnzx", "plpaboutit", "jnoqzdute", "sfvkdqf", "fvvdtpnzx", "jkqonvenhx", "jnoqzdute", "nkpllqzjzp", "jnoqzdute", "fvvdtpnzx", "jkqonvenhx", "hhqpvvt", "isnjmy", "jkqonvenhx", "ssnanizsav", "jnoqzdute", "jkqonvenhx", "fvvdtpnzx", "hhqpvvt", "bwumsj", "nkpllqzjzp", "bwumsj", "jkqonvenhx", "jnoqzdute", "pnqsz", "foqqenbey", "sfvkdqf", "sfvkdqf"]
test = Test()
print(test.topKFrequent(s,5))
print(test.topKFrequent(s, 5))

111
dataStructure/binaryTree.py
View File

@ -12,61 +12,86 @@
from functools import total_ordering
@total_ordering
class node:
def __init__(self,val,left=None,right=None,freq = 1):
self.val=val
self.left=left
self.right=right
def __init__(self, val, left=None, right=None, freq=1):
self.val = val
self.left = left
self.right = right
self.freq = freq
def __lt__(self,nd):
return self.val<nd.val
def __eq__(self,nd):
return self.val==nd.val
def __lt__(self, nd):
return self.val < nd.val
def __eq__(self, nd):
return self.val == nd.val
def __repr__(self):
return 'node({})'.format(self.val)
class binaryTree:
def __init__(self):
self.root=None
def add(self,val):
def _add(nd,newNode):
if nd<newNode:
if nd.right is None:nd.right = newNode
else:_add(nd.right,newNode)
elif nd>newNode:
if nd.left is None:nd.left = newNode
else : _add(nd.left,newNode)
else:nd.freq +=1
_add(self.root,node(val))
def find(self,val):
prt= self._findPrt(self.root,node(val),None)
if prt.left and prt.left.val==val:
self.root = None
def add(self, val):
def _add(nd, newNode):
if nd < newNode:
if nd.right is None:
nd.right = newNode
else:
_add(nd.right, newNode)
elif nd > newNode:
if nd.left is None:
nd.left = newNode
else:
_add(nd.left, newNode)
else:
nd.freq += 1
_add(self.root, node(val))
def find(self, val):
prt = self._findPrt(self.root, node(val), None)
if prt.left and prt.left.val == val:
return prt.left
elif prt.right and prt.right.val==val:return prt.right
else :return None
def _findPrt(self,nd,tgt,prt):
if nd==tgt or nd is None:return prt
elif nd<tgt:return self._findPrt(nd.right,tgt,nd)
else:return self._findPrt(nd.left,tgt,nd)
def delete(self,val):
prt= self._findPrt(self.root,node(val),None)
if prt.left and prt.left.val==val:
l=prt.left
if l.left is None:prt.left = l.right
elif l.right is None : prt.left = l.left
elif prt.right and prt.right.val == val:
return prt.right
else:
return None
def _findPrt(self, nd, tgt, prt):
if nd == tgt or nd is None:
return prt
elif nd < tgt:
return self._findPrt(nd.right, tgt, nd)
else:
return self._findPrt(nd.left, tgt, nd)
def delete(self, val):
prt = self._findPrt(self.root, node(val), None)
if prt.left and prt.left.val == val:
l = prt.left
if l.left is None:
prt.left = l.right
elif l.right is None:
prt.left = l.left
else:
nd = l.left
while nd.right is not None:nd = nd.right
while nd.right is not None:
nd = nd.right
nd.right = l.right
prt.left = l.left
elif prt.right and prt.right.val==val:
r=prt.right
if r.right is None:prt.right = r.right
elif r.right is None : prt.right = r.left
elif prt.right and prt.right.val == val:
r = prt.right
if r.right is None:
prt.right = r.right
elif r.right is None:
prt.right = r.left
else:
nd = r.left
while nd.right is not None:nd = nd.right
while nd.right is not None:
nd = nd.right
nd.right = r.right
prt.left = r.left
@ -77,7 +102,9 @@ class binaryTree:
_p(nd.left)
_p(nd.right)
_p(self.root)
if __name__=="__main__":
if __name__ == "__main__":
t = binaryTree()
for i in range(10):
t.add((i-4)**2)

18
dataStructure/circularQueue.py
View File

@ -9,6 +9,8 @@
# Description:
#########################################################################
'''
class MyCircularQueue:
def __init__(self, k):
@ -29,8 +31,9 @@ class MyCircularQueue:
if self.isFull():
return False
self.data[self.rear] = value
self.rear = (self.rear+1)%self.size
self.rear = (self.rear+1) % self.size
return True
def deQueue(self):
"""
Delete an element from the circular queue. Return true if the operation is successful.
@ -38,9 +41,9 @@ class MyCircularQueue:
"""
if self.isEmpty():
return False
self.head = (self.head+1)%self.size
self.head = (self.head+1) % self.size
return True
def Front(self):
"""
Get the front item from the queue.
@ -49,7 +52,6 @@ class MyCircularQueue:
if self.isEmpty():
return -1
return self.data[self.head]
def Rear(self):
"""
@ -58,23 +60,21 @@ class MyCircularQueue:
"""
if self.isEmpty():
return -1
return self.data[(self.rear-1)%self.size]
return self.data[(self.rear-1) % self.size]
def isEmpty(self):
"""
Checks whether the circular queue is empty or not.
:rtype: bool
"""
return self.head ==self.rear
return self.head == self.rear
def isFull(self):
"""
Checks whether the circular queue is full or not.
:rtype: bool
"""
return (self.head - self.rear)%self.size ==1
return (self.head - self.rear) % self.size == 1
# Your MyCircularQueue object will be instantiated and called as such:

72
dataStructure/hashTable.py
View File

@ -10,18 +10,23 @@
#########################################################################
'''
class item:
def __init__(self,key,val,nextItem=None):
def __init__(self, key, val, nextItem=None):
self.key = key
self.val = val
self.next = nextItem
def to(self,it):
def to(self, it):
self.next = it
def __eq__(self,it):
def __eq__(self, it):
'''using keyword <in> '''
return self.key == it.key
def __bool__(self):
return self.key is not None
def __str__(self):
li = []
nd = self
@ -29,27 +34,33 @@ class item:
li.append(f'({nd.key}:{nd.val})')
nd = nd.next
return ' -> '.join(li)
def __repr__(self):
return f'item({self.key},{self.val})'
class hashTable:
def __init__(self,size=100):
def __init__(self, size=100):
self.size = size
self.slots=[item(None,None) for i in range(self.size)]
def __setitem__(self,key,val):
self.slots = [item(None, None) for i in range(self.size)]
def __setitem__(self, key, val):
nd = self.slots[self.myhash(key)]
while nd.next:
if nd.key ==key:
if nd.val!=val: nd.val=val
if nd.key == key:
if nd.val != val:
nd.val = val
return
nd = nd.next
nd.next = item(key,val)
nd = nd.next
nd.next = item(key, val)
def myhash(self,key):
if isinstance(key,str):
def myhash(self, key):
if isinstance(key, str):
key = sum(ord(i) for i in key)
if not isinstance(key,int):
if not isinstance(key, int):
key = hash(key)
return key % self.size
def __iter__(self):
'''when using keyword <in>, such as ' if key in dic',
the dic's __iter__ method will be called,(if hasn't, calls __getitem__
@ -57,18 +68,20 @@ class hashTable:
'''
for nd in self.slots:
nd = nd.next
while nd :
while nd:
yield nd.key
nd = nd.next
def __getitem__(self,key):
nd =self.slots[ self.myhash(key)].next
def __getitem__(self, key):
nd = self.slots[self.myhash(key)].next
while nd:
if nd.key==key:
if nd.key == key:
return nd.val
nd = nd.next
raise Exception(f'[KeyError]: {self.__class__.__name__} has no key {key}')
raise Exception(
f'[KeyError]: {self.__class__.__name__} has no key {key}')
def __delitem__(self,key):
def __delitem__(self, key):
'''note that None item and item(None,None) differ with each other,
which means you should take care of them and correctly cop with None item
especially when deleting items
@ -77,31 +90,34 @@ class hashTable:
nd = self.slots[n].next
if nd.key == key:
if nd.next is None:
self.slots[n] = item(None,None) # be careful
else:self.slots[n] = nd.next
self.slots[n] = item(None, None) # be careful
else:
self.slots[n] = nd.next
return
while nd:
if nd.next is None: break # necessary
if nd.next.key ==key:
if nd.next is None:
break # necessary
if nd.next.key == key:
nd.next = nd.next.next
nd = nd.next
def __str__(self):
li = ['\n\n'+'-'*5+'hashTable'+'-'*5]
for i,nd in enumerate(self.slots):
for i, nd in enumerate(self.slots):
li.append(f'{i}: '+str(nd.next))
return '\n'.join(li)
if __name__ =='__main__':
if __name__ == '__main__':
from random import randint
dic = hashTable(16)
n = 100
li = [1,2,5,40,324,123,6,22,18,34,50]
li = [1, 2, 5, 40, 324, 123, 6, 22, 18, 34, 50]
print(f'build hashTable using {li}')
for i in li:
dic[i] = '$'+str(i)
print(dic)
for i in [1,34,45,123]:
for i in [1, 34, 45, 123]:
if i in dic:
print(f'{i} in dic, deleting it')
del dic[i]

497
dataStructure/huffman/huffman.cc
View File

@ -28,348 +28,437 @@ using namespace std;
void cat(string s)
{
FILE* f=fopen(s.c_str(),"rb");
cout<<"file content"<<endl;
while(!feof(f)){
cout<<fgetc(f);
FILE* f = fopen(s.c_str(), "rb");
cout << "file content" << endl;
while (!feof(f)) {
cout << fgetc(f);
}
cout<<endl;
cout << endl;
}
string uniFileName(string file)
{
FILE * check = fopen(file.c_str(),"rb");
if(check){
FILE * check = fopen(file.c_str(), "rb");
if (check) {
char c;
cout<<"the file "<<file<<" already exists! continue? [Y/n]:"<<flush;
c=cin.get();
if(c=='n')exit(0);
int p,q;
p= file.find('(');
q=file.rfind('.');
if(q==string::npos)q=file.size();
if(p==string::npos)p=q;
string name=file.substr(0,p),suffix=file.substr(q,file.size());
int n=0;
while(true){
cout << "the file " << file << " already exists! continue? [Y/n]:" << flush;
c = cin.get();
if (c == 'n')exit(0);
int p, q;
p = file.find('(');
q = file.rfind('.');
if (q == string::npos)q = file.size();
if (p == string::npos)p = q;
string name = file.substr(0, p), suffix = file.substr(q, file.size());
int n = 0;
while (true) {
char s[3];
n+=1;
snprintf(s,3,"%d",n);
file=(name+"("+s+")"+suffix);
FILE* f=fopen(file.c_str(),"rb");
if(!f)break;
n += 1;
snprintf(s, 3, "%d", n);
file = (name + "(" + s + ")" + suffix);
FILE* f = fopen(file.c_str(), "rb");
if (!f)break;
else fclose(f);
}
}
return file;
}
template<class t1, class t2>
void mapprint(map<t1,t2> &f)
void mapprint(map<t1, t2> &f)
{
for(class map<t1,t2>::iterator i = f.begin();i!=f.end();++i)
cout<<i->first<<") : "<<i->second<<endl;
for (class map<t1, t2>::iterator i = f.begin(); i != f.end(); ++i)
cout << i->first << ") : " << i->second << endl;
}
template<typename ky,typename wt>
template<typename ky, typename wt>
class node
{
public:
public:
ky key;
wt val;
bool visited;
node * left,*right;
node(const node &a){val = a.val;key= a.key;visited = a.visited;left= a.left;right=a.right;}
node(ky k=0,wt v=0):key(k),val(v),visited(false),left(NULL),right(NULL){};
bool operator<(const node<ky,wt> & a)const{return val>a.val;};
node * left, *right;
node(const node &a)
{
val = a.val;
key = a.key;
visited = a.visited;
left = a.left;
right = a.right;
}
node(ky k = 0, wt v = 0): key(k), val(v), visited(false), left(NULL), right(NULL) {};
bool operator<(const node<ky, wt> & a)const
{
return val > a.val;
};
};
template<typename ky,typename wt>
template<typename ky, typename wt>
class huffman
{
private:
node<ky,wt> root;
node<ky, wt> root;
string res;
public:
long total(){return root.val;}
map<ky,string> encode_map;
map<string,ky> decode_map;
huffman(map<ky,wt>& mp);
long total()
{
return root.val;
}
map<ky, string> encode_map;
map<string, ky> decode_map;
huffman(map<ky, wt>& mp);
void display();
string encode(string,long &);
string decode(string,long&);
void preOrder(node<ky,wt>*,string);
string encode(string, long &);
string decode(string, long&);
void preOrder(node<ky, wt>*, string);
};
template<typename ky,typename wt>
huffman<ky,wt>::huffman(map<ky,wt>& mp)
template<typename ky, typename wt>
huffman<ky, wt>::huffman(map<ky, wt>& mp)
{
if(mp.empty()){
cout<<"Error! No data!"<<endl;
root=NULL;
if (mp.empty()) {
cout << "Error! No data!" << endl;
root = NULL;
return ;
}
priority_queue<node<ky,wt> > hp;
for(typename map<ky,wt>::iterator i=mp.begin();i!=mp.end();++i){
hp.push( node<ky,wt>(i->first,i->second));
priority_queue<node<ky, wt> > hp;
for (typename map<ky, wt>::iterator i = mp.begin(); i != mp.end(); ++i) {
hp.push(node<ky, wt>(i->first, i->second));
}
int n =hp.size();
if(n==1){
int n = hp.size();
if (n == 1) {
root = hp.top();
return;
}
while(--n>=1){
node<ky,wt> *a = new node<ky,wt>(hp.top());
while (--n >= 1) {
node<ky, wt> *a = new node<ky, wt>(hp.top());
hp.pop();
node<ky,wt> *b = new node<ky,wt>(hp.top());
node<ky, wt> *b = new node<ky, wt>(hp.top());
hp.pop();
node<ky,wt> * tmp = new node<ky,wt>(0,a->val+b->val);
tmp->left = a,tmp->right = b;
node<ky, wt> * tmp = new node<ky, wt>(0, a->val + b->val);
tmp->left = a, tmp->right = b;
hp.push(*tmp);
}
root = hp.top();
preOrder(&root,string());
preOrder(&root, string());
}
template<typename ky,typename wt>
void huffman<ky,wt>::preOrder(node<ky, wt>* nd,string s)
template<typename ky, typename wt>
void huffman<ky, wt>::preOrder(node<ky, wt>* nd, string s)
{
if(nd->left == NULL){
encode_map[nd->key] =s;
if (nd->left == NULL) {
encode_map[nd->key] = s;
decode_map[s] = nd->key;
delete nd;
return ;
}
preOrder(nd->left,s+'0');
preOrder(nd->right,s+'1');
preOrder(nd->left, s + '0');
preOrder(nd->right, s + '1');
delete nd;
}
template<typename ky,typename wt>
string huffman<ky,wt>::decode(string zipfile_name,long &charNum)
template<typename ky, typename wt>
string huffman<ky, wt>::decode(string zipfile_name, long &charNum)
{
string uniFileName(string);
FILE * src = fopen(zipfile_name.c_str(),"rb");
FILE * src = fopen(zipfile_name.c_str(), "rb");
char file_name[nameLength];
fgets(file_name,nameLength,src);
int ct=-1;
while(file_name[++ct]!='\n');
fgets(file_name, nameLength, src);
int ct = -1;
while (file_name[++ct] != '\n');
int pos = zipfile_name.find('.');
if(pos==string::npos)pos=zipfile_name.size();
string name(zipfile_name.substr(0,pos)) ,suffix(file_name,file_name+ct),file(name+suffix);
file=uniFileName(file);
cout<<"extracting compressed file :"<<zipfile_name<<endl;
FILE * f = fopen(file.c_str(),"wb");
if (pos == string::npos)pos = zipfile_name.size();
string name(zipfile_name.substr(0, pos)), suffix(file_name, file_name + ct), file(name + suffix);
file = uniFileName(file);
cout << "extracting compressed file :" << zipfile_name << endl;
FILE * f = fopen(file.c_str(), "wb");
char t[numDigit];
fgets(t,numDigit,src);
int sz=atoi(t);
fgets(t, numDigit, src);
int sz = atoi(t);
char code[sz];
fread(code,sz,1,src);
int idx=0;
for(int i =0;i<sz;++i ){
if(code[i]==' '){
decode_map[string(code+idx,code+i)]=code[++i];
idx=i+1;
fread(code, sz, 1, src);
int idx = 0;
for (int i = 0; i < sz; ++i) {
if (code[i] == ' ') {
decode_map[string(code + idx, code + i)] = code[++i];
idx = i + 1;
}
}
for(int i=0;i<starNum;++i)cout<<"@";
cout<<endl;
for (int i = 0; i < starNum; ++i)cout << "@";
cout << endl;
char c;
long cur=charNum,gap=charNum/starNum;
while(cur){
c=fgetc(src);
if(!((--cur)%gap))cout<<"@"<<flush;
for(int i =0;i<8;++i){
if(c&(1<<i))res.append(1,'1');
else res.append(1,'0');
if(decode_map.count(res)!=0){
fputc(decode_map[res],f);
long cur = charNum, gap = charNum / starNum;
while (cur) {
c = fgetc(src);
if (!((--cur) % gap))cout << "@" << flush;
for (int i = 0; i < 8; ++i) {
if (c & (1 << i))res.append(1, '1');
else res.append(1, '0');
if (decode_map.count(res) != 0) {
fputc(decode_map[res], f);
res.clear();
}
}
}
cout<<endl;
c=fgetc(src);
int dgt=fgetc(src);
cout<<feof(f);
if((int)dgt!=-1 ){
for(int i =0;i<dgt;++i){
if(c&(1<<i))res.append(1,'1');
else res.append(1,'0');
if(decode_map.count(res)!=0){
fputc(decode_map[res],f);
cout << endl;
c = fgetc(src);
int dgt = fgetc(src);
cout << feof(f);
if ((int)dgt != -1) {
for (int i = 0; i < dgt; ++i) {
if (c & (1 << i))res.append(1, '1');
else res.append(1, '0');
if (decode_map.count(res) != 0) {
fputc(decode_map[res], f);
res.clear();
break;
}
}
}
fclose(src);
fclose(f);
cout<<"get "<<file <<" successfully"<<endl;
cout << "get " << file << " successfully" << endl;
return file;
}
template<typename ky,typename wt>
string huffman<ky,wt>::encode(string file_name,long &charNum)
template<typename ky, typename wt>
string huffman<ky, wt>::encode(string file_name, long &charNum)
{
charNum=0;
charNum = 0;
string uniFileName(string);
int pos =file_name.rfind('.');
if(pos==string::npos)pos=file_name.size();
string zipfile = file_name.substr(0,pos)+string(".zzip");
int pos = file_name.rfind('.');
if (pos == string::npos)pos = file_name.size();
string zipfile = file_name.substr(0, pos) + string(".zzip");
zipfile = uniFileName(zipfile);
cout<<"generating zip file :"<<zipfile<<endl;
FILE * dst = fopen(zipfile.c_str(),"wb");
FILE * f = fopen(file_name.c_str(),"rb");
fputs(file_name.substr(pos).c_str(),dst);
fputc('\n',dst);
cout << "generating zip file :" << zipfile << endl;
FILE * dst = fopen(zipfile.c_str(), "wb");
FILE * f = fopen(file_name.c_str(), "rb");
fputs(file_name.substr(pos).c_str(), dst);
fputc('\n', dst);
string data;
for(class map<string,ky>::iterator i=decode_map.begin();i!=decode_map.end() ;++i ){
for (class map<string, ky>::iterator i = decode_map.begin(); i != decode_map.end() ; ++i) {
data.append((i->first));
data.append(" ");
data+=(i->second);
data += (i->second);
}
int data_size = data.size(); // calculate the size of the code_data
char sz[numDigit];
snprintf(sz,numDigit,"%d",data_size);
int ct=0;
for(;sz[ct];++ct)fputc(sz[ct],dst);
fputc('\n',dst);
fwrite(data.c_str(),data_size,1,dst);
int sum=0,digit=0,num;
snprintf(sz, numDigit, "%d", data_size);
int ct = 0;
for (; sz[ct]; ++ct)fputc(sz[ct], dst);
fputc('\n', dst);
fwrite(data.c_str(), data_size, 1, dst);
int sum = 0, digit = 0, num;
string code8;
for(int i=0;i<starNum;++i)cout<<"@";
cout<<endl;
long gap=root.val/starNum,cur=0;
while(!feof(f)){
code8=encode_map[fgetc(f)];
if(!((++cur)%gap))cout<<"@";
for(int i=0;i<code8.size();++i){
if(code8[i]=='1')sum += 1<<(digit); //mistake if(tmp[j])
for (int i = 0; i < starNum; ++i)cout << "@";
cout << endl;
long gap = root.val / starNum, cur = 0;
while (!feof(f)) {
code8 = encode_map[fgetc(f)];
if (!((++cur) % gap))cout << "@";
for (int i = 0; i < code8.size(); ++i) {
if (code8[i] == '1')sum += 1 << (digit); //mistake if(tmp[j])
++digit;
if(digit==8){
if (digit == 8) {
++charNum;
fputc(sum,dst);
digit=sum=0;
fputc(sum, dst);
digit = sum = 0;
}
}
}
cout<<endl;
if(digit!=0){ //mark
fputc(sum,dst);
fputc(digit,dst);
cout << endl;
if (digit != 0) { //mark
fputc(sum, dst);
fputc(digit, dst);
}
fclose(f);
fclose(dst);
cout<<"compress "<<file_name <<" successfully"<<endl;
cout << "compress " << file_name << " successfully" << endl;
return zipfile;
}
template<typename ky,typename wt>
void huffman<ky,wt>::display()
template<typename ky, typename wt>
void huffman<ky, wt>::display()
{
cout<<"the encoding map,huffman codes are as bellow:"<<endl;
for (typename map<ky,string>::iterator i=encode_map.begin();i!=encode_map.end() ;++i )
cout<<i->first<<"("<<(int)i->first<<"):"<<i->second<<endl;
cout << "the encoding map,huffman codes are as bellow:" << endl;
for (typename map<ky, string>::iterator i = encode_map.begin(); i != encode_map.end() ; ++i)
cout << i->first << "(" << (int)i->first << "):" << i->second << endl;
}
bool handle_one(string file_name,vector<long> &origin,vector<long> &compressed)
bool handle_one(string file_name, vector<long> &origin, vector<long> &compressed)
{
int name_length = file_name.size();
FILE *src=fopen(file_name.c_str(),"rb");
cout<<"opening "<<file_name<<"..."<<endl;
if(!src){
cout<<"Path Error! Opening "<<file_name<<" Failed"<<endl;
FILE *src = fopen(file_name.c_str(), "rb");
cout << "opening " << file_name << "..." << endl;
if (!src) {
cout << "Path Error! Opening " << file_name << " Failed" << endl;
origin.push_back(0);
compressed.push_back(0);
return false;
}
char cur;
map<char,long> mp;
while(!feof(src)){
fread(&cur,sizeof(char),1,src);
if(mp.count(cur)){
mp[cur]+=1;
}
else mp[cur]=1;
map<char, long> mp;
while (!feof(src)) {
fread(&cur, sizeof(char), 1, src);
if (mp.count(cur)) {
mp[cur] += 1;
} else mp[cur] = 1;
}
fclose(src);
huffman<char,long> hf(mp);
huffman<char, long> hf(mp);
long sz;
string s(hf.encode(file_name,sz));
origin.push_back(hf.total()),compressed.push_back(sz);
cout<<"\ncontinue to uncompress? [Y/n]"<<endl;
char c=cin.get();
if(c=='n')return true;
hf.decode(s,sz);
string s(hf.encode(file_name, sz));
origin.push_back(hf.total()), compressed.push_back(sz);
cout << "\ncontinue to uncompress? [Y/n]" << endl;
char c = cin.get();
if (c == 'n')return true;
hf.decode(s, sz);
return true;
}
bool isSep(char c)
{
return c==' '||c=='\n'||c=='\t'||c==',';
return c == ' ' || c == '\n' || c == '\t' || c == ',';
}
void splitToVec(char * s,vector<string>& v)
void splitToVec(char * s, vector<string>& v)
{
int i=0,last=0;
for(;s[i];++i){
if(isSep(s[i])){
v.push_back(string(s+last,s+i));
while(s[++i]&&isSep(s[i]));
last=i;
int i = 0, last = 0;
for (; s[i]; ++i) {
if (isSep(s[i])) {
v.push_back(string(s + last, s + i));
while (s[++i] && isSep(s[i]));
last = i;
}
}
if(s[last])v.push_back(string(s+last,s+i));
if (s[last])v.push_back(string(s + last, s + i));
}
bool lenStr(string &a,string &b)
bool lenStr(string &a, string &b)
{
return a.size()<b.size();
return a.size() < b.size();
}
void go(vector<string> & names)
{
vector<long> originSize,compressedSize;
vector<long> originSize, compressedSize;
vector<int> deltaTime;
double last;
vector<bool> indicator;
bool bl;
for(vector<string>::iterator i=names.begin();i!=names.end();++i){
for (vector<string>::iterator i = names.begin(); i != names.end(); ++i) {
struct timeval tv;
gettimeofday(&tv,NULL);
last=tv.tv_sec;
bl=handle_one(*i,originSize,compressedSize);
gettimeofday(&tv, NULL);
last = tv.tv_sec;
bl = handle_one(*i, originSize, compressedSize);
indicator.push_back(bl);
gettimeofday(&tv,NULL);
deltaTime.push_back(tv.tv_sec-last);
gettimeofday(&tv, NULL);
deltaTime.push_back(tv.tv_sec - last);
}
cout<<"\nDealt file number "<<originSize.size()<<fixed<<setprecision(2)<<endl;
vector<string>::iterator p=max_element(names.begin(),names.end(),lenStr);
int len = p->size()+2;
for(int i =0;i<names.size();++i){
if(! indicator[i]){continue;}
cout<<names[i]<<string(len-names[i].size(),' ');
cout<<deltaTime[i]<<"s "<<compressedSize[i]/1024.0<<"KB/"<<originSize[i]/1024.0<<"KB :";
cout<<compressedSize[i]*100.0/originSize[i]<<"%"<<endl;
cout << "\nDealt file number " << originSize.size() << fixed << setprecision(2) << endl;
vector<string>::iterator p = max_element(names.begin(), names.end(), lenStr);
int len = p->size() + 2;
for (int i = 0; i < names.size(); ++i) {
if (! indicator[i]) {
continue;
}
cout << names[i] << string(len - names[i].size(), ' ');
cout << deltaTime[i] << "s " << compressedSize[i] / 1024.0 << "KB/" << originSize[i] / 1024.0 << "KB :";
cout << compressedSize[i] * 100.0 / originSize[i] << "%" << endl;
}
cout<<endl;
cout << endl;
system("pause");
}
int main(int argv,char ** argc)
int main(int argv, char ** argc)
{
char cwd[50];
cout<<getcwd(cwd,50)<<endl;
cout << getcwd(cwd, 50) << endl;
vector<string> names;
string file;
if(argv>1){
for(int i=1;i<argv;++i){
string file;
if (argv > 1) {
for (int i = 1; i < argv; ++i) {
names.push_back(argc[i]);
}
go(names);
names.clear();
}
char mk;
while(1){
while (1) {
char s[201];
cout<<"Input file names separated by space "<<endl;
if(cin.peek()=='\n')names.push_back(file);
cout << "Input file names separated by space " << endl;
if (cin.peek() == '\n')names.push_back(file);
else {
cin.getline(s,200);
splitToVec(s,names);
cin.getline(s, 200);
splitToVec(s, names);
}
cout<<endl;
cout << endl;
go(names);
cout<<"Continue? [Y/n]:"<<flush;
mk= cin.get();
if(mk=='n')break;
cout << "Continue? [Y/n]:" << flush;
mk = cin.get();
if (mk == 'n')break;
names.clear();
}
return 0;
}

26
dataStructure/insert_remove_getRandom.py
View File

@ -13,11 +13,12 @@
#######################################################################
'''
class RandomizedCollection:
def __init__(self):
self.vals=[]
self.index={}
self.vals = []
self.index = {}
def insert(self, val: int) -> bool:
self.vals.append(val)
@ -27,32 +28,35 @@ class RandomizedCollection:
else:
self.index[val] = {len(self.vals)-1}
return True
def removeAll(self, val: int) -> bool:
if val not in self.index:
return False
begin = end = len(self.vals)-len(self.index[val])
for idx in self.index.pop(val):
if idx<begin:
while self.vals[end]==val:
end+=1
self.vals[idx]=self.vals[end]
for idx in self.index.pop(val):
if idx < begin:
while self.vals[end] == val:
end += 1
self.vals[idx] = self.vals[end]
self.index[self.vals[idx]].remove(end)
self.index[self.vals[idx]].add(idx)
self.vals = self.vals[:begin]
return True
def remove(self,val):
def remove(self, val):
if val not in self.index:
return False
last = len(self.vals)-1
idx = self.index[val].pop()
if len(self.index[val])==0:
if len(self.index[val]) == 0:
del self.index[val]
if idx!=last:
if idx != last:
self.vals[idx] = self.vals[last]
self.index[self.vals[idx]].remove(last)
self.index[self.vals[idx]].add(idx)
self.vals.pop()
return True
def getRandom(self) -> int:
if self.vals:
return self.vals[random.randint(0,len(self.vals)-1)]
return self.vals[random.randint(0, len(self.vals)-1)]

119
dataStructure/intervalTree.py
View File

@ -9,60 +9,80 @@
# Description:
#########################################################################
'''
from random import randint, shuffle
from redBlackTree import redBlackTree
from functools import total_ordering
@total_ordering
class node:
def __init__(self,low,high,left=None,right=None,isBlack=False):
self.val = low # self.val is the low
def __init__(self, low, high, left=None, right=None, isBlack=False):
self.val = low # self.val is the low
self.high = high
self.max = high
self.left = left
self.right = right
self.parent=None
self.parent = None
self.isBlack = isBlack
def __lt__(self,nd):
def __lt__(self, nd):
return self.val < nd.val
def __eq__(self,nd):
def __eq__(self, nd):
return nd is not None and self.val == nd.val
def setChild(self,nd,isLeft = True):
if isLeft: self.left = nd
else: self.right = nd
if nd is not None: nd.parent = self
def getChild(self,isLeft):
if isLeft: return self.left
else: return self.right
def setChild(self, nd, isLeft=True):
if isLeft:
self.left = nd
else:
self.right = nd
if nd is not None:
nd.parent = self
def getChild(self, isLeft):
if isLeft:
return self.left
else:
return self.right
def __bool__(self):
return self.val is not None
def __str__(self):
color = 'B' if self.isBlack else 'R'
return f'{color}[{self.val},{self.high}]-{self.max}'
def __repr__(self):
return f'intervalNode({self.val},{self.high},{self.max},isBlack={self.isBlack})'
def overlap(self,low,high):
return self.val<=high and self.high>=low
def overlap(self, low, high):
return self.val <= high and self.high >= low
def setMax(self):
l = 0 if self.left is None else self.left.max
r = 0 if self.right is None else self.right.max
self.max = max(self.high, l, r)
return self.max
class intervalTree(redBlackTree):
def search(self,low,high):
def search(self, low, high):
nd = self.root
while nd is not None and not nd.overlap(low,high):
if nd.left is not None and nd.left.max>=low:
while nd is not None and not nd.overlap(low, high):
if nd.left is not None and nd.left.max >= low:
nd = nd.left
else:nd = nd.right
else:
nd = nd.right
return nd
def insert(self,nd):
super(intervalTree,self).insert(nd)
def insert(self, nd):
super(intervalTree, self).insert(nd)
while nd is not None:
nd.setMax()
nd = nd.parent
def delete(self,val):
def delete(self, val):
nd = self.find(val)
if nd is not None:
nd.max = 0
@ -70,56 +90,61 @@ class intervalTree(redBlackTree):
while tmp is not None:
tmp.setMax()
tmp = tmp.parent
super(intervalTree,self).delete(val)
def rotate(self,prt,chd):
super(intervalTree, self).delete(val)
def rotate(self, prt, chd):
'''rotate prt, and return new prt, namyly the original chd'''
super(intervalTree,self).rotate(prt,chd)
super(intervalTree, self).rotate(prt, chd)
prt.setMax()
chd.setMax()
def copyNode(self,src,des):
def copyNode(self, src, des):
des.val = src.val
des.high = src.high
des.setMax()
from random import randint, shuffle
def genNum(n =10,upper=10):
nums ={}
def genNum(n=10, upper=10):
nums = {}
for i in range(n):
while 1:
d = randint(0,100)
d = randint(0, 100)
if d not in nums:
nums[d] = (d,randint(d,d+upper))
nums[d] = (d, randint(d, d+upper))
break
return nums.values()
def buildTree(n=10,nums=None,visitor=None):
def buildTree(n=10, nums=None, visitor=None):
#if nums is None or nums ==[]: nums = genNum(n)
tree = intervalTree()
print(f'build a red-black tree using {nums}')
for i in nums:
tree.insert(node(*i))
if visitor:
visitor(tree,i)
return tree,nums
visitor(tree, i)
return tree, nums
def testInsert(nums=None):
def visitor(t,val):
def visitor(t, val):
print('inserting', val)
print(t)
tree,nums = buildTree(visitor = visitor,nums=nums)
print('-'*5+ 'in-order visit' + '-'*5)
for i,j in enumerate(tree.sort()):
tree, nums = buildTree(visitor=visitor, nums=nums)
print('-'*5 + 'in-order visit' + '-'*5)
for i, j in enumerate(tree.sort()):
print(f'{i+1}: {j}')
return tree
def testSuc(nums=None):
tree,nums = buildTree(nums=nums)
tree, nums = buildTree(nums=nums)
for i in tree.sort():
print(f'{i}\'s suc is {tree.getSuccessor(i)}')
def testDelete(nums=None):
tree,nums = buildTree(nums = nums)
tree, nums = buildTree(nums=nums)
print(tree)
for i in nums:
print(f'deleting {i}')
@ -127,14 +152,16 @@ def testDelete(nums=None):
print(tree)
return tree
if __name__=='__main__':
lst = [(0,3),(5,8),(6,10),(26,26),(25,30),(8,9),(19,20),(15,23),(16,21),(17,19)]
if __name__ == '__main__':
lst = [(0, 3), (5, 8), (6, 10), (26, 26), (25, 30),
(8, 9), (19, 20), (15, 23), (16, 21), (17, 19)]
#lst = None
#testSuc(lst)
# testSuc(lst)
tree = testInsert(lst)
#tree,_= buildTree(lst)
while 1:
a =int( input('low:'))
b =int( input('high:'))
res = tree.search(a,b)
a = int(input('low:'))
b = int(input('high:'))
res = tree.search(a, b)
print(res)

172
dataStructure/leftHeap.py
View File

@ -11,108 +11,137 @@
'''
from functools import total_ordering
@total_ordering
@total_ordering
class node:
def __init__(self,val,freq=1,s=1,left=None,right=None):
self.val=val
self.freq=freq
self.s=s
def __init__(self, val, freq=1, s=1, left=None, right=None):
self.val = val
self.freq = freq
self.s = s
if left is None or right is None:
self.left = left if left is not None else right
self.right =None
self.right = None
else:
if left.s<right.s:
left,right =right, left
self.left=left
self.right=right
self.s+=self.right.s
def __eq__(self,nd):
return self.val==nd.val
def __lt__(self,nd):
return self.val<nd.val
if left.s < right.s:
left, right = right, left
self.left = left
self.right = right
self.s += self.right.s
def __eq__(self, nd):
return self.val == nd.val
def __lt__(self, nd):
return self.val < nd.val
def __repr__(self):
return 'node(val=%d,freq=%d,s=%d)'%(self.val,self.freq,self.s)
return 'node(val=%d,freq=%d,s=%d)' % (self.val, self.freq, self.s)
class leftHeap:
def __init__(self,root=None):
self.root=root
def __init__(self, root=None):
self.root = root
def __bool__(self):
return self.root is not None
@staticmethod
def _merge(root,t): #-> int
if root is None:return t
if t is None:return root
if root<t:
root,t=t,root
root.right = leftHeap._merge(root.right,t)
def _merge(root, t): # -> int
if root is None:
return t
if t is None:
return root
if root < t:
root, t = t, root
root.right = leftHeap._merge(root.right, t)
if root.left is None or root.right is None:
root.s=1
root.s = 1
if root.left is None:
root.left,root.right = root.right,None
root.left, root.right = root.right, None
else:
if root.left.s<root.right.s:
root.left,root.right = root.right,root.left
if root.left.s < root.right.s:
root.left, root.right = root.right, root.left
root.s = root.right.s+1
return root
def insert(self,nd):
if not isinstance(nd,node):nd = node(nd)
def insert(self, nd):
if not isinstance(nd, node):
nd = node(nd)
if self.root is None:
self.root=nd
self.root = nd
return
if self.root==nd:
self.root.freq+=1
if self.root == nd:
self.root.freq += 1
return
prt =self. _findPrt(self.root,nd,None)
prt = self. _findPrt(self.root, nd, None)
if prt is None:
self.root=leftHeap._merge(self.root,nd)
else :
if prt.left==nd:
prt.left.freq+=1
else:prt.right.freq+=1
def remove(self,nd):
if not isinstance(nd,node):nd = node(nd)
if self.root==nd:
self.root=leftHeap._merge(self.root.left,self.root.right)
self.root = leftHeap._merge(self.root, nd)
else:
prt = self._findPrt(self.root,nd,None)
if prt.left == nd:
prt.left.freq += 1
else:
prt.right.freq += 1
def remove(self, nd):
if not isinstance(nd, node):
nd = node(nd)
if self.root == nd:
self.root = leftHeap._merge(self.root.left, self.root.right)
else:
prt = self._findPrt(self.root, nd, None)
if prt is not None:
if prt.left==nd:
prt.left=leftHeap._merge(prt.left.left,prt.left.right)
if prt.left == nd:
prt.left = leftHeap._merge(prt.left.left, prt.left.right)
else:
prt.right=leftHeap._merge(prt.right.left,prt.right.right)
def find(self,nd):
if not isinstance(nd,node):nd = node(nd)
prt = self._findPrt(self.root,nd,self.root)
if prt is None or prt==nd:return prt
elif prt.left==nd:return prt.left
else:return prt.right
def _findPrt(self,root,nd,parent):
if not isinstance(nd,node):nd = node(nd)
if root is None or root<nd:return None
if root==nd:return parent
l=self._findPrt(root.left,nd,root)
return l if l is not None else self._findPrt(root.right,nd,root)
prt.right = leftHeap._merge(
prt.right.left, prt.right.right)
def find(self, nd):
if not isinstance(nd, node):
nd = node(nd)
prt = self._findPrt(self.root, nd, self.root)
if prt is None or prt == nd:
return prt
elif prt.left == nd:
return prt.left
else:
return prt.right
def _findPrt(self, root, nd, parent):
if not isinstance(nd, node):
nd = node(nd)
if root is None or root < nd:
return None
if root == nd:
return parent
l = self._findPrt(root.left, nd, root)
return l if l is not None else self._findPrt(root.right, nd, root)
def getTop(self):
return self.root
def pop(self):
nd = self.root
self.remove(self.root.val)
return nd
def levelTraverse(self):
li = [(self.root,0)]
cur=0
li = [(self.root, 0)]
cur = 0
while li:
nd,lv = li.pop(0)
if cur<lv:
cur=lv
nd, lv = li.pop(0)
if cur < lv:
cur = lv
print()
print(nd,end=' ')
else:print(nd,end=' ')
if nd.left is not None:li.append((nd.left,lv+1))
if nd.right is not None:li.append((nd.right,lv+1))
print(nd, end=' ')
else:
print(nd, end=' ')
if nd.left is not None:
li.append((nd.left, lv+1))
if nd.right is not None:
li.append((nd.right, lv+1))
if __name__ == '__main__':
lh = leftHeap()
@ -123,7 +152,8 @@ if __name__ == '__main__':
print()
for i in data:
print(lh.getTop())
if lh.find(i) is not None:lh.remove(i)
if lh.find(i) is not None:
lh.remove(i)
'''
data = [(i-10)**2 for i in range(20)]
node(100,freq=1,s=3)

31
dataStructure/linkedList.py
View File

@ -9,17 +9,21 @@
# Description:
#########################################################################
'''
class node:
def __init__(self,val,follow=None):
def __init__(self, val, follow=None):
self.val = val
self.follow = follow
class MyLinkedList:
def __init__(self):
"""
Initialize your data structure here.
"""
self.tail = self.head = node(None)
def get(self, index):
@ -31,7 +35,8 @@ class MyLinkedList:
nd = self.head
for i in range(index+1):
nd = nd.follow
if nd is None:return -1
if nd is None:
return -1
return nd.val
def addAtHead(self, val):
@ -40,9 +45,11 @@ class MyLinkedList:
:type val: int
:rtype: void
"""
nd = node(val,self.head.follow)
nd = node(val, self.head.follow)
self.head .follow = nd
if self.tail.val is None:self.tail = nd
if self.tail.val is None:
self.tail = nd
def addAtTail(self, val):
"""
Append a node of value val to the last element of the linked list.
@ -51,7 +58,6 @@ class MyLinkedList:
"""
self.tail.follow = node(val)
self.tail = self.tail.follow
def addAtIndex(self, index, val):
"""
@ -65,11 +71,10 @@ class MyLinkedList:
nd = nd.follow
if nd is None:
return
new = node(val,nd.follow)
new = node(val, nd.follow)
nd.follow = new
if self.tail == nd:
self.tail = new
def deleteAtIndex(self, index):
"""
@ -80,10 +85,12 @@ class MyLinkedList:
nd = self.head
for i in range(index):
nd = nd.follow
if nd is None:return
if self.tail == nd.follow:self.tail = nd
if nd.follow:nd.follow = nd.follow.follow
if nd is None:
return
if self.tail == nd.follow:
self.tail = nd
if nd.follow:
nd.follow = nd.follow.follow
# Your MyLinkedList object will be instantiated and called as such:

146
dataStructure/map.cc
View File

@ -13,138 +13,158 @@
#include<stdio.h>
bool isZero(float a)
{
return a<0.00001&&-a<0.00001;
return a < 0.00001 && -a < 0.00001;
}
template<class,class> class map;
//notice that if you declare a class template,declare the class first like this.
template<class t1,class t2>
template<class, class> class map;
//notice that if you declare a class template,declare the class first like this.
template<class t1, class t2>
class pair
{
friend class map<t1,t2>;
pair<t1,t2> *next;
public:
friend class map<t1, t2>;
pair<t1, t2> *next;
public:
t1 first;
t2 second;
};
template<class t1,class t2>
template<class t1, class t2>
class map
{
int n;
pair<t1,t2> head;
pair<t1, t2> head;
int cur;
pair<t1,t2> *last_visit;
public:
pair<t1, t2> *last_visit;
public:
map();
~map();
bool has(t1);
void erase(t1);
t2& operator[](t1);
pair<t1,t2> &locate(int index = -1);
pair<t1, t2> &locate(int index = -1);
int size();
};
template<class t1,class t2>
map<t1,t2>::map(){
n=0;
cur=-1;
last_visit= &head;
head.next=NULL;
template<class t1, class t2>
map<t1, t2>::map()
{
n = 0;
cur = -1;
last_visit = &head;
head.next = NULL;
head.first = head.second = 0;
}
template<class t1,class t2>
map<t1,t2>::~map()
template<class t1, class t2>
map<t1, t2>::~map()
{
pair<t1,t2> *p,*q=&head;
while(q!=NULL){
p=q->next;
pair<t1, t2> *p, *q = &head;
while (q != NULL) {
p = q->next;
delete q;
q=p;
q = p;
}
}
template<class t1,class t2>
bool map<t1,t2>::has(t1 key)
template<class t1, class t2>
bool map<t1, t2>::has(t1 key)
{
pair<t1,t2> *p = head.next;
for(int i = 0;i<n&&p->first<=key;++i){
if(isZero(p->first-key)) return 1;
p=p->next;
pair<t1, t2> *p = head.next;
for (int i = 0; i < n && p->first <= key; ++i) {
if (isZero(p->first - key)) return 1;
p = p->next;
}
return 0;
}
template<class t1,class t2>
pair<t1,t2>& map<t1,t2>::locate(int index)
template<class t1, class t2>
pair<t1, t2>& map<t1, t2>::locate(int index)
{
if(index>=n||index<0){
if (index >= n || index < 0) {
printf("the index is out of range\n");
return head;
}
if(cur>index){
if (cur > index) {
last_visit = &head;
cur = -1;
}
while(cur<index){
while (cur < index) {
last_visit = last_visit->next;
++cur;
}
return *last_visit;
}
template<class t1,class t2>
int map<t1,t2>::size()
template<class t1, class t2>
int map<t1, t2>::size()
{
return n;
}
template<class t1,class t2>
t2& map<t1,t2>::operator[](t1 key)
template<class t1, class t2>
t2& map<t1, t2>::operator[](t1 key)
{
pair<t1,t2> * p=&head;
while(p->next!=NULL){
if(isZero(p->next->first-key)) return p->next->second;
else if(p->next->first>key){break;}
p=p->next;
pair<t1, t2> * p = &head;
while (p->next != NULL) {
if (isZero(p->next->first - key)) return p->next->second;
else if (p->next->first > key) {
break;
}
p = p->next;
}
cur=-1;
last_visit= &head;
pair<t1,t2> *tmp = new pair<t1,t2>;
cur = -1;
last_visit = &head;
pair<t1, t2> *tmp = new pair<t1, t2>;
tmp ->next = p->next;
tmp->first = key;
p->next = tmp;
++n;
return tmp->second;
}
template<class t1,class t2>
void map<t1,t2>::erase(t1 key)
template<class t1, class t2>
void map<t1, t2>::erase(t1 key)
{
pair<t1,t2> *p = &head;
while(p->next!=NULL){
if(isZero(p->next->first-key)){
pair<t1,t2> *q = p->next;
pair<t1, t2> *p = &head;
while (p->next != NULL) {
if (isZero(p->next->first - key)) {
pair<t1, t2> *q = p->next;
p->next = p->next->next;
delete q;
--n;
break;
}
p=p->next;
p = p->next;
}
cur=-1;
last_visit= &head;
cur = -1;
last_visit = &head;
}
int main()
{
map<double,float> b;
for(int i = 0;i<40;++i){
map<double, float> b;
for (int i = 0; i < 40; ++i) {
b[i] = i;
if(i%3){
if (i % 3) {
b[i] = 1;
}
if(i%2){
if (i % 2) {
b.erase(i);
}
}
for (int i = 0; i < b.size(); ++i) {
printf("item %d %g:%g\n", i, b.locate(i).first, b.locate(i).second);
}
for(int i = 0;i<b.size();++i){
printf("item %d %g:%g\n",i,b.locate(i).first,b.locate(i).second);
}
return 0;
}

345
dataStructure/polynomial.cpp
View File

@ -10,7 +10,7 @@
#########################################################################
*/
#include<cstdlib>
#include<cstdlib>
#include<cstdio>
#include<cstring>
#include<cmath>
@ -19,16 +19,17 @@
using namespace std;
#if defined(__linux__)
#define LINUX true
#define LINUX true
#elif defined(_WIN32)
#define LINUX false
#define LINUX false
#endif
bool isZero(double a)
{
if((a<0.00001)&&-a<0.00001)
if ((a < 0.00001) && -a < 0.00001)
return true;
return false;
}
class node
@ -42,9 +43,9 @@ class polynomial
int SIZE;
int n;
node* p;
public:
polynomial(int sz=50);
polynomial(const polynomial & );
public:
polynomial(int sz = 50);
polynomial(const polynomial &);
~polynomial();
double cal(double);
void getData();
@ -54,10 +55,10 @@ class polynomial
polynomial operator-(const polynomial &);
polynomial operator*(const polynomial &);
};
polynomial::polynomial(int sz):n(0),SIZE(sz)
polynomial::polynomial(int sz): n(0), SIZE(sz)
{
p = (node*) new node[SIZE];
memset(p,0,sizeof(p));
memset(p, 0, sizeof(p));
}
polynomial::~polynomial()
{
@ -65,18 +66,21 @@ polynomial::~polynomial()
}
double polynomial::cal(double x)
{
double rst=0;
for(int i =0;i<n;++i){
rst += pow(x,p[i].index)*p[i].coefficient;
double rst = 0;
for (int i = 0; i < n; ++i) {
rst += pow(x, p[i].index) * p[i].coefficient;
}
return rst;
}
polynomial::polynomial(const polynomial &a)
{
p = (node*) new node[50];
memset(p,0,sizeof(p));
memset(p, 0, sizeof(p));
n = a.n;
for(int i = 0;i<a.n;++i){
for (int i = 0; i < a.n; ++i) {
p[i].index = a.p[i].index;
p[i].coefficient = a.p[i].coefficient;
}
@ -84,59 +88,72 @@ polynomial::polynomial(const polynomial &a)
polynomial polynomial::operator=(const polynomial& a)
{
n = a.n;
for(int i = 0;i<a.n;++i){
for (int i = 0; i < a.n; ++i) {
p[i].index = a.p[i].index;
p[i].coefficient = a.p[i].coefficient;
}
return *this;
}
void polynomial::display()
{
node * tmp = p;
if(n == 0){
if (n == 0) {
printf("0\n");
return;
}
// char *fmt = ("x"); printf(fmt,...);
for(int i = n-1;i>=0;--i){
// char *fmt = ("x"); printf(fmt,...);
for (int i = n - 1; i >= 0; --i) {
double t = tmp[i].coefficient;
double idx = tmp[i].index;
if(isZero(idx)){
printf("%+g",t);
if (isZero(idx)) {
printf("%+g", t);
continue;
}
if(isZero(t-1)) printf("+");
else if(isZero(t+1))printf("-");
else printf("%+g",t);
if (isZero(t - 1)) printf("+");
else if (isZero(t + 1))printf("-");
else printf("%+g", t);
printf("x");
if(!isZero(idx-1)) printf("^%g",idx);
if (!isZero(idx - 1)) printf("^%g", idx);
}
printf("\n");
}
void polynomial::getData()
{
printf("Please input data . \n");
printf("For every item,Coefficient first .Use space to separate,EOF to end\n");
map<double,double> mp;
map<double, double> mp;
double idx;
double coef;
while(scanf("%lf%lf",&coef,&idx)!=EOF){
if(isZero(coef)) continue;
if(mp.count(idx) == 0){
while (scanf("%lf%lf", &coef, &idx) != EOF) {
if (isZero(coef)) continue;
if (mp.count(idx) == 0) {
mp[idx] = coef;
}
else{
} else {
mp[idx] += coef;
if(isZero(mp[idx])){
if (isZero(mp[idx])) {
mp.erase(idx);
}
}
}
if(mp.size()>SIZE){
SIZE *=2;
p = (node*)realloc(p,sizeof(node)*SIZE) ;
if (mp.size() > SIZE) {
SIZE *= 2;
p = (node*)realloc(p, sizeof(node) * SIZE) ;
}
for(map<double,double>::iterator it = mp.begin();it!=mp.end();++it){
for (map<double, double>::iterator it = mp.begin(); it != mp.end(); ++it) {
p[n].index = it->first;
p[n++].coefficient = it->second;
}
@ -144,48 +161,52 @@ void polynomial::getData()
polynomial polynomial::operator+(const polynomial & a)
{
polynomial rst ;
int p1 = 0,p2 = 0,p3 = 0;
int p1 = 0, p2 = 0, p3 = 0;
double exp1 = p[p1].index;
double exp2 = a.p[p2].index;
while(p1<n && p2<a.n){
while(p1<n &&exp1<exp2){
rst.p[p3].index = exp1;
rst.p[p3].coefficient = p[p1].coefficient;
++p1,++p3;
exp1 = p[p1].index;;
while (p1 < n && p2 < a.n) {
while (p1 < n && exp1 < exp2) {
rst.p[p3].index = exp1;
rst.p[p3].coefficient = p[p1].coefficient;
++p1, ++p3;
exp1 = p[p1].index;;
}
while(p2<a.n &&exp1>exp2){
rst.p[p3].index = exp2;
rst.p[p3].coefficient = a.p[p2].coefficient;
++p2,++p3;
exp2 = a.p[p2].index;;
while (p2 < a.n && exp1 > exp2) {
rst.p[p3].index = exp2;
rst.p[p3].coefficient = a.p[p2].coefficient;
++p2, ++p3;
exp2 = a.p[p2].index;;
}
if(isZero(exp1-exp2)){
double tmp= p[p1].coefficient + a.p[p2].coefficient;
if(isZero(tmp)){
++p1,++p2;
}
else{
if (isZero(exp1 - exp2)) {
double tmp = p[p1].coefficient + a.p[p2].coefficient;
if (isZero(tmp)) {
++p1, ++p2;
} else {
rst.p[p3].index = p[p1].index;
rst.p[p3].coefficient = tmp;
++p1,++p2,++p3;
++p1, ++p2, ++p3;
}
}
}
if(p1 == n){
while(p2<a.n){
if (p1 == n) {
while (p2 < a.n) {
rst.p[p3].index = a.p[p2].index;
rst.p[p3].coefficient = a.p[p2].coefficient;
++p2,++p3;
++p2, ++p3;
}
}
else{
while(p1<n){
} else {
while (p1 < n) {
rst.p[p3].index = p[p1].index;
rst.p[p3].coefficient = p[p1].coefficient;
++p1,++p3;
++p1, ++p3;
}
}
rst.n = p3;
return rst;
}
@ -193,40 +214,50 @@ polynomial polynomial::operator-(const polynomial & a)
{
polynomial rst(a) ;
int i = 0;
while(i<rst.n){
while (i < rst.n) {
rst.p[i].coefficient = -rst.p[i].coefficient;
++i;
}
return (*this + rst);
}
polynomial polynomial::operator*(const polynomial & a)
{
map<double,double> mp;
for(int i = 0;i<n;++i){
map<double, double> mp;
for (int i = 0; i < n; ++i) {
double idx = p[i].index;
double coef = p[i].coefficient;
for(int j = 0;j<a.n;++j){
double index = idx+a.p[j].index;
if(mp.count(index)==0){
mp[index] = coef*a.p[j].coefficient;
}
else{
mp[index] += coef*a.p[j].coefficient;
if(isZero(mp[index])){
for (int j = 0; j < a.n; ++j) {
double index = idx + a.p[j].index;
if (mp.count(index) == 0) {
mp[index] = coef * a.p[j].coefficient;
} else {
mp[index] += coef * a.p[j].coefficient;
if (isZero(mp[index])) {
mp.erase(index);
}
}
}
}
int sz =50;
while(mp.size()>sz){
sz *=2;
int sz = 50;
while (mp.size() > sz) {
sz *= 2;
}
polynomial rst(sz);
for(map<double,double>::iterator it = mp.begin();it!=mp.end();++it){
for (map<double, double>::iterator it = mp.begin(); it != mp.end(); ++it) {
rst.p[rst.n].index = it->first;
rst.p[rst.n++].coefficient = it->second;
}
return rst;
}
int num = 0;
@ -250,94 +281,94 @@ void menu()
void loop()
{
int op;
while(scanf("%d",&op)!=EOF){
if(op == 0){
pl[num].getData();
++num;
printf("You've created polynomial %d:\n",num);
pl[num-1].display();
while (scanf("%d", &op) != EOF) {
if (op == 0) {
pl[num].getData();
++num;
printf("You've created polynomial %d:\n", num);
pl[num - 1].display();
} else if (op == 1 || op == 2 || op == 3) {
if (num < 2) {
printf("Oops! you've got less two polynomial\nPlease choose another operation\n");
continue;
}
else if(op==1||op==2||op==3){
if(num<2){
printf("Oops! you've got less two polynomial\nPlease choose another operation\n");
continue;
}
printf("input two nums of the two polynomial to be operated.eg: 1 2\n");
int t1=100,t2=100;
while(1){
scanf("%d%d",&t1,&t2);
if(t1>num||t2>num||t1<0||t2<0){
printf("wrong num ,please input again\n");
}
else break;
}
printf("the rst is:\n");
t1 -=1,t2-=1;
if(op == 1){
(pl[t1]+pl[t2]).display();
}
else if(op == 2){
(pl[t1]-pl[t2]).display();
}
else (pl[t1]*pl[t2]).display();
printf("input two nums of the two polynomial to be operated.eg: 1 2\n");
int t1 = 100, t2 = 100;
while (1) {
scanf("%d%d", &t1, &t2);
if (t1 > num || t2 > num || t1 < 0 || t2 < 0) {
printf("wrong num ,please input again\n");
} else break;
}
else if(op == 4){
printf("input a polynomial's num to display it\n");
int tmp;
scanf("%d",&tmp);
if(tmp>num){
printf("wrong num");
}
else{
printf("info of polynomial %d\n",tmp);
pl[tmp-1].display();
}
printf("the rst is:\n");
t1 -= 1, t2 -= 1;
if (op == 1) {
(pl[t1] + pl[t2]).display();
} else if (op == 2) {
(pl[t1] - pl[t2]).display();
} else (pl[t1]*pl[t2]).display();
} else if (op == 4) {
printf("input a polynomial's num to display it\n");
int tmp;
scanf("%d", &tmp);
if (tmp > num) {
printf("wrong num");
} else {
printf("info of polynomial %d\n", tmp);
pl[tmp - 1].display();
}
else if(op == 9){
for(int i = 0;i<num;++i){
printf("polynomial %d : ",i+1);
pl[i].display();
}
} else if (op == 9) {
for (int i = 0; i < num; ++i) {
printf("polynomial %d : ", i + 1);
pl[i].display();
}
else if(op == 5){
menu();
} else if (op == 5) {
menu();
} else if (op == 6) {
if (LINUX) system("clear");
else system("cls");
menu();
} else if (op == 10) {
double x;
int t;
printf("choose a polynomial\n");
scanf("%d", &t);
if (t > num || t < 0) {
printf("wrong num\n");
} else {
printf("input a value\n");
scanf("%lf", &x);
pl[t - 1].display();
printf("%g\n", pl[t - 1].cal(x));
}
else if(op == 6){
if(LINUX) system("clear");
else system("cls");
menu();
} else if (op == 8) {
if (num == 0) {
printf("you have'nt any polynomial tp copy\n");
continue;
}
else if(op == 10){
double x;
int t;
printf("choose a polynomial\n");
scanf("%d",&t);
if(t>num||t<0){
printf("wrong num\n");
}
else {
printf("input a value\n");
scanf("%lf",&x);
pl[t-1].display();
printf("%g\n",pl[t-1].cal(x));
}
int n = num + 1;
while (n > num) {
printf("input the number of an existing polynomial you want to copy\n");
scanf("%d", &n);
}
else if(op == 8){
if(num == 0){
printf("you have'nt any polynomial tp copy\n");
continue;
}
int n = num+1;
while(n>num){
printf("input the number of an existing polynomial you want to copy\n");
scanf("%d",&n);
}
(pl[num] = pl[n-1]);
printf("You've copyed this polynomial:\n");
pl[num++].display();
}
else exit(0);
printf("select an operation\n");
(pl[num] = pl[n - 1]);
printf("You've copyed this polynomial:\n");
pl[num++].display();
} else exit(0);
printf("select an operation\n");
}
}
int main(void)

136
dataStructure/polynomial.py
View File

@ -11,61 +11,71 @@
'''
#!/bin/python3
# notice that creating a class's initialization won't conflict with __call__ method
# notice that creating a class's initialization won't conflict with __call__ method
# because the former call class ,and the latter call instance
# to be implemented
class polynomial:
pls= []
pls = []
n = 0
def dictize(pl):
if isinstance(pl,int) or isinstance(pl,float):
pl = {0:pl}
if isinstance(pl,polynomial):
if isinstance(pl, int) or isinstance(pl, float):
pl = {0: pl}
if isinstance(pl, polynomial):
pl = pl.polynomial.copy()
return pl
def isZero(n):
return abs(n)<0.000001
def __init__(self,s='0 0'):
return abs(n) < 0.000001
def __init__(self, s='0 0'):
polynomial.pls.append(self)
polynomial.n +=1
if isinstance(s,polynomial):
self.polynomial=s.polynomial.copy()
# don't write like this .**self.polynomial = s.polynomial**,it's ref
polynomial.n += 1
if isinstance(s, polynomial):
self.polynomial = s.polynomial.copy()
# don't write like this .**self.polynomial = s.polynomial**,it's ref
return
elif isinstance(s,dict):
elif isinstance(s, dict):
self.polynomial = s.copy()
return
s= s.replace(',',' ')
s= s.replace('x',' ')
s= s.replace('x^',' ')
s = s.replace(':',' ')
s = s.replace('\n',' ')
s = s.replace(',', ' ')
s = s.replace('x', ' ')
s = s.replace('x^', ' ')
s = s.replace(':', ' ')
s = s.replace('\n', ' ')
s = s.split(' ')
num = len(s)
i = 0
print(s)
self.polynomial = dict()
li = [float(i) for i in s]
while i<num:
while i < num:
if not polynomial.isZero(li[i]):
index = li[i+1]
if index in self.polynomial.keys():
self.polynomial[index] += li[i]
else:self.polynomial[index] = li[i]
i+=2
else:
self.polynomial[index] = li[i]
i += 2
if not self.polynomial:
self.polynomial = {0:0}
self.polynomial = {0: 0}
def __iter__(self):
return iter(list(self.polynomial.keys()))
def __getitem__(self,key):
def __getitem__(self, key):
return self.polynomial[key]
def __setitem__(self,key,val):
def __setitem__(self, key, val):
self.polynomial[key] = val
def __delitem__(self,k):
def __delitem__(self, k):
del self.polynomial[k]
def __add__(self,pl):
def __add__(self, pl):
pl = polynomial.dictize(pl)
rst = self.polynomial.copy()
for i in pl:
@ -76,7 +86,8 @@ class polynomial:
if polynomial.isZero(rst[i]):
del rst[i]
return polynomial(rst)
def __iadd__(self,pl):
def __iadd__(self, pl):
pl = polynomial.dictize(pl)
for i in pl:
if i not in self:
@ -86,72 +97,90 @@ class polynomial:
if polynomial.isZero(self[i]):
del self[i]
return self
def __sub__(self,pl):
def __sub__(self, pl):
pl = polynomial.dictize(pl)
tmp = {i:-j for i,j in pl.items()}
tmp = {i: -j for i, j in pl.items()}
return self + tmp
def __mul__(self,pl):
def __mul__(self, pl):
pl = polynomial.dictize(pl)
dic = dict()
for i in pl:
for j in self:
index= i+j
index = i+j
if index in dic:
dic[index] += pl[i]*self[j]
else:dic[index] = pl[i]*self[j]
return polynomial({i:j for i,j in dic.items() if not polynomial.isZero(j)})
def __imul__(self,pl):
else:
dic[index] = pl[i]*self[j]
return polynomial({i: j for i, j in dic.items() if not polynomial.isZero(j)})
def __imul__(self, pl):
self = self*pl
return self
def __pow__(self,n):
rst = polynomial({0:1})
def __pow__(self, n):
rst = polynomial({0: 1})
for i in range(n):
rst*=self.polynomial
rst *= self.polynomial
return rst
def __repr__(self):
return self.__str__()
def __str__(self):
output = ''
if self.polynomial:
key = sorted(self.polynomial.keys(),reverse = True)
key = sorted(self.polynomial.keys(), reverse=True)
num = len(key)
for j,i in enumerate(key):
for j, i in enumerate(key):
if polynomial.isZero(i):
output +='%+g'%self[i]
output += '%+g' % self[i]
continue
if not polynomial.isZero(self[i]-1):
if not polynomial.isZero(self[i]+1):
output +="%+g"%self[i]
else:output +='-'
else:output +='+'
if not polynomial.isZero(i): output +='x'
if not polynomial.isZero(i-1):output +='^%g'%i
output += "%+g" % self[i]
else:
output += '-'
else:
output += '+'
if not polynomial.isZero(i):
output += 'x'
if not polynomial.isZero(i-1):
output += '^%g' % i
if output[0] == '+':
return output[1:]
return output
def iterPolynomial(self,s):
rst = polynomial({0:0})
def iterPolynomial(self, s):
rst = polynomial({0: 0})
for i in self:
rst += s**int(i)*self[i]
return rst
def __call__(self,s):
if isinstance(s,polynomial):
return self.iterPolynomial(s)
def __call__(self, s):
if isinstance(s, polynomial):
return self.iterPolynomial(s)
sum = 0
for i in self:
sum += self[i] * s**i
return sum
def __xor__(self,n):
def __xor__(self, n):
tmp = polynomial(self)
for i in range(n):
self = self.iterPolynomial(tmp)
return self
def save(self):
polynomial.pls.append(self)
polynomial.n +=1
def delPlynomial(self,n):
polynomial.n += 1
def delPlynomial(self, n):
return polynomial.pls.pop(n-1)
def menu():
print('polynomial operations')
print('1.create')
@ -166,5 +195,6 @@ def menu():
print('10.menu')
print('11.exit')
if __name__ == '__main__':
pass

242
dataStructure/redBlackTree.py
View File

@ -12,36 +12,50 @@
from functools import total_ordering
from random import randint, shuffle
@total_ordering
class node:
def __init__(self,val,left=None,right=None,isBlack=False):
self.val =val
def __init__(self, val, left=None, right=None, isBlack=False):
self.val = val
self.left = left
self.right = right
self.parent= None
self.isBlack = isBlack
def __lt__(self,nd):
return self.val < nd.val
def __eq__(self,nd):
return nd is not None and self.val == nd.val
def setChild(self,nd,isLeft):
if isLeft: self.left = nd
else: self.right = nd
if nd is not None: nd.parent = self
self.parent = None
self.isBlack = isBlack
def __lt__(self, nd):
return self.val < nd.val
def __eq__(self, nd):
return nd is not None and self.val == nd.val
def setChild(self, nd, isLeft):
if isLeft:
self.left = nd
else:
self.right = nd
if nd is not None:
nd.parent = self
def getChild(self, isLeft):
if isLeft:
return self.left
else:
return self.right
def getChild(self,isLeft):
if isLeft: return self.left
else: return self.right
def __bool__(self):
return self.val is not None
def __str__(self):
color = 'B' if self.isBlack else 'R'
val = '-' if self.parent==None else self.parent.val
val = '-' if self.parent == None else self.parent.val
return f'{color}-{self.val}'
def __repr__(self):
return f'node({self.val},isBlack={self.isBlack})'
class redBlackTree:
def __init__(self,unique=False):
def __init__(self, unique=False):
'''if unique is True, all node'vals are unique, else there may be equal vals'''
self.root = None
self.unique = unique
@ -49,23 +63,29 @@ class redBlackTree:
@staticmethod
def checkBlack(nd):
return nd is None or nd.isBlack
@staticmethod
def setBlack(nd,isBlack):
def setBlack(nd, isBlack):
if nd is not None:
if isBlack is None or isBlack:
nd.isBlack = True
else:nd.isBlack = False
def setRoot(self,nd):
if nd is not None: nd.parent=None
self.root= nd
def find(self,val):
else:
nd.isBlack = False
def setRoot(self, nd):
if nd is not None:
nd.parent = None
self.root = nd
def find(self, val):
nd = self.root
while nd:
if nd.val ==val:
if nd.val == val:
return nd
else:
nd = nd.getChild(nd.val>val)
def getSuccessor(self,nd):
nd = nd.getChild(nd.val > val)
def getSuccessor(self, nd):
if nd:
if nd.right:
nd = nd.right
@ -76,18 +96,20 @@ class redBlackTree:
while nd.parent is not None and nd.parent.right is nd:
nd = nd.parent
return None if nd is self.root else nd.parent
def rotate(self,prt,chd):
'''rotate prt with the center of chd'''
def rotate(self, prt, chd):
'''rotate prt with the center of chd'''
if self.root is prt:
self.setRoot(chd)
else:
prt.parent.setChild(chd, prt.parent.left is prt)
isLeftChd = prt.left is chd
prt.setChild(chd.getChild(not isLeftChd), isLeftChd)
chd.setChild(prt,not isLeftChd)
chd.setChild(prt, not isLeftChd)
def insert(self,nd):
if nd.isBlack: nd.isBlack = False
def insert(self, nd):
if nd.isBlack:
nd.isBlack = False
if self.root is None:
self.setRoot(nd)
@ -95,16 +117,18 @@ class redBlackTree:
else:
parent = self.root
while parent:
if parent == nd : return None
if parent == nd:
return None
isLeft = parent > nd
chd = parent.getChild(isLeft)
chd = parent.getChild(isLeft)
if chd is None:
parent.setChild(nd,isLeft)
parent.setChild(nd, isLeft)
break
else:
parent = chd
self.fixUpInsert(parent,nd)
def fixUpInsert(self,parent,nd):
self.fixUpInsert(parent, nd)
def fixUpInsert(self, parent, nd):
''' adjust color and level, there are two red nodes: the new one and its parent'''
while not self.checkBlack(parent):
grand = parent.parent
@ -125,8 +149,8 @@ class redBlackTree:
# grand grand
# parent or parent
# nd nd
self.rotate(parent,nd) #parent rotate
nd,parent = parent,nd
self.rotate(parent, nd) # parent rotate
nd, parent = parent, nd
# case 3 (case 2.2) the new node is inserted in left-left or right-right form
# grand grand
# parent or parent
@ -134,25 +158,29 @@ class redBlackTree:
self.setBlack(grand, False)
self.setBlack(parent, True)
self.rotate(grand,parent)
self.setBlack(self.root,True)
self.rotate(grand, parent)
self.setBlack(self.root, True)
def copyNode(self,src,des):
def copyNode(self, src, des):
'''when deleting a node which has two kids,
copy its succesor's data to his position
data exclude left, right , isBlack
'''
des.val = src.val
def delete(self,val):
def delete(self, val):
'''delete node in a binary search tree'''
if isinstance(val,node): val = val.val
if isinstance(val, node):
val = val.val
nd = self.find(val)
if nd is None: return
if nd is None:
return
self._delete(nd)
def _delete(self,nd):
def _delete(self, nd):
y = None
if nd.left and nd.right:
y= self.getSuccessor(nd)
y = self.getSuccessor(nd)
else:
y = nd
py = y.parent
@ -160,58 +188,60 @@ class redBlackTree:
if py is None:
self.setRoot(x)
else:
py.setChild(x,py.left is y)
py.setChild(x, py.left is y)
if y != nd:
self.copyNode(y,nd)
if self.checkBlack(y): self.fixUpDel(py,x)
def fixUpDel(self,prt,chd):
self.copyNode(y, nd)
if self.checkBlack(y):
self.fixUpDel(py, x)
def fixUpDel(self, prt, chd):
''' adjust colors and rotate '''
while self.root != chd and self.checkBlack(chd):
isLeft =prt.left is chd
isLeft = prt.left is chd
brother = prt.getChild(not isLeft)
# brother is black
lb = self.checkBlack(brother.getChild(isLeft))
rb = self.checkBlack(brother.getChild(not isLeft))
if not self.checkBlack(brother):
if not self.checkBlack(brother):
# case 1: brother is red. converted to case 2,3,4
self.setBlack(prt,False)
self.setBlack(brother,True)
self.rotate(prt,brother)
self.setBlack(prt, False)
self.setBlack(brother, True)
self.rotate(prt, brother)
elif lb and rb:
# case 2: brother is black and two kids are black.
elif lb and rb:
# case 2: brother is black and two kids are black.
# conveted to the begin case
self.setBlack(brother,False)
self.setBlack(brother, False)
chd = prt
prt= chd.parent
prt = chd.parent
else:
if rb:
if rb:
# case 3: brother is black and left kid is red and right child is black
# rotate bro to make g w wl wr in one line
# uncle's son is nephew, and niece for uncle's daughter
nephew = brother.getChild(isLeft)
self.setBlack(nephew,True)
self.setBlack(brother,False)
self.setBlack(nephew, True)
self.setBlack(brother, False)
# brother (not isLeft) rotate
self.rotate(brother,nephew)
self.rotate(brother, nephew)
brother = nephew
# case 4: brother is black and right child is red
brother.isBlack = prt.isBlack
self.setBlack(prt,True)
self.setBlack(brother.getChild(not isLeft),True)
self.setBlack(prt, True)
self.setBlack(brother.getChild(not isLeft), True)
self.rotate(prt,brother)
self.rotate(prt, brother)
chd = self.root
self.setBlack(chd,True)
self.setBlack(chd, True)
def sort(self,reverse = False):
def sort(self, reverse=False):
''' return a generator of sorted data'''
def inOrder(root):
if root is None:return
if root is None:
return
if reverse:
yield from inOrder(root.right)
else:
@ -225,8 +255,10 @@ class redBlackTree:
def display(self):
def getHeight(nd):
if nd is None:return 0
return max(getHeight(nd.left),getHeight(nd.right)) +1
if nd is None:
return 0
return max(getHeight(nd.left), getHeight(nd.right)) + 1
def levelVisit(root):
from collections import deque
lst = deque([root])
@ -234,24 +266,26 @@ class redBlackTree:
h = getHeight(root)
ct = lv = 0
while 1:
ct+=1
ct += 1
nd = lst.popleft()
if ct >= 2**lv:
lv+=1
if lv>h:break
lv += 1
if lv > h:
break
level.append([])
level[-1].append(str(nd))
if nd is not None:
lst += [nd.left,nd.right]
lst += [nd.left, nd.right]
else:
lst +=[None,None]
lst += [None, None]
return level
def addBlank(lines):
width = 1+len(str(self.root))
sep = ' '*width
n = len(lines)
for i,oneline in enumerate(lines):
k = 2**(n-i) -1
for i, oneline in enumerate(lines):
k = 2**(n-i) - 1
new = [sep*((k-1)//2)]
for s in oneline:
new.append(s.ljust(width))
@ -262,59 +296,67 @@ class redBlackTree:
lines = levelVisit(self.root)
lines = addBlank(lines)
li = [''.join(line) for line in lines]
length = 10 if li==[] else max(len(i) for i in li)//2
begin ='\n'+ 'red-black-tree'.rjust(length+14,'-') + '-'*(length)
length = 10 if li == [] else max(len(i) for i in li)//2
begin = '\n' + 'red-black-tree'.rjust(length+14, '-') + '-'*(length)
end = '-'*(length*2+14)+'\n'
return '\n'.join([begin,*li,end])
return '\n'.join([begin, *li, end])
def __str__(self):
return self.display()
def genNum(n =10):
nums =[]
def genNum(n=10):
nums = []
for i in range(n):
while 1:
d = randint(0,100)
d = randint(0, 100)
if d not in nums:
nums.append(d)
break
return nums
def buildTree(n=10,nums=None,visitor=None):
if nums is None or nums ==[]: nums = genNum(n)
def buildTree(n=10, nums=None, visitor=None):
if nums is None or nums == []:
nums = genNum(n)
rbtree = redBlackTree()
print(f'build a red-black tree using {nums}')
for i in nums:
rbtree.insert(node(i))
print(rbtree)
if visitor:
visitor(rbtree,i)
return rbtree,nums
visitor(rbtree, i)
return rbtree, nums
def testInsert(nums=None):
def visitor(t,val):
def visitor(t, val):
print('inserting', val)
print(t)
rbtree,nums = buildTree(visitor = visitor,nums=nums)
print('-'*5+ 'in-order visit' + '-'*5)
for i,j in enumerate(rbtree.sort()):
rbtree, nums = buildTree(visitor=visitor, nums=nums)
print('-'*5 + 'in-order visit' + '-'*5)
for i, j in enumerate(rbtree.sort()):
print(f'{i+1}: {j}')
def testSuc(nums=None):
rbtree,nums = buildTree(nums=nums)
rbtree, nums = buildTree(nums=nums)
for i in rbtree.sort():
print(f'{i}\'s suc is {rbtree.getSuccessor(i)}')
def testDelete(nums=None):
rbtree,nums = buildTree(nums = nums)
rbtree, nums = buildTree(nums=nums)
print(rbtree)
for i in sorted(nums):
print(f'deleting {i}')
rbtree.delete(i)
print(rbtree)
if __name__=='__main__':
lst =[45, 30, 64, 36, 95, 38, 76, 34, 50, 1]
lst = [0,3,5,6,26,25,8,19,15,16,17]
#testSuc(lst)
#testInsert(lst)
if __name__ == '__main__':
lst = [45, 30, 64, 36, 95, 38, 76, 34, 50, 1]
lst = [0, 3, 5, 6, 26, 25, 8, 19, 15, 16, 17]
# testSuc(lst)
# testInsert(lst)
testDelete()

188
dataStructure/splayTree.py
View File

@ -10,148 +10,190 @@
#########################################################################
'''
from collections import deque,Iterable
from collections import deque, Iterable
# use isinstance(obj,Iterable) to judge if an obj is iterable
class node:
def __init__(self,val = None,left=None,right=None,parent=None):
def __init__(self, val=None, left=None, right=None, parent=None):
self.val = val
if val :self.freq = 1
else :self.freq = 0
if val:
self.freq = 1
else:
self.freq = 0
self.left = left
self.right = right
self.parent = parent
def getChild(self,s=0):
if isinstance(s,int):s =[s]
self.parent = parent
def getChild(self, s=0):
if isinstance(s, int):
s = [s]
last = self
for i in s:
if not last:return None
if i == 0: last = last.left
else:last = last.right
if not last:
return None
if i == 0:
last = last.left
else:
last = last.right
return last
def setChild(self,child,s=0):
if isinstance(s,Iterable):
def setChild(self, child, s=0):
if isinstance(s, Iterable):
i = s[0]
del s[0]
if i == 0:self.left.setChild(child,s)
else:self.right.setChild(child,s)
elif s:self.right = child
else:self.left = child
if i == 0:
self.left.setChild(child, s)
else:
self.right.setChild(child, s)
elif s:
self.right = child
else:
self.left = child
class splayTree:
def __init__(self,s=[]):
def __init__(self, s=[]):
s = list(s)
self.root = None
s = sorted(s,reverse = True)
s = sorted(s, reverse=True)
for i in s:
self.insert(self.root,i)
def insert(self,k):
if not self.root :self.root = node(k)
else:self._insert(self.root,k)
def _insert(self,root,k):
if root.val == k :
root.freq +=1
elif root.val<k:
self.insert(self.root, i)
def insert(self, k):
if not self.root:
self.root = node(k)
else:
self._insert(self.root, k)
def _insert(self, root, k):
if root.val == k:
root.freq += 1
elif root.val < k:
if not root.right:
root.right = node(k)
root.right.parent = root
else:self._insert(root.right,k)
else:
self._insert(root.right, k)
else:
if not root.left:
root.left = node(k)
root.left.parent = root
else:self._insert(root.left,k)
def _zigzagRotate(self,i,j,root,parent,grand):
parent.setChild(root.getChild(i),j)
root.setChild(parent,i)
grand.setChild(root.getChild(j),i)
root.setChild(grand,j)
if root.parent:root.parent = grand.parent
else:
self._insert(root.left, k)
def _zigzagRotate(self, i, j, root, parent, grand):
parent.setChild(root.getChild(i), j)
root.setChild(parent, i)
grand.setChild(root.getChild(j), i)
root.setChild(grand, j)
if root.parent:
root.parent = grand.parent
parent.parent = root
grand.parent = root
def _lineRotate(self,i,root,parent,grand):
grand.setChild(parent.getChild(i^1),i)
parent.setChild(grand,i^1)
parent.setChild(root.getChild(i^1),i)
root.setChild(parent,i^1)
if root.parent:root.parent = grand.parent
parent.parent = root
def _lineRotate(self, i, root, parent, grand):
grand.setChild(parent.getChild(i ^ 1), i)
parent.setChild(grand, i ^ 1)
parent.setChild(root.getChild(i ^ 1), i)
root.setChild(parent, i ^ 1)
if root.parent:
root.parent = grand.parent
parent.parent = root
grand.parent = parent
def _rotate(self,root):
if root == self.root:return
def _rotate(self, root):
if root == self.root:
return
if root.parent == self.root:
for i in range(2):
if root.parent.getChild(i) == root:
root.parent.parent = root
root.parent.setChild(root.getChild(i^1),i)
root.parent.setChild(root.getChild(i ^ 1), i)
root.parent = None
root.setChild(self.root,i^1)
root.setChild(self.root, i ^ 1)
self.root = root
else:
grand = root.parent.parent
parent = root.parent
if grand == self.root:
self.root = root
root.parent = None
self.root = root
root.parent = None
else:
for i in range(2):
if grand.parent.getChild(i) == grand:
grand.parent.setChild(root,i)
if grand.parent.getChild(i) == grand:
grand.parent.setChild(root, i)
for i in range(2):
for j in range(2):
if i!=j and grand.getChild([i,j]) == root:
self._zigzagRotate(i,j,root,parent,grand)
elif i==j and grand.getChild([i,i]) == root:
self._lineRotate(i,root,parent,grand)
if i != j and grand.getChild([i, j]) == root:
self._zigzagRotate(i, j, root, parent, grand)
elif i == j and grand.getChild([i, i]) == root:
self._lineRotate(i, root, parent, grand)
self._rotate(root)
def _find(self,root,k):
if not root:return 0
def _find(self, root, k):
if not root:
return 0
if root.val > k:
return self._find(root.left,k)
elif root.val<k:
return self._find(root.right,k)
return self._find(root.left, k)
elif root.val < k:
return self._find(root.right, k)
else:
self._rotate(root)
return root.freq
def _maxmin(self,root,i=0):
if not root:return None
def _maxmin(self, root, i=0):
if not root:
return None
if root.getChild(i):
return self._maxmin(root.getChild(i))
return root
def Max(self):
return self._maxmin(self.root,1)
return self._maxmin(self.root, 1)
def Min(self):
return self._maxmin(self.root,0)
def remove(self,k):
return self._maxmin(self.root, 0)
def remove(self, k):
tmp = self.find(k)
if not tmp:raise ValueError
if not tmp:
raise ValueError
else:
if self.root.left:
r = self.root.right
self.root = self.root.left
self.root.parent = None
Max = self.Max()
Max.right= r
Max.right = r
if r:
r.parent = Max
else:
self.root = self.root.right
def find(self,k):
return self._find(self.root,k)
def find(self, k):
return self._find(self.root, k)
def levelTraverse(self):
q = deque()
q.append((self.root,0))
q.append((self.root, 0))
rst = []
while q:
tmp,n= q.popleft()
tmp, n = q.popleft()
rst.append(tmp)
if tmp.left:q.append((tmp.left,n+1))
if tmp.right:q.append((tmp.right,n+1))
if tmp.left:
q.append((tmp.left, n+1))
if tmp.right:
q.append((tmp.right, n+1))
return rst
def display(self):
data = self.levelTraverse()
for i in data:
print (i.val,end=' ')
print(i.val, end=' ')
print('')
if __name__ == '__main__':
a = splayTree()
a.insert(5)
@ -165,7 +207,7 @@ if __name__ == '__main__':
print('initial:5,1,4,2,7,8,2')
a.display()
tmp = a.find(2)
print("after find(2):%d"%tmp)
print("after find(2):%d" % tmp)
a.display()
print("remove(4)")
a.remove(4)

12
dataStructure/unionFindSet.py Normal file
View File

@ -0,0 +1,12 @@
class unionFindSet:
def __init__(self, S):
self.S = {i: i for i in S}
def find(self, x):
if x != self.S[x]:
self.S[x] = self.find(self.S[x])
return self.S[x]
def union(self, a, b, key=lambda x: x):
x, y = sorted((self.find(a), self.find(b)), key=key)
self.S[a] = self.S[b] = self.S[y] = x

99
dataStructure/unionFindSet/accountsMerge.py
View File

@ -1,99 +0,0 @@
#coding: utf-8
''' mbinary
#######################################################################
# File : accountsMerge.py
# Author: mbinary
# Mail: zhuheqin1@gmail.com
# Blog: https://mbinary.xyz
# Github: https://github.com/mbinary
# Created Time: 2018-12-18 17:07
# Description:
给定一个列表 accounts，每个元素 accounts[i] 是一个字符串列表，其中第一个元素 accounts[i][0] 是 名称 (name)，其余元素是 emails 表示该帐户的邮箱地址。
现在，我们想合并这些帐户。如果两个帐户都有一些共同的邮件地址，则两个帐户必定属于同一个人。请注意，即使两个帐户具有相同的名称，它们也可能属于不同的人，因为人们可能具有相同的名称。一个人最初可以拥有任意数量的帐户，但其所有帐户都具有相同的名称。
合并帐户后，按以下格式返回帐户：每个帐户的第一个元素是名称，其余元素是按顺序排列的邮箱地址。accounts 本身可以以任意顺序返回。
例子 1:
Input:
accounts = [["John", "johnsmith@mail.com", "john00@mail.com"], ["John", "johnnybravo@mail.com"], ["John", "johnsmith@mail.com", "john_newyork@mail.com"], ["Mary", "mary@mail.com"]]
Output: [["John", 'john00@mail.com', 'john_newyork@mail.com', 'johnsmith@mail.com'], ["John", "johnnybravo@mail.com"], ["Mary", "mary@mail.com"]]
Explanation:
第一个和第三个 John 是同一个人，因为他们有共同的电子邮件 "johnsmith@mail.com"。
第二个 John 和 Mary 是不同的人，因为他们的电子邮件地址没有被其他帐户使用。
#######################################################################
'''
class Solution(object):
def accountsMerge(self, accounts):
"""
:type accounts: List[List[str]]
:rtype: List[List[str]]
"""
mailDic = {}
for ct,i in enumerate(accounts):
for j in i[1:]:
mailDic[j] = (ct,i[0])
mails = {mail:idx for idx,mail in enumerate(mailDic.keys())}
mailNum = len(mails)
self.findSet = [i for i in range(mailNum)]
for li in accounts:
n = len(li)
for i in range(1,n-1):
for j in range(i+1,n):
self.union(mails[li[i]],mails[li[j]])
dic = {}
mails = {j:i for i,j in mails.items()}
for i in range(mailNum):
mail = mails[i]
n = mailDic[mails[self.find(i)]][0]
if n in dic:
dic[n].append(mail)
else:
dic[n] = [mail]
nameId = {i[0]:i[1] for i in mailDic.values()}
return [[nameId[i]]+sorted(mail) for i,mail in dic.items()]
def find(self,i):
if self.findSet[i]!=i:
n = self.find(self.findSet[i])
self.findSet[i] = n
return self.findSet[i]
def union(self,i,j):
if i!=j:
n = self.find(i)
if n!=self.find(j):
self.findSet[n] = self.findSet[j]
class Solution2:
'''并查映射'''
def accountsMerge(self, accounts):
"""
:type accounts: List[List[str]]
:rtype: List[List[str]]
"""
mailDic = {j:ct for ct,i in enumerate(accounts) for j in i[1:]}
self.findSet = {i:i for i in mailDic}
for li in accounts:
n = len(li)
for i in range(1,n-1):
for j in range(i+1,n):
self.union(li[i],li[j])
dic = {}
for mail in self.findSet:
n = mailDic[self.find(mail)]
if n in dic:
dic[n].append(mail)
else:
dic[n] = [mail]
return [[accounts[i][0]]+sorted(mail) for i,mail in dic.items()]
def find(self,i):
if self.findSet[i]!=i:
n = self.find(self.findSet[i])
self.findSet[i] = n
return self.findSet[i]
def union(self,i,j):
if i!=j:
n = self.find(i)
if n!=self.find(j):
self.findSet[n] = self.findSet[j]

42
dataStructure/unionFindSet/friendsCircle.py
View File

@ -1,42 +0,0 @@
#coding: utf-8
''' mbinary
#######################################################################
# File : unionFind.py
# Author: mbinary
# Mail: zhuheqin1@gmail.com
# Blog: https://mbinary.xyz
# Github: https://github.com/mbinary
# Created Time: 2018-12-18 14:53
# Description:
班上有 N 名学生。其中有些人是朋友，有些则不是。他们的友谊具有是传递性。如果已知 A 是 B 的朋友，B 是 C 的朋友，那么我们可以认为 A 也是 C 的朋友。所谓的朋友圈，是指所有朋友的集合。
给定一个 N * N 的矩阵 M，表示班级中学生之间的朋友关系。如果 M[i][j] = 1，表示已知第 i 个和 j 个学生互为朋友关系，否则为不知道。你必须输出所有学生中的已知的朋友圈总数。
#######################################################################
'''
class Solution(object):
def findCircleNum(self, M):
"""
:type M: List[List[int]]
:rtype: int
"""
n = len(M)
self.data = [i for i in range(n)]
for i in range(n):
for j in range(n):
if M[i][j]==1:
self.union(i,j)
ret = set()
for i in range(n):
ret.add(self.find(i))
return len(ret)
def find(self,i):
if self.data[i]!=i:
self.data[i] = self.find(self.data[i])
return self.data[i]
def union(self,i,j):
if i!=j:
n = self.find(i)
if n!=self.find(j):
self.data[n]= self.data[j]

108
dataStructure/winnerTree.py
View File

@ -10,6 +10,7 @@
#########################################################################
'''
class winnerTree:
'''if i<lowExt p = (i+offset)//2
else p = (i+n-1-lowExt)//2
@ -18,79 +19,92 @@ class winnerTree:
i is the index of players
lowExt is the double node num of the lowest layer of the tree
'''
def __init__(self,players,reverse=False):
self.n=len(players)
def __init__(self, players, reverse=False):
self.n = len(players)
self.tree = [0]*self.n
players.insert(0,0)
self.players=players
self.reverse=reverse
self.getNum()
players.insert(0, 0)
self.players = players
self.reverse = reverse
self.getNum()
self.initTree(1)
def getNum(self):
i=1
while 2*i< self.n:i=i*2
if 2*i ==self. n:
self.lowExt=0
i = 1
while 2*i < self.n:
i = i*2
if 2*i == self. n:
self.lowExt = 0
self.s = 2*i-1
else:
self.lowExt = (self.n-i)*2
self.s = i-1
self.offset = 2*i-1
def treeToArray(self,p):
return 2*p-self.offset if p>self.s else 2*p+self.lowExt-self.n+1
def arrayToTree(self,i):
return (i+self.offset)//2 if i<=self.lowExt else (i-self.lowExt+ self.n-1)//2
def win(self,a,b):
return a<b if self.reverse else a>b
def initTree(self,p):
if p>=self.n:
delta = p%2 #!!! good job notice delta mark the lchild or rchlid
def treeToArray(self, p):
return 2*p-self.offset if p > self.s else 2*p+self.lowExt-self.n+1
def arrayToTree(self, i):
return (i+self.offset)//2 if i <= self.lowExt else (i-self.lowExt + self.n-1)//2
def win(self, a, b):
return a < b if self.reverse else a > b
def initTree(self, p):
if p >= self.n:
delta = p % 2 # !!! good job notice delta mark the lchild or rchlid
return self.players[self.treeToArray(p//2)+delta]
l = self.initTree(2*p)
r = self.initTree(2*p+1)
self.tree[p] = l if self.win(l,r) else r
self.tree[p] = l if self.win(l, r) else r
return self.tree[p]
def winner(self):
idx = 1
while 2*idx<self.n:
while 2*idx < self.n:
idx = 2*idx if self.tree[2*idx] == self.tree[idx] else idx*2+1
num = self.treeToArray(idx)
num = num+1 if self.players[num] !=self.tree[1] else num
return self.tree[1],num
def getOppo(self,i,x,p):
oppo=None
if 2*p<self.n:oppo=self.tree[2*p]
elif i<=self.lowExt:oppo=self.players[i-1+i%2*2]
num = num+1 if self.players[num] != self.tree[1] else num
return self.tree[1], num
def getOppo(self, i, x, p):
oppo = None
if 2*p < self.n:
oppo = self.tree[2*p]
elif i <= self.lowExt:
oppo = self.players[i-1+i % 2*2]
else:
lpl= self.players[2*p+self.lowExt-self.n+1]
oppo = lpl if lpl!=x else self.players[2*p+self.lowExt-self.n+2]
lpl = self.players[2*p+self.lowExt-self.n+1]
oppo = lpl if lpl != x else self.players[2*p+self.lowExt-self.n+2]
return oppo
def update(self,i,x):
def update(self, i, x):
''' i is 1-indexed which is the num of player
and x is the new val of the player '''
self.players[i]=x
self.players[i] = x
p = self.arrayToTree(i)
oppo =self.getOppo(i,x,p)
self.tree[p] = x if self.win(x,oppo) else oppo
p=p//2
oppo = self.getOppo(i, x, p)
self.tree[p] = x if self.win(x, oppo) else oppo
p = p//2
while p:
l = self.tree[p*2]
r = None
if 2*p+1<self.n:r=self.tree[p*2+1] #notice this !!!
else:r = self.players[2*p+self.lowExt-self.n+1]
self.tree[p] = l if self.win(l,r) else r
p=p//2
if __name__ =='__main__':
s= [4,1,6,7,9,5234,0,2,7,4,123]
if 2*p+1 < self.n:
r = self.tree[p*2+1] # notice this !!!
else:
r = self.players[2*p+self.lowExt-self.n+1]
self.tree[p] = l if self.win(l, r) else r
p = p//2
if __name__ == '__main__':
s = [4, 1, 6, 7, 9, 5234, 0, 2, 7, 4, 123]
t = winnerTree(s)
print(t.players,t.tree)
print(t.players, t.tree)
for i in s:
val,idx=t.winner()
print(val,idx)
t.update(idx,-1)
val, idx = t.winner()
print(val, idx)
t.update(idx, -1)
'''

141
divideAndConquer/min_distance_of_n_points.py
View File

@ -13,123 +13,146 @@ from random import randint
from time import time
from functools import total_ordering
@total_ordering
class point:
def __init__(self,x,y):
self.x=x
self.y=y
def __init__(self, x, y):
self.x = x
self.y = y
def __neg__(self):
return pont(-self.x, -self.y)
def __len__(self):
return self.norm(2)
def __lt__(self,p):
return self.x<p.x or (self.x==p.x and self.y<p.y)
def __eq__(self,p):
return self.x==p.x and self.y == p.y
def __lt__(self, p):
return self.x < p.x or (self.x == p.x and self.y < p.y)
def __eq__(self, p):
return self.x == p.x and self.y == p.y
def __hash__(self):
return hash((self.x,self.y))
return hash((self.x, self.y))
def __repr__(self):
return 'point({},{})'.format(self.x,self.y)
return 'point({},{})'.format(self.x, self.y)
def __str__(self):
return self.__repr__()
def norm(self,n=2):
if n<=0: return max(abs(self.x),abs(self.y))
def norm(self, n=2):
if n <= 0:
return max(abs(self.x), abs(self.y))
return (abs(self.x)**n+abs(self.y)**n)**(1/n)
def distance(self,p):
def distance(self, p):
return ((self.x-p.x)**2+(self.y-p.y)**2)**0.5
def minDistance_n2(points):
n = len(points)
if n<=1: return 0
p,q=points[:2]
if n <= 1:
return 0
p, q = points[:2]
minD = points[0].distance(points[1])
for i in range(n-1):
for j in range(i+1,n):
for j in range(i+1, n):
d = points[i].distance(points[j])
if d<minD:
if d < minD:
minD = d
p = points[i]
q= points[j]
return minD, p,q
q = points[j]
return minD, p, q
def findif(points, f,reverse = False):
def findif(points, f, reverse=False):
n = len(points)
rg = range(n-1,-1,-1) if reverse else range(n)
for i in rg:
if not f(points[i]):
return points[i+1:] if reverse else points[:i]
return points.copy() # note that don't return exactly points, return a copy one
rg = range(n-1, -1, -1) if reverse else range(n)
for i in rg:
if not f(points[i]):
return points[i+1:] if reverse else points[:i]
return points.copy() # note that don't return exactly points, return a copy one
def floatEql(f1, f2, epsilon=1e-6):
return abs(f1-f2) < epsilon
def floatEql(f1,f2,epsilon=1e-6):
return abs(f1-f2)<epsilon
def minDistance_nlogn(n_points):
def _min(pts):
n = len(pts)
if n==2: return pts[0].distance(pts[1]) , pts[0],pts[1]
if n==3:
if n == 2:
return pts[0].distance(pts[1]), pts[0], pts[1]
if n == 3:
minD = pts[0].distance(pts[1])
p,q = pts[0],pts[1]
p, q = pts[0], pts[1]
d2 = pts[2].distance(pts[1])
if minD>d2:
if minD > d2:
minD = d2
p,q = pts[1], pts[2]
p, q = pts[1], pts[2]
d2 = pts[0].distance(pts[2])
if minD>d2: return d2, pts[0],pts[2]
else : return minD, p,q
if minD > d2:
return d2, pts[0], pts[2]
else:
return minD, p, q
n2 = n//2
mid = (pts[n2].x +pts[n2-1].x)/2
mid = (pts[n2].x + pts[n2-1].x)/2
s1 = pts[:n2]
s2 = pts[n2:]
minD ,p,q = _min(s1)
minD, p, q = _min(s1)
d2, p2, q2 = _min(s2)
#print('\n\n',minD,p,q,s1)
#print(d2,p2,q2,s2)
if minD> d2:
minD,p,q = d2, p2, q2
# print('\n\n',minD,p,q,s1)
# print(d2,p2,q2,s2)
if minD > d2:
minD, p, q = d2, p2, q2
linePoints = findif(s1,lambda pt:floatEql(pt.x,mid),reverse=True)
linePoints += findif(s2,lambda pt:floatEql(pt.x,mid))
linePoints = findif(s1, lambda pt: floatEql(pt.x, mid), reverse=True)
linePoints += findif(s2, lambda pt: floatEql(pt.x, mid))
n = len(linePoints)
if n>1:
for i in range(1,n):
dis = linePoints[i].y -linePoints[i-1].y
if dis<minD:
if n > 1:
for i in range(1, n):
dis = linePoints[i].y - linePoints[i-1].y
if dis < minD:
minD = dis
p,q = linePoints[i-1], linePoints[i]
leftPoints = findif(s1,lambda pt:pt.x>= mid-minD,reverse=True)
rightPoints = findif(s2,lambda pt:pt.x<= mid+minD)
p, q = linePoints[i-1], linePoints[i]
leftPoints = findif(s1, lambda pt: pt.x >= mid-minD, reverse=True)
rightPoints = findif(s2, lambda pt: pt.x <= mid+minD)
for lp in leftPoints:
y1,y2 = lp.y-minD, lp.y+minD
y1, y2 = lp.y-minD, lp.y+minD
for rp in rightPoints:
if y1< rp.y <y2:
if y1 < rp.y < y2:
dis = lp.distance(rp)
if dis< minD:
if dis < minD:
minD = dis
p,q = lp,rp
return minD, p,q
p, q = lp, rp
return minD, p, q
return _min(sorted(n_points))
def test(f=minDistance_n2):
print('\ntest : ', f.__name__)
begin = time()
minD, p, q = f(points)
print('time : {:.6f} s'.format(time()-begin))
print('result: {:.2f} {} {}\n'.format(minD, p,q))
print('result: {:.2f} {} {}\n'.format(minD, p, q))
def genData(n,unique=True):
def genData(n, unique=True):
upper = 1000000
if unique:
points = set()
for i in range(n):
points.add(point(randint(1,upper),randint(1,upper)))
points.add(point(randint(1, upper), randint(1, upper)))
return list(points)
else:return [point(randint(1,upper),randint(1,upper)) for i in range(n)]
else:
return [point(randint(1, upper), randint(1, upper)) for i in range(n)]
if __name__ =='__main__':
if __name__ == '__main__':
n = 1000
points = genData(n, unique=True)
print('min distance of {} points'.format(n))
#print(sorted(points))
# print(sorted(points))
test(minDistance_n2)
test(minDistance_nlogn)

5
dynamicProgramming/last-stone-weight.py
View File

@ -21,12 +21,13 @@ leetcode 1049: https://leetcode-cn.com/problems/last-stone-weight-ii/
#######################################################################
'''
class Solution:
def lastStoneWeightII(self, stones: List[int]) -> int:
sm = sum(stones)
ans = sm//2
dp = [0]*(ans+1)
for x in stones:
for j in range(ans,x-1,-1):
dp[j] = max(dp[j],dp[j-x]+x)
for j in range(ans, x-1, -1):
dp[j] = max(dp[j], dp[j-x]+x)
return sm-2*dp[ans]

29
dynamicProgramming/lcs.py
View File

@ -10,41 +10,44 @@
#########################################################################
'''
def lcs(a,b):
def lcs(a, b):
'''time: O(mn); space: O(mn)'''
m,n= len(a),len(b)
m, n = len(a), len(b)
board = [[[] for i in range(n+1)] for i in range(m+1)]
for i in range(m):
for j in range(n):
if a[i]==b[j]:
board[i+1][j+1] =board[i][j]+[a[i]]
if a[i] == b[j]:
board[i+1][j+1] = board[i][j]+[a[i]]
elif len(board[i][j+1]) < len(board[i+1][j]):
board[i+1][j+1] = board[i+1][j]
else :
else:
board[i+1][j+1] = board[i][1+j]
return board[m][n]
def lcs2(a,b):
def lcs2(a, b):
'''time: O(mn); space: O(m)'''
m,n= len(a),len(b)
m, n = len(a), len(b)
board = [[] for i in range(n+1)]
for i in range(m):
upperLevel = board[0].copy()
for j in range(n):
tmp = board[j+1].copy()
if a[i]==b[j]:
if a[i] == b[j]:
board[j+1] = upperLevel+[a[i]]
elif len(board[j+1]) < len(board[j]):
board[j+1] = board[j].copy() # copy is needed
board[j+1] = board[j].copy() # copy is needed
upperLevel = tmp
return board[n]
if __name__ =='__main__':
if __name__ == '__main__':
a = 'ABCBDAB'
b = 'BDCABA'
print('s1:',a)
print('s2:',b)
print('s1:', a)
print('s2:', b)
while 1:
print('lcs:',lcs2(a,b))
print('lcs:', lcs2(a, b))
a = input('s1: ')
b = input('s2: ')

14
dynamicProgramming/max-len-of-repeated-subarray.py
View File

@ -11,11 +11,13 @@
给两个整数数组 A 和 B ，返回两个数组中公共的、长度最长的子数组的长度。
#######################################################################
'''
def findLength(A,B):
n,m = len(A),len(B)
def findLength(A, B):
n, m = len(A), len(B)
dp = [[0]*(m+1) for i in range(n+1)]
for i in range(1,n+1):
for j in range(1,m+1):
if A[i-1]==B[j-1]:
dp[i][j]=dp[i-1][j-1]+1
for i in range(1, n+1):
for j in range(1, m+1):
if A[i-1] == B[j-1]:
dp[i][j] = dp[i-1][j-1]+1
return max(max(row) for row in dp)

41
dynamicProgramming/splitStripe.py
View File

@ -16,33 +16,36 @@
then find the maximum price to split the stripe in different shorter stripes
( including the original length if possible)
'''
def count(n,prices):
def best(cur):
def count(n, prices):
def best(cur):
# note that copying the list or create a new list in the following new_stripes codes
if cur in values: return values[cur],stripes[cur]
if cur in values:
return values[cur], stripes[cur]
maxPrice = 0
new_stripes=[]
for i,j in prices.items():
if i<=cur:
new_stripes = []
for i, j in prices.items():
if i <= cur:
p, tmp = best(cur-i)
if maxPrice<p+j:
new_stripes = tmp+[i] # if the list is not copyed, create a new list, don't use append
maxPrice =p+j
if maxPrice < p+j:
# if the list is not copyed, create a new list, don't use append
new_stripes = tmp+[i]
maxPrice = p+j
values[cur] = maxPrice
stripes[cur] = new_stripes
return maxPrice,new_stripes
values = {0:0}
stripes = {0:[]}
return maxPrice, new_stripes
values = {0: 0}
stripes = {0: []}
return best(n)
if __name__=='__main__':
li = [(1,1),(2,5),(3,8),(4,9),(5,10),(6,17),(7,17),(8,20),(9,24),(10,30)]
prices = {i:j for i,j in li}
if __name__ == '__main__':
li = [(1, 1), (2, 5), (3, 8), (4, 9), (5, 10),
(6, 17), (7, 17), (8, 20), (9, 24), (10, 30)]
prices = {i: j for i, j in li}
n = 40
d = {i:count(i,prices) for i in range(n+1)}
d = {i: count(i, prices) for i in range(n+1)}
for i in range(n+1):
print(i,d[i])
print(i, d[i])

6
dynamicProgramming/stoneGame.py
View File

@ -1,4 +1,4 @@
#coding: utf-8
# coding: utf-8
''' mbinary
#######################################################################
# File : stoneGame.py
@ -14,6 +14,8 @@
leetcode-cn 877: https://leetcode-cn.com/problems/stone-game/
#######################################################################
'''
def stoneGame(li):
'''li: list, len(li)%2==0, sum(li)%2==1'''
def f(p,q):
@ -29,7 +31,7 @@ def stoneGame(li):
n2 = li[q] + min(-li[p]+f(p+1,q-1),-li[q-1]+f(p,q-2))
ret = max(n1,n2)
dp[p][q] = ret
#print(li[p:q+1],ret)
# print(li[p:q+1],ret)
return ret
n = len(li)
dp = [[None for i in range(n)] for i in range(n)]

21
graph/cloneGraph.cpp
View File

@ -9,18 +9,23 @@
# Description:
#########################################################################
*/
class Solution {
class Solution
{
public:
map<Node*,Node*> st;
Node *cloneGraph(Node *node){
Node* ret = new Node(node->val,vector<Node*>());
st[node]=ret;
for(auto x:node->neighbors){
map<Node*, Node*> st;
Node *cloneGraph(Node *node)
{
Node* ret = new Node(node->val, vector<Node*>());
st[node] = ret;
for (auto x : node->neighbors) {
auto p = st.find(x);
if(p==st.end()){
if (p == st.end()) {
ret->neighbors.push_back(cloneGraph(x));
}else ret->neighbors.push_back(p->second);
} else ret->neighbors.push_back(p->second);
}
return ret;
}
};

38
graph/dfs.py
View File

@ -20,36 +20,37 @@
#######################################################################
'''
class Solution:
def longestStrChain(self, words: List[str]) -> int:
def isAdj(s1,s2):
if len(s1)>len(s2):
s1,s2 = s2,s1
n1,n2 = len(s1),len(s2)
if n2-n1!=1:
def isAdj(s1, s2):
if len(s1) > len(s2):
s1, s2 = s2, s1
n1, n2 = len(s1), len(s2)
if n2-n1 != 1:
return False
i=j=0
i = j = 0
flag = False
while i<n1 and j<n2:
if s1[i]!=s2[j]:
while i < n1 and j < n2:
if s1[i] != s2[j]:
if flag:
return False
flag = True
j+=1
j += 1
else:
i+=1
j+=1
i += 1
j += 1
return True
def dfs(begin):
ans = 1
w = words[begin]
n = len(w)
if n+1 in lenDic:
for nd in lenDic[n+1]:
#print(w,words[nd],isAdj(w,words[nd]))
if isAdj(w,words[nd]):
ans = max(ans,1+dfs(nd))
# print(w,words[nd],isAdj(w,words[nd]))
if isAdj(w, words[nd]):
ans = max(ans, 1+dfs(nd))
return ans
lenDic = {}
for i in range(len(words)):
@ -57,14 +58,13 @@ class Solution:
if n in lenDic:
lenDic[n].add(i)
else:
lenDic[n]={i}
lenDic[n] = {i}
lens = sorted(lenDic)
n = len(lens)
ans = 0
for i in range(n):
if ans < n-i:
for nd in lenDic[lens[i]]:
ans = max(ans,dfs(nd))
ans = max(ans, dfs(nd))
return ans

15
graph/isBipartGraph.py
View File

@ -21,10 +21,13 @@ def isBipartite(self, graph):
"""
n = len(graph)
self.node = graph
self.color = {i:None for i in range(n)}
return all(self.dfs(i,True) for i in range(n) if self.color[i] is None)
def dfs(self,n,col=True):
self.color = {i: None for i in range(n)}
return all(self.dfs(i, True) for i in range(n) if self.color[i] is None)
def dfs(self, n, col=True):
if self.color[n] is None:
self.color[n]=col
return all(self.dfs(i,not col) for i in self.node[n])
else:return col==self.color[n]
self.color[n] = col
return all(self.dfs(i, not col) for i in self.node[n])
else:
return col == self.color[n]

2
math/dft.py
View File

@ -54,7 +54,7 @@ def _fft2(a, invert=False):
N = len(a)
if N & (N - 1) == 0: # O(nlogn), 2^k
r = int(np.log(N))
c = np.array(a,dtype='complex')
c = np.array(a, dtype='complex')
i = 2j if invert else -2j
w = np.exp(i * np.pi / N)
for h in range(r - 1, -1, -1):

22
math/fastPow.py
View File

@ -11,21 +11,23 @@
#######################################################################
'''
def fastPow(a,n):
def fastPow(a, n):
'''a^n'''
rst = 1
while n:
if n%2:
rst *=a
n>>=1
a*=a
if n % 2:
rst *= a
n >>= 1
a *= a
return rst
def fastMul(a,b):
def fastMul(a, b):
'''a*b'''
rst = 0
while b:
if b&1:
rst +=a
b>>=1
a*=2
if b & 1:
rst += a
b >>= 1
a *= 2

40
math/fibonacci/fibonacci.py
View File

@ -11,27 +11,31 @@
#######################################################################
'''
def fib(n):
"""Calculates the nth Fibonacci number"""
mat,p = (1,1,1,0),n-2
if n<=0: # for negative fib item, use f(n) = f(n+2)-f(n-1) to calculate
mat = (0,1,1,-1),2-n
li = matrix_pow((0,1,1,-1),1-n)
return li[0]+li[1]
def matrix_pow(mat,n):
ans = (1,0,0,1) # element matrix
while n>0:
if n%2==1:
ans = matrix_mul(ans,mat)
n>>=1
mat = matrix_mul(mat,mat)
"""Calculates the nth Fibonacci number"""
mat, p = (1, 1, 1, 0), n-2
if n <= 0: # for negative fib item, use f(n) = f(n+2)-f(n-1) to calculate
mat = (0, 1, 1, -1), 2-n
li = matrix_pow((0, 1, 1, -1), 1-n)
return li[0]+li[1]
def matrix_pow(mat, n):
ans = (1, 0, 0, 1) # element matrix
while n > 0:
if n % 2 == 1:
ans = matrix_mul(ans, mat)
n >>= 1
mat = matrix_mul(mat, mat)
return ans
def matrix_mul(a,b):
def matrix_mul(a, b):
'''a,b are four-item tuple, represent matrix [[a[0],a[1]],[a[2],a[3]]]'''
return a[0]*b[0]+a[1]*b[2], a[0]*b[1]+a[1]*b[3], a[2]*b[0]+a[3]*b[2],a[2]*b[1]+a[3]*b[3]
return a[0]*b[0]+a[1]*b[2], a[0]*b[1]+a[1]*b[3], a[2]*b[0]+a[3]*b[2], a[2]*b[1]+a[3]*b[3]
if __name__=='__main__':
for i in range(-5,5):
print(i,fib(i))
if __name__ == '__main__':
for i in range(-5, 5):
print(i, fib(i))

16
math/numWeight/addNegaBin.py
View File

@ -23,6 +23,7 @@ eg
'''
from nega import nega
def addNegaBin(arr1: list, arr2: list) -> list:
if len(arr1) < len(arr2):
arr1, arr2 = arr2, arr1
@ -42,19 +43,20 @@ def addNegaBin(arr1: list, arr2: list) -> list:
elif arr1[i] == 0 and arr2[i] == 1:
arr1[i] = arr2[i]
#print(arr1,arr2,i)
# print(arr1,arr2,i)
while len(arr1) > 1 and arr1[0] == 0:
arr1.pop(0)
return arr1
if __name__=='__main__':
if __name__ == '__main__':
while 1:
print("input q to quit or input x1 x2: ")
s = input()
if s=='q':
if s == 'q':
break
n1,n2 =[int(i) for i in s.split()]
l1,l2 = nega(n1),nega(n2)
print(n1,l1)
print(n2,l2)
n1, n2 = [int(i) for i in s.split()]
l1, l2 = nega(n1), nega(n2)
print(n1, l1)
print(n2, l2)
print(f'{n1}+{n2}={n1+n2}: {addNegaBin(l1,l2)}')

45
math/numWeight/convertWeight.py
View File

@ -10,34 +10,37 @@
#########################################################################
'''
def covert(s,basefrom=10,baseto=2):
return d2n(n2d(s,basefrom),baseto)
def n2d(s,base=16):
def covert(s, basefrom=10, baseto=2):
return d2n(n2d(s, basefrom), baseto)
def n2d(s, base=16):
''' num of base_n(n<36) to decimal'''
dic = {chr(i+ord('0')):i for i in range(10)}
s=s.upper()
if base>10:
dic.update({chr(i+ord('A')):i+10 for i in range(26)})
#if base in [16,8,2] :
dic = {chr(i+ord('0')): i for i in range(10)}
s = s.upper()
if base > 10:
dic.update({chr(i+ord('A')): i+10 for i in range(26)})
# if base in [16,8,2] :
# p=max(map(s.find,'OBX'))
# s=s[p+1:] #remove prefix of hex or bin or oct
rst=0
rst = 0
for i in s:
rst=dic[i]+rst*base
rst = dic[i]+rst*base
return rst
def d2n(n,base=16):
''' num of base_n(n<36) to decimal'''
dic = {i:chr(i+ord('0')) for i in range(10)}
if base>10:
dic.update({i+10:chr(i+ord('A')) for i in range(26)})
rst=[]
while n!=0:
i=int(n/base)
rst.append(dic[n-i*base])
n=i
return ''.join(rst[::-1])
def d2n(n, base=16):
''' num of base_n(n<36) to decimal'''
dic = {i: chr(i+ord('0')) for i in range(10)}
if base > 10:
dic.update({i+10: chr(i+ord('A')) for i in range(26)})
rst = []
while n != 0:
i = int(n/base)
rst.append(dic[n-i*base])
n = i
return ''.join(rst[::-1])
'''

15
math/numWeight/nega.py
View File

@ -9,15 +9,18 @@
# Description:
#########################################################################
'''
def nega(n:int,base=-2:int)->:list:
def nega(n: int, base=-2: int)->: list:
'''return list of num, the first is the highest digit'''
if base>-2:
raise Exception(f"[Error]: invalid base: {base}, base should be no more than -2")
if base > -2:
raise Exception(
f"[Error]: invalid base: {base}, base should be no more than -2")
ans = []
while n:
k = n%base
if k<0:
k-=base
k = n % base
if k < 0:
k -= base
ans.append(k)
n = (n-k)//base
return ans[::-1]

17
math/numberTheory/euler.py
View File

@ -17,17 +17,20 @@ from factor import factor
from collections import Counter
from functools import reduce
from operator import mul
def phi(n):
st = set(factor(n))
return round(reduce(mul,(1-1/p for p in st),n))
st = set(factor(n))
return round(reduce(mul, (1-1/p for p in st), n))
def sigma(n):
ct = Counter(factor(n))
return reduce(mul,(round((p**(ct[p]+1)-1)/(p-1)) for p in ct),1)
return reduce(mul, (round((p**(ct[p]+1)-1)/(p-1)) for p in ct), 1)
if __name__=='__main__':
if __name__ == '__main__':
while 1:
n = int(input('n: '))
print('phi(n):',phi(n))
print('sigma(n):',sigma(n))
print('phi(n):', phi(n))
print('sigma(n):', sigma(n))

48
math/numberTheory/factor.py
View File

@ -13,41 +13,49 @@
from random import randint
from isPrime import isPrime
from gcd import gcd
from gcd import gcd
def factor(n):
'''pollard's rho algorithm'''
if n<1:raise Exception('[Error]: {} is less than 1'.format(n))
if n==1: return []
if isPrime(n):return [n]
fact=1
cycle_size=2
if n < 1:
raise Exception('[Error]: {} is less than 1'.format(n))
if n == 1:
return []
if isPrime(n):
return [n]
fact = 1
cycle_size = 2
x = x_fixed = 2
c = randint(1,n)
while fact==1:
c = randint(1, n)
while fact == 1:
for i in range(cycle_size):
if fact>1:break
x=(x*x+c)%n
if x==x_fixed:
c = randint(1,n)
if fact > 1:
break
x = (x*x+c) % n
if x == x_fixed:
c = randint(1, n)
continue
fact = gcd(x-x_fixed,n)
cycle_size *=2
fact = gcd(x-x_fixed, n)
cycle_size *= 2
x_fixed = x
return factor(fact)+factor(n//fact)
def fact(n):
f=2
f = 2
ret = []
while f*f<=n:
while not n%f:
while f*f <= n:
while not n % f:
ret.append(f)
n//f
f+=1
if n>1:ret.append(n)
f += 1
if n > 1:
ret.append(n)
return ret
if __name__=='__main__':
if __name__ == '__main__':
while 1:
n = int(input('n: '))
print(factor(n))

33
math/numberTheory/gcd.py
View File

@ -11,23 +11,28 @@
#######################################################################
'''
def gcd(a,b):
while b!=0:
a,b=b,a%b
def gcd(a, b):
while b != 0:
a, b = b, a % b
return a
def lcm(a,b):
return int(a*b/gcd(a,b))
def xgcd(a,b):
'''return gcd(a,b), x,y where ax+by=gcd(a,b)'''
if b==0:return a,1,0
g,x,y = xgcd(b,a%b)
return g,y,x-a//b*y
if __name__=='__main__':
def lcm(a, b):
return int(a*b/gcd(a, b))
def xgcd(a, b):
'''return gcd(a,b), x,y where ax+by=gcd(a,b)'''
if b == 0:
return a, 1, 0
g, x, y = xgcd(b, a % b)
return g, y, x-a//b*y
if __name__ == '__main__':
while 1:
a = int(input('a: '))
b = int(input('b: '))
print('gcd :',gcd(a,b))
print('xgcd:',xgcd(a,b))
print('gcd :', gcd(a, b))
print('xgcd:', xgcd(a, b))

45
math/numberTheory/hammingDistance.py
View File

@ -13,48 +13,51 @@
#######################################################################
'''
def hammingDistance(a,b):
if isinstance(a,int):
n = a^b
def hammingDistance(a, b):
if isinstance(a, int):
n = a ^ b
ct = 0
while n:
ct+=n%2
n>>=1
ct += n % 2
n >>= 1
return ct
else:
n,m = len(a),len(b)
n, m = len(a), len(b)
ret = 0
for i,j in zip(a,b):
ret+= i==j
for i, j in zip(a, b):
ret += i == j
return ret+abs(n-m)
def totalHammingDistance(lst):
'''return sum of any two items(num or lst( str)) in lst'''
length = len(lst)
if length ==0:return 0
if isinstance(lst[0],int):
length = len(lst)
if length == 0:
return 0
if isinstance(lst[0], int):
bits = [0] * len(bin(max(lst)))
for n in lst:
ct = 0
while n:
if n%2==1:
bits[ct]+=1
ct+=1
n>>=1
if n % 2 == 1:
bits[ct] += 1
ct += 1
n >>= 1
return sum(i*(length-i) for i in bits)
else:
mx = len(max(lst,key=len))
mx = len(max(lst, key=len))
position = [dict() for i in range(mx)]
for li in lst:
for i,x in enumerate(li):
for i, x in enumerate(li):
if x in position[i]:
position[i][x] +=1
position[i][x] += 1
else:
position[i][x] =1
position[i][x] = 1
ret = 0
for dic in position:
left = length
for i in dic.values():
ret+=i*(left-i) # key step
left -=i # key step
ret += i*(left-i) # key step
left -= i # key step
return ret

105
math/numberTheory/isPrime.py
View File

@ -12,56 +12,61 @@
from random import randint
def quickMulMod(a,b,m):
def quickMulMod(a, b, m):
'''a*b%m, quick'''
ret = 0
while b:
if b&1:
ret = (a+ret)%m
b//=2
a = (a+a)%m
if b & 1:
ret = (a+ret) % m
b //= 2
a = (a+a) % m
return ret
def quickPowMod(a,b,m):
def quickPowMod(a, b, m):
'''a^b %m, quick, O(logn)'''
ret =1
ret = 1
while b:
if b&1:
ret =quickMulMod(ret,a,m)
b//=2
a = quickMulMod(a,a,m)
if b & 1:
ret = quickMulMod(ret, a, m)
b //= 2
a = quickMulMod(a, a, m)
return ret
def isPrime(n,t=5):
def isPrime(n, t=5):
'''miller rabin primality test, a probability result
t is the number of iteration(witness)
'''
t = min(n-3,t)
if n<2:
t = min(n-3, t)
if n < 2:
print('[Error]: {} can\'t be classed with prime or composite'.format(n))
return
if n==2: return True
if n == 2:
return True
d = n-1
r = 0
while d%2==0:
r+=1
d//=2
tested=set()
while d % 2 == 0:
r += 1
d //= 2
tested = set()
for i in range(t):
a = randint(2,n-2)
a = randint(2, n-2)
while a in tested:
a = randint(2,n-2)
a = randint(2, n-2)
tested.add(a)
x= quickPowMod(a,d,n)
if x==1 or x==n-1: continue #success,
x = quickPowMod(a, d, n)
if x == 1 or x == n-1:
continue # success,
for j in range(r-1):
x= quickMulMod(x,x,n)
if x==n-1:break
x = quickMulMod(x, x, n)
if x == n-1:
break
else:
return False
return True
'''
we shouldn't use Fermat's little theory
Namyly:
@ -73,49 +78,23 @@ The inverse theorem of it is not True.
a counter-example: 2^340 \equiv 1 (mod 341), but 341 is a composite
'''
class primeSieve:
'''sieve of Eratosthenes, It will be more efficient when judging many times'''
primes = [2,3,5,7,11,13]
def isPrime(self,x):
if x<=primes[-1]:
return twoDivideFind(x,self.primes)
while x>self.primes[-1]:
left = self.primes[-1]
right = (left+1)**2
lst = []
for i in range(left,right):
for j in self.primes:
if i%j==0:break
else:lst.append(i)
self.primes+=lst
return twoDivideFind(x,lst)
def nPrime(n):
'''return the n-th prime'''
i=n-len(self.primes)
last = self.primes[-1]
for _ in range(i):
while 1:
last +=2
for p in self.primes:
if last%p==0:
break
else:
self.primes.append(last)
break
return self.primes[n-1]
def twoDivideFind(x,li):
a,b = 0, len(li)
while a<=b:
def twoDivideFind(x, li):
a, b = 0, len(li)
while a <= b:
mid = (a+b)//2
if li[mid]<x:a=mid+1
elif li[mid]>x: b= mid-1
else:return mid
if li[mid] < x:
a = mid+1
elif li[mid] > x:
b = mid-1
else:
return mid
return -1
if __name__=='__main__':
if __name__ == '__main__':
n = 100
print('prime numbers below',n)
print('prime numbers below', n)
print([i for i in range(n) if isPrime(i)])
while 1:
n = int(input('n: '))

116
math/numberTheory/modulo_equation.py
View File

@ -18,110 +18,124 @@ from euler import phi
from isPrime import isPrime
from factor import factor
def ind(m,g):
''' mod m ,primary root g -> {n:indg n}'''
return {j:i for i in range(m-1) \
for j in range(m) if (g**i-j)%m==0}
def gs(m,num=100):
'''return list of m's primary roots below num'''
def ind(m, g):
''' mod m ,primary root g -> {n:indg n}'''
return {j: i for i in range(m-1)
for j in range(m) if (g**i-j) % m == 0}
def gs(m, num=100):
'''return list of m's primary roots below num'''
p = phi(m)
mp = factor(p)
checkLst = [p//i for i in mp]
return [i for i in range(2,num) if all((i**n-1)%m !=0 for n in checkLst)]
return [i for i in range(2, num) if all((i**n-1) % m != 0 for n in checkLst)]
def minG(m):
p = phi(m)
mp = factor(p)
checkLst = [p//i for i in mp]
i=2
while 1:
if all((i**n-1)%m !=0 for n in checkLst):return i
i+=1
i = 2
while 1:
if all((i**n-1) % m != 0 for n in checkLst):
return i
i += 1
class solve:
def __init__(self,equ=None):
self.linearPat= re.compile(r'\s*(\d+)\s*--\s*(\d+)[\s\(]*mod\s*(\d+)')
self.sol = []
def __init__(self, equ=None):
self.linearPat = re.compile(r'\s*(\d+)\s*--\s*(\d+)[\s\(]*mod\s*(\d+)')
self.sol = []
#self.m = m
#self.ind_mp = ind(m,minG(m))
def noSol(self):
print('equation {equ} has no solution'.format(equ=self.equ))
def error(self):
print("Error! The divisor m must be postive integer")
def solveLinear(self,a,b,m):
def solveLinear(self, a, b, m):
'''ax--b(mod m): solve linear equation with one unknown
return ([x1,x2,...],m)
'''
a,b,m = self.check(a,b,m)
g,x,y=xgcd(a,m)
if a*b%g!=0:
a, b, m = self.check(a, b, m)
g, x, y = xgcd(a, m)
if a*b % g != 0:
self.noSol()
return None
sol=x*b//g
sol = x*b//g
m0 = m//g
sols = [(sol+i*m0)%m for i in range(g)]
print('{}x--{}(mod {}), solution: {} mod {}'.format(a,b,m,sols,m))
return (sols,m)
def check(self,a,b,m):
if m<=0:
sols = [(sol+i*m0) % m for i in range(g)]
print('{}x--{}(mod {}), solution: {} mod {}'.format(a, b, m, sols, m))
return (sols, m)
def check(self, a, b, m):
if m <= 0:
self.error()
return None
if a<0:a,b=-a,-b ## important
if b<0:b+= -b//m * m
return a,b,m
if a < 0:
a, b = -a, -b # important
if b < 0:
b += -b//m * m
return a, b, m
def solveHigh(self,a,n,b,m):
def solveHigh(self, a, n, b, m):
''' ax^n -- b (mod m) ind_mp is a dict of m's {n: indg n}'''
ind_mp = ind(m,minG(m))
ind_mp = ind(m, minG(m))
tmp = ind_mp[b] - ind_mp[a]
if tmp < 0:tmp+=m
sol = self.solveLinear(n,tmp,phi(m))
re_mp = {j:i for i ,j in ind_mp.items()}
if tmp < 0:
tmp += m
sol = self.solveLinear(n, tmp, phi(m))
re_mp = {j: i for i, j in ind_mp.items()}
sols = [re_mp[i] for i in sol[0]]
print('{}x^{}--{}(mod {}), solution: {} mod {}'.format(a,n,b,m,sols,m))
return sols,m
print('{}x^{}--{}(mod {}), solution: {} mod {}'.format(a, n, b, m, sols, m))
return sols, m
def solveGroup(self,tups):
def solveGroup(self, tups):
'''tups is a list of tongyu equation groups, like
[(a1,b1,m1),(a2,b2,m2)...]
and, m1,m2... are all primes
'''
mp = {}
print('solving group of equations: ')
for a,b,m in tups:
print('{}x--{}(mod {})'.format(a,b,m))
for a, b, m in tups:
print('{}x--{}(mod {})'.format(a, b, m))
if m in mp:
if mp[m][0]*b!=mp[m][1]*a:
if mp[m][0]*b != mp[m][1]*a:
self.noSol()
return
else:mp[m] = (a,b)
else:
mp[m] = (a, b)
product = 1
for i in mp.keys():
product *=i
product *= i
sol = [0]
for i in mp:
xs,m = self.solveLinear(product//i*mp[i][0],1,i)
xs, m = self.solveLinear(product//i*mp[i][0], 1, i)
new = []
for x in xs:
cur = x*product//i*mp[i][1]
for old in sol:
new.append(old+cur)
sol = new
sol= [i%product for i in sol]
print('final solution: {} mod {}'.format(sol,product))
return sol,product
sol = [i % product for i in sol]
print('final solution: {} mod {}'.format(sol, product))
return sol, product
def __call__(self):
s=input('输入同余方程，用--代表同于号，形如3--5(mod 7)代表3x模7同余于5')
li= self.linearPat.findall(s)
li = [(int(a),int(b),int(m)) for a,b,m in li]
s = input('输入同余方程，用--代表同于号，形如3--5(mod 7)代表3x模7同余于5')
li = self.linearPat.findall(s)
li = [(int(a), int(b), int(m)) for a, b, m in li]
print(self.solveLinear(li[0]))
if __name__ == '__main__':
solver = solve()
res = solver.solveLinear(3,6,9)
solver = solve()
res = solver.solveLinear(3, 6, 9)
print()
res = solver.solveHigh(1,8,3,11)
res = solver.solveHigh(1, 8, 3, 11)
print()
res = solver.solveGroup([(5,11,2),(3,8,5),(4,1,7)])
res = solver.solveGroup([(5, 11, 2), (3, 8, 5), (4, 1, 7)])

2
math/numberTheory/primesLEn.hs
View File

@ -1,3 +1,3 @@
genPrimes 2= [2]
genPrimes n = let li = genPrimes $n-1
in if all (\x-> mod n x /=0) li then n:li else li
in if all (\x-> mod n x /=0) li then n:li else li

56
math/numberTheory/sievePrime.py Normal file
View File

@ -0,0 +1,56 @@
def sievePrime(n):
if n < 2:
return 0
prime = [1] * (n + 1)
prime[0] = prime[1] = 0
for i in range(2, int(n**0.5) + 1):
if prime[i] == 1:
prime[i*i:n + 1:i] = [0]*len(prime[i*i:n + 1:i])
return [i for i in range(n+1) if prime[i] == 1]
class primeSiever:
'''sieve of Eratosthenes, It will be more efficient when judging many times'''
primes = [2, 3, 5, 7, 11, 13]
def isPrime(self, x):
if x <= primes[-1]:
return twoDivideFind(x, self.primes)
while x > self.primes[-1]:
left = self.primes[-1]
right = (left+1)**2
lst = []
for i in range(left, right):
for j in self.primes:
if i % j == 0:
break
else:
lst.append(i)
self.primes += lst
return twoDivideFind(x, lst)
def nPrime(n):
'''return the n-th prime'''
i = n-len(self.primes)
last = self.primes[-1]
for _ in range(i):
while 1:
last += 2
for p in self.primes:
if last % p == 0:
break
else:
self.primes.append(last)
break
return self.primes[n-1]
if __name__ == "__main__":
import sys
if len(sys.argv) < 2:
n = 100
else:
n = int(sys.argv[1])
ans = sievePrime(n)
print(f'primes <= {n}, nums: {len(ans)}')
print(ans)

69
math/numericalAnalysis/interplotion.py
View File

@ -26,58 +26,65 @@ from collections import namedtuple
from functools import reduce
from operator import mul
X = sympy.Symbol ('x')
point = namedtuple('point',['x','y'])
X = sympy.Symbol('x')
point = namedtuple('point', ['x', 'y'])
class interplotion:
def __init__(self,points):
self.points = [point(x,y) for x,y in points]
self.xs= [i for i,j in points]
self.poly,self.rem = self.newton(self.points,0,len(self.points)-1)
def __init__(self, points):
self.points = [point(x, y) for x, y in points]
self.xs = [i for i, j in points]
self.poly, self.rem = self.newton(self.points, 0, len(self.points)-1)
def newton(self,li,a,b):
def newton(self, li, a, b):
'''li:[(x,f(x))...]'''
qs = [li[0].y]
def quoDiff(begin,end):
if begin == end:return li[begin].y
q = (quoDiff(begin+1,end)-quoDiff(begin,end-1))/(li[end].x-li[begin].x)
if begin == a:qs.append(q)
def quoDiff(begin, end):
if begin == end:
return li[begin].y
q = (quoDiff(begin+1, end)-quoDiff(begin, end-1)) / \
(li[end].x-li[begin].x)
if begin == a:
qs.append(q)
return q
quoDiff(a,b)
poly ,base = 0, 1
for i,q in enumerate(qs):
quoDiff(a, b)
poly, base = 0, 1
for i, q in enumerate(qs):
poly += q*base
base*= X-li[i].x
base *= X-li[i].x
return poly, base*qs[-1]
def lagrange(self,points=None):
def lagrange(self, points=None):
xs = None
if points is None:
xs = self.xs
points = self.points
else: xs =[x for x,y in points]
product = reduce(mul,[X-x for x in xs],1)
else:
xs = [x for x, y in points]
product = reduce(mul, [X-x for x in xs], 1)
poly = 0
for x,y in points:
tmp = product/(X-x)
coef = y/(tmp.subs(X,x))
poly+= coef *tmp
for x, y in points:
tmp = product/(X-x)
coef = y/(tmp.subs(X, x))
poly += coef * tmp
return poly
def predict(self,val,poly = None):
if poly is None:poly = self.poly
return poly.subs(X,val) # note the func subs
def predict(self, val, poly=None):
if poly is None:
poly = self.poly
return poly.subs(X, val) # note the func subs
if __name__ == '__main__':
f = interplotion([(81,9),(100,10),(121,11)])
f = interplotion([(81, 9), (100, 10), (121, 11)])
p = f.lagrange()
print(p.subs(X,105))
print(p.subs(X, 105))
print(p)
intor = interplotion([(0,11),(0.02,9),(0.04,7),(0.06,10)])
intor = interplotion([(0, 11), (0.02, 9), (0.04, 7), (0.06, 10)])
p = intor.lagrange()
print(p)
res = intor.predict(0.08)

98
math/numericalAnalysis/iteration.py
View File

@ -15,94 +15,98 @@ import numpy as np
from math import sqrt
def newton(y:sympy.core,x0:float,epsilon:float=0.00001,maxtime:int=50) ->(list,list):
def newton(y: sympy.core, x0: float, epsilon: float = 0.00001, maxtime: int = 50) ->(list, list):
'''
newton 's iteration method for finding a zeropoint of a func
y is the func, x0 is the init x val: int float epsilon is the accurrency
'''
if epsilon <0:epsilon = -epsilon
ct =0
t = y.free_symbols
varsymbol = 'x' if len(t)==0 else t.pop()
x0= float(x0)
if epsilon < 0:
epsilon = -epsilon
ct = 0
t = y.free_symbols
varsymbol = 'x' if len(t) == 0 else t.pop()
x0 = float(x0)
y_diff = y.diff()
li = [x0]
vals = []
while 1:
val = y.subs(varsymbol,x0)
val = y.subs(varsymbol, x0)
vals.append(val)
x = x0- val/y_diff.subs(varsymbol,x0)
x = x0 - val/y_diff.subs(varsymbol, x0)
li.append(x)
ct+=1
if ct>maxtime:
ct += 1
if ct > maxtime:
print("after iteration for {} times, I still havn't reach the accurrency.\
Maybe this function havsn't zeropoint\n".format(ct))
return li ,val
if abs(x-x0)<epsilon:return li,vals
return li, val
if abs(x-x0) < epsilon:
return li, vals
x0 = x
def secant(y:sympy.core,x0:float,x1:float,epsilon:float =0.00001,maxtime:int=50) ->(list,list):
def secant(y: sympy.core, x0: float, x1: float, epsilon: float = 0.00001, maxtime: int = 50) ->(list, list):
'''
弦截法, 使用newton 差商计算,每次只需计算一次f(x)
secant method for finding a zeropoint of a func
y is the func , x0 is the init x val, epsilon is the accurrency
'''
if epsilon <0:epsilon = -epsilon
ct =0
x0,x1 = float(x0),float(x1)
li = [x0,x1]
t = y.free_symbols
varsymbol = 'x' if len(t)==0 else t.pop()
last = y.subs(varsymbol,x0)
if epsilon < 0:
epsilon = -epsilon
ct = 0
x0, x1 = float(x0), float(x1)
li = [x0, x1]
t = y.free_symbols
varsymbol = 'x' if len(t) == 0 else t.pop()
last = y.subs(varsymbol, x0)
vals = [last]
while 1:
cur = y.subs(varsymbol,x1)
cur = y.subs(varsymbol, x1)
vals.append(cur)
x = x1-cur*(x1-x0)/(cur-last)
x0 ,x1= x1,x
x0, x1 = x1, x
last = cur
li.append(x)
ct+=1
if ct>maxtime:
ct += 1
if ct > maxtime:
print("after iteration for {} times, I still havn't reach the accurrency.\
Maybe this function havsn't zeropoint\n".format(ct))
return li,vals
if abs(x0-x1)<epsilon:return li,vals
return li, vals
if abs(x0-x1) < epsilon:
return li, vals
x0 = x
def solveNonlinearEquations(funcs:[sympy.core],init_dic:dict,epsilon:float=0.001,maxtime:int=50)->dict:
def solveNonlinearEquations(funcs: [sympy.core], init_dic: dict, epsilon: float = 0.001, maxtime: int = 50)->dict:
'''solve nonlinear equations:'''
li = list(init_dic.keys())
delta = {i:0 for i in li}
delta = {i: 0 for i in li}
ct = 0
while 1:
ys = np.array([f.subs(init_dic) for f in funcs],dtype = 'float')
mat = np.matrix([[i.diff(x).subs(init_dic) for x in li] for i in funcs ],dtype = 'float')
delt = np.linalg.solve(mat,-ys)
for i,j in enumerate(delt):
init_dic[li[i]] +=j
ys = np.array([f.subs(init_dic) for f in funcs], dtype='float')
mat = np.matrix([[i.diff(x).subs(init_dic) for x in li]
for i in funcs], dtype='float')
delt = np.linalg.solve(mat, -ys)
for i, j in enumerate(delt):
init_dic[li[i]] += j
delta[li[i]] = j
if ct>maxtime:
if ct > maxtime:
print("after iteration for {} times, I still havn't reach the accurrency.\
Maybe this function havsn't zeropoint\n".format(ct))
return init_dic
if sqrt(sum(i**2 for i in delta.values()))<epsilon:return init_dic
if sqrt(sum(i**2 for i in delta.values())) < epsilon:
return init_dic
if __name__ =='__main__':
x,y,z = sympy.symbols('x y z')
res,res2= newton(x**5-9,2,0.01)
print(res,res2)
if __name__ == '__main__':
x, y, z = sympy.symbols('x y z')
res, res2 = newton(x**5-9, 2, 0.01)
print(res, res2)
res,res2 = secant (x**3-3*x-2,1,3,1e-3)
print(res,res2)
res, res2 = secant(x**3-3*x-2, 1, 3, 1e-3)
print(res, res2)
funcs=[x**2+y**2-1,x**3-y]
init = {x:0.8,y:0.6}
res_dic = solveNonlinearEquations(funcs,init,0.001)
funcs = [x**2+y**2-1, x**3-y]
init = {x: 0.8, y: 0.6}
res_dic = solveNonlinearEquations(funcs, init, 0.001)
print(res_dic)

75
math/numericalAnalysis/least_square.py
View File

@ -20,12 +20,11 @@
************************************************************************'''
import re
import numpy as np
def solveConflitEqualtion(A,y):
def solveConflitEqualtion(A, y):
'''solve equation like this: Av = y,
A:m*n v:n*1 y:m*1
return vector v
@ -35,43 +34,49 @@ def solveConflitEqualtion(A,y):
ata = A.T*A
print('AtA')
print(ata)
return np.linalg.solve(ata,A.T*y) # note that is numpy.linalg.solve
return np.linalg.solve(ata, A.T*y) # note that is numpy.linalg.solve
def solveLinear(point,index):
def solveLinear(point, index):
y = [[i[1]] for i in point]
x = [[i[0]] for i in point]
A = []
for i in x:
A.append([i[0]**j for j in index])
res = solveConflitEqualtion(A,y)
print('the solution is : \n',res)
res = solveConflitEqualtion(A, y)
print('the solution is : \n', res)
print('namely: ')
items = ['{:.4f}x^{}'.format(res[i,0],j) for i, j in enumerate(index)]
print('phi(x) = ',' + '.join(items))
items = ['{:.4f}x^{}'.format(res[i, 0], j) for i, j in enumerate(index)]
print('phi(x) = ', ' + '.join(items))
def handleInput(s=None,y=None):
def handleInput(s=None, y=None):
# numPt = re.compile (r'\d*\.{0,1}\d+')
if not s: s = input('input matrix A:m*n //m>=n\n')
s = s.replace(' ','')
li = re.findall(r'(\[(\d+)(,(\d+))+\])',s)
li = [parseLst(i[0]) for i in li]
if not y:y = input('input a vector y:n*1\n')
if not s:
s = input('input matrix A:m*n //m>=n\n')
s = s.replace(' ', '')
li = re.findall(r'(\[(\d+)(,(\d+))+\])', s)
li = [parseLst(i[0]) for i in li]
if not y:
y = input('input a vector y:n*1\n')
y = parseLst(y)
print('Equation: Av = y:')
print('y is as follows: ')
print(y)
print('A is as follows: ')
for i in li:
for j in i:
print('{}'.format(j).rjust(5),end='')
print('{}'.format(j).rjust(5), end='')
print('')
print('result v is as follows: ')
res = solveConflitEqualtion(li,y)
res = solveConflitEqualtion(li, y)
print(res)
def parseLst(s):
s = s.strip('[]')
s = s.strip('[]')
li = s.split(',')
li = [float(j) for j in li]
return li
@ -86,19 +91,19 @@ if __name__ == '__main__':
s = input('input y to continue, n for exit')
if s!='y':break
'''
point = [(-3,14.3),(-2,8.3),(-1,4.7),(2,-8.3),(4,-22.7)]
lst = [0,3]
solveLinear(point,lst)
point = [(-3, 14.3), (-2, 8.3), (-1, 4.7), (2, -8.3), (4, -22.7)]
lst = [0, 3]
solveLinear(point, lst)
point = [(-3, 14.3), (-2, 8.3), (-1, 4.7), (2, 8.3), (4, 22.7)]
lst = [0, 2]
solveLinear(point, lst)
A = [[1, 2], [2, 1], [1, 1]]
y = [[5], [6], [4]]
res = solveConflitEqualtion(A, y)
point= [(-3,14.3),(-2,8.3),(-1,4.7),(2,8.3),(4,22.7)]
lst = [0,2]
solveLinear(point,lst)
A = [[1,2],[2,1],[1,1]]
y = [[5],[6],[4]]
res = solveConflitEqualtion(A,y)
print(res)
A = [[1,-2],[1,5],[2,1],[1,1]]
y = [[1],[13.1],[7.9],[5.1]]
print(solveConflitEqualtion(A,y))
A = [[1, -2], [1, 5], [2, 1], [1, 1]]
y = [[1], [13.1], [7.9], [5.1]]
print(solveConflitEqualtion(A, y))

108
math/numericalAnalysis/linear_equation.py
View File

@ -19,86 +19,105 @@
> Created Time: 2018-04-20 08:32
************************************************************************'''
import numpy as np
def getLU(A):
'''doolittle : A = LU,
L is in down-triangle form,
U is in up-triangle form
'''
m,n = A.shape
if m!=n:raise Exception("this matrix is not inversable")
m, n = A.shape
if m != n:
raise Exception("this matrix is not inversable")
L = np.zeros([m,m])
U = np.zeros([m,m])
L = np.zeros([m, m])
U = np.zeros([m, m])
L = np.matrix(L)
U = np. matrix(U)
U[0] = A[0]
L[:,0] = A[:,0] / A[0,0]
for i in range(1,m):
for j in range(i,m):
U[i,j]= A[i,j] - sum(L[i,k]*U[k,j] for k in range(i))
L[j,i] = (A[j,i] - sum(L[j,k]*U[k,i] for k in range(i)))/U[i,i]
L[:, 0] = A[:, 0] / A[0, 0]
for i in range(1, m):
for j in range(i, m):
U[i, j] = A[i, j] - sum(L[i, k]*U[k, j] for k in range(i))
L[j, i] = (A[j, i] - sum(L[j, k]*U[k, i]
for k in range(i)))/U[i, i]
print(L)
print(U)
return L,U
return L, U
def gauss_prior_elimination(A):
'''using guass elimination,get up_trianglge form of A'''
m,n = A.shape
if m!=n:raise Exception("[Error]: matrix is not inversable")
B = np.matrix(A,dtype=float) # necessary,otherwise when the dtype of A is int, then it will be wrong
for i in range(m-1):
col = abs(B[i:,i]) # note using abs value, return a matrix in (m-i)x1 form
m, n = A.shape
if m != n:
raise Exception("[Error]: matrix is not inversable")
# necessary,otherwise when the dtype of A is int, then it will be wrong
B = np.matrix(A, dtype=float)
for i in range(m-1):
# note using abs value, return a matrix in (m-i)x1 form
col = abs(B[i:, i])
mx = col.max()
if mx==0: raise Exception("[Error]: matrix is not inversable")
if mx == 0:
raise Exception("[Error]: matrix is not inversable")
pos = i+col.argmax()
if pos != i : B[[pos,i],:] = B[[i,pos],:] # note how to swap cols/rows
B[i,:] = 1/mx*B[i,:]
for j in range(i+1,m):
#print(B)
B[j,:] -= B[j,i] * B[i,:]
if pos != i:
B[[pos, i], :] = B[[i, pos], :] # note how to swap cols/rows
B[i, :] = 1/mx*B[i, :]
for j in range(i+1, m):
# print(B)
B[j, :] -= B[j, i] * B[i, :]
print(B)
return B
def solveDown(A,b):
def solveDown(A, b):
'''A is a matrix in down-triangle form'''
sol = np.zeros(b.shape)
for i in range(b.shape[0]):
sol[i,0] = (b[i,0]-sum(A[i,j]*sol[j,0] for j in range(i)))/A[i,i]
sol[i, 0] = (b[i, 0]-sum(A[i, j]*sol[j, 0] for j in range(i)))/A[i, i]
return sol
def solveUp(A,b):
def solveUp(A, b):
'''A is a matrix in up-triangle form'''
sol = np.zeros(b.shape)
n = b.shape[0]
for i in range(n-1,-1,-1):
sol[i,0] = (b[i,0]-sum(A[i,j]*sol[j,0] for j in range(n-1,i,-1)))/A[i,i]
for i in range(n-1, -1, -1):
sol[i, 0] = (b[i, 0]-sum(A[i, j]*sol[j, 0]
for j in range(n-1, i, -1)))/A[i, i]
return sol
def doolittle(A,b):
L,U = getLU(A)
y = solveDown(L,b)
x = solveUp(U,y)
def doolittle(A, b):
L, U = getLU(A)
y = solveDown(L, b)
x = solveUp(U, y)
print(y)
print(x)
return x
def ldlt(A,b):
L,U = getLU(A)
def ldlt(A, b):
L, U = getLU(A)
D = np.diag(np.diag(U))
print(D,"D")
z = np.linalg.solve(L,b)
print(z,"z")
y = np.linalg.solve(D,z)
print(y,"y")
x = np.linalg.solve(L.T,y)
print(x,"x")
print(D, "D")
z = np.linalg.solve(L, b)
print(z, "z")
y = np.linalg.solve(D, z)
print(y, "y")
x = np.linalg.solve(L.T, y)
print(x, "x")
return x
if __name__ == '__main__':
A = np.matrix([[10,5,0,0],
[2,2,1,0],
[0,10,0,5],
[0,0,2,1]])
b = np.matrix([[5],[3],[27],[6]])
A = np.matrix([[10, 5, 0, 0],
[2, 2, 1, 0],
[0, 10, 0, 5],
[0, 0, 2, 1]])
b = np.matrix([[5], [3], [27], [6]])
gauss_prior_elimination(A)
'''ldlt
@ -115,4 +134,3 @@ if __name__ == '__main__':
b = np.matrix([[4],[6],[5]])
doolittle(A,b)
'''

13
math/numericalAnalysis/numerical_differential.py
View File

@ -1,13 +0,0 @@
''' mbinary
#########################################################################
# File : numerical_differential.py
# Author: mbinary
# Mail: zhuheqin1@gmail.com
# Blog: https://mbinary.xyz
# Github: https://github.com/mbinary
# Created Time: 2018-10-02 21:14
# Description:
#########################################################################
'''

47
math/numericalAnalysis/numerical_integration.py
View File

@ -18,53 +18,56 @@
# Blog: https://mbinary.xyz
# Github: https://github.com/mbinary
# Created Time: 2018-05-11 08:58
# Description:
# Description:
# numerical intergration: using Newton-Cotes integration, and Simpson
# 数值积分, 使用 牛顿-科特斯积分, 辛普森
#########################################################################
import numpy as np
def trapezoidal(a,b,h,fs):
def trapezoidal(a, b, h, fs):
'''梯形积分公式'''
xs = [i for i in np.arange(a,b+h,h)]
xs = [i for i in np.arange(a, b+h, h)]
print(xs)
ret = h*(sum(fs)-fs[0]/2 - fs[-1]/2)
print(ret)
return ret
def simpson(a,b,h,fs):
def simpson(a, b, h, fs):
'''辛普森积分公式'''
xs = [i for i in np.arange(a,b+h,h)]
xs = [i for i in np.arange(a, b+h, h)]
print(xs)
ret = h/3*(4* sum(fs[1::2])+ 2*sum(fs[2:-1:2]) + fs[0]+fs[-1])
ret = h/3*(4 * sum(fs[1::2]) + 2*sum(fs[2:-1:2]) + fs[0]+fs[-1])
print(ret)
return ret
def romberg(a,b,f,epcilon):
def romberg(a, b, f, epcilon):
'''romberg(龙贝格) 数值积分'''
h = b-a
lst1=[h*(f(a)+f(b))/2]
lst1 = [h*(f(a)+f(b))/2]
print(lst1)
delta = epcilon
k=1
k = 1
while delta >= epcilon:
h/=2
k+=1
lst2=[]
lst2.append((lst1[0]+h*2*sum(f(a+(2*i-1)*h) for i in range(1,2**(k-2)+1)))/2)
for j in range(0,k-1):
h /= 2
k += 1
lst2 = []
lst2.append((lst1[0]+h*2*sum(f(a+(2*i-1)*h)
for i in range(1, 2**(k-2)+1)))/2)
for j in range(0, k-1):
lst2.append(lst2[j]+(lst2[j]-lst1[j])/(4**(j+1)-1))
delta = abs(lst2[-1]-lst1[-1])
lst1=lst2
lst1 = lst2
print(lst1)
if __name__=='__main__':
a,b,h = 0.6,1.8,0.2
fs=[5.7,4.6,3.5,3.7,4.9,5.2,5.5]
trapezoidal(a,b,h,fs)
simpson(a,b,h,fs)
romberg(1,2,lambda x:sin(x**4),1e-4)
if __name__ == '__main__':
a, b, h = 0.6, 1.8, 0.2
fs = [5.7, 4.6, 3.5, 3.7, 4.9, 5.2, 5.5]
trapezoidal(a, b, h, fs)
simpson(a, b, h, fs)
romberg(1, 2, lambda x: sin(x**4), 1e-4)

133
math/numericalAnalysis/solve-linear-by-iteration.py
View File

@ -21,46 +21,59 @@
# Description:
#########################################################################
'''
import numpy as np
from operator import le,lt
def jacob(A,b,x,accuracy=None,times=6):
import numpy as np
from operator import le, lt
def jacob(A, b, x, accuracy=None, times=6):
''' Ax=b, arg x is the init val, times is the time of iterating'''
A,b,x = np.matrix(A),np.matrix(b),np.matrix(x)
n,m = A.shape
if n!=m:raise Exception("Not square matrix: {A}".format(A=A))
if b.shape !=( n,1) : raise Exception('Error: {b} must be {n} x1 in dimension'.format(b = b,n=n))
A, b, x = np.matrix(A), np.matrix(b), np.matrix(x)
n, m = A.shape
if n != m:
raise Exception("Not square matrix: {A}".format(A=A))
if b.shape != (n, 1):
raise Exception(
'Error: {b} must be {n} x1 in dimension'.format(b=b, n=n))
D = np.diag(np.diag(A))
DI = np.zeros([n,n])
for i in range(n):DI[i,i]= 1/D[i,i]
DI = np.zeros([n, n])
for i in range(n):
DI[i, i] = 1/D[i, i]
R = np.eye(n) - DI * A
g = DI * b
print('R =\n{}'.format(R))
print('g =\n{}'.format(g))
last = -x
if accuracy != None:
ct=0
ct = 0
while 1:
ct+=1
ct += 1
tmp = x-last
last = x
mx = max ( abs(i) for i in tmp)
if mx<accuracy:return x
mx = max(abs(i) for i in tmp)
if mx < accuracy:
return x
x = R*x+g
print('x{ct} =\n{x}'.format(ct = ct,x=x))
print('x{ct} =\n{x}'.format(ct=ct, x=x))
else:
for i in range(times):
x = R*x+g
print('x{ct} = \n{x}'.format(ct=i+1,x=x))
print('x{ct} = \n{x}'.format(ct=i+1, x=x))
print('isLimitd: {}'.format(isLimited(A)))
return x
def gauss_seidel(A,b,x,accuracy=None,times=6):
def gauss_seidel(A, b, x, accuracy=None, times=6):
''' Ax=b, arg x is the init val, times is the time of iterating'''
A,b,x = np.matrix(A),np.matrix(b),np.matrix(x)
n,m = A.shape
if n!=m:raise Exception("Not square matrix: {A}".format(A=A))
if b.shape !=( n,1) : raise Exception('Error: {b} must be {n} x1 in dimension'.format(b = b,n=n))
D =np. matrix(np.diag(np.diag(A)))
A, b, x = np.matrix(A), np.matrix(b), np.matrix(x)
n, m = A.shape
if n != m:
raise Exception("Not square matrix: {A}".format(A=A))
if b.shape != (n, 1):
raise Exception(
'Error: {b} must be {n} x1 in dimension'.format(b=b, n=n))
D = np. matrix(np.diag(np.diag(A)))
L = np.tril(A) - D # L = np.triu(D.T) - D
U = np.triu(A) - D
DLI = (D+L).I
@ -70,61 +83,69 @@ def gauss_seidel(A,b,x,accuracy=None,times=6):
print('f =\n{}'.format(f))
last = -x
if accuracy != None:
ct=0
ct = 0
while 1:
ct+=1
ct += 1
tmp = x-last
last = x
mx = max ( abs(i) for i in tmp)
if mx<accuracy:return x
mx = max(abs(i) for i in tmp)
if mx < accuracy:
return x
x = S*x+f
print('x{ct} =\n{x}'.format(ct=ct,x=x))
print('x{ct} =\n{x}'.format(ct=ct, x=x))
else:
for i in range(times):
x = S*x+f
print('x{ct} = \n{x}'.format(ct=i+1,x=x))
print('x{ct} = \n{x}'.format(ct=i+1, x=x))
print('isLimitd: {}'.format(isLimited(A)))
return x
def isLimited(A,strict=False):
def isLimited(A, strict=False):
'''通过检查A是否是[严格]对角优来判断迭代是否收敛, 即对角线上的值是否都大于对应行(或者列)的值'''
diag = np.diag(A)
op = lt if strict else le
if op(A.max(axis=0),diag).all(): return True
if op(A.max(axis=1), diag).all(): return True
if op(A.max(axis=0), diag).all():
return True
if op(A.max(axis=1), diag).all():
return True
return False
testcase=[]
testcase = []
def test():
for func,A,b,x,*args in testcase:
acc =None
for func, A, b, x, *args in testcase:
acc = None
times = 6
if args !=[] :
if isinstance(args[0],int):times = args[0]
else : acc = args[0]
return func(A,b,x,acc,times)
if args != []:
if isinstance(args[0], int):
times = args[0]
else:
acc = args[0]
return func(A, b, x, acc, times)
if __name__ =='__main__':
A = [[2,-1,-1],
[1,5,-1],
[1,1,10]
]
b = [[-5],[8],[11]]
x = [[1],[1],[1]]
#testcase.append([gauss_seidel,A,b,x])
if __name__ == '__main__':
A = [[2, -1, -1],
[1, 5, -1],
[1, 1, 10]
]
b = [[-5], [8], [11]]
x = [[1], [1], [1]]
# testcase.append([gauss_seidel,A,b,x])
A = [[2,-1,1],[3,3,9],[3,3,5]]
b = [[-1],[0],[4]]
x = [[0],[0],[0]]
#testcase.append([jacob,A,b,x])
A = [[2, -1, 1], [3, 3, 9], [3, 3, 5]]
b = [[-1], [0], [4]]
x = [[0], [0], [0]]
# testcase.append([jacob,A,b,x])
A = [[5,-1,-1],
[3,6,2],
[1,-1,2]
]
b= [[16],[11],[-2]]
x = [[1],[1],[-1]]
testcase.append([gauss_seidel,A,b,x,0.001])
A = [[5, -1, -1],
[3, 6, 2],
[1, -1, 2]
]
b = [[16], [11], [-2]]
x = [[1], [1], [-1]]
testcase.append([gauss_seidel, A, b, x, 0.001])
test()

112
math/numericalAnalysis/vector_norm.py
View File

@ -10,35 +10,43 @@
#########################################################################
'''
from random import randint,random
from random import randint, random
import numpy as np
from operator import neg,and_
from operator import neg, and_
from functools import reduce
class obj():
def __init__(self,data):
self.data=np.array(data)
def __add__(self,x):
data = x.data if self.__class__ == x.__class__ else x
class obj():
def __init__(self, data):
self.data = np.array(data)
def __add__(self, x):
data = x.data if self.__class__ == x.__class__ else x
return self.__class__(self.data + data)
def __radd__(self,x):
data = x.data if self.__class__ == x.__class__ else x
return self.__class__(data +self.data)
def __iadd__(self,x):
data = x.data if self.__class__ == x.__class__ else x
def __radd__(self, x):
data = x.data if self.__class__ == x.__class__ else x
return self.__class__(data + self.data)
def __iadd__(self, x):
data = x.data if self.__class__ == x.__class__ else x
self.data += data
def __mul__(self,x):
data = x.data if self.__class__ == x.__class__ else x
def __mul__(self, x):
data = x.data if self.__class__ == x.__class__ else x
return self.__class__(self.data * data)
def __imul__(self,x):
data = x.data if self.__class__ == x.__class__ else x
def __imul__(self, x):
data = x.data if self.__class__ == x.__class__ else x
self.data *= data
def __rmul__(self,x):
data = x.data if self.__class__ == x.__class__ else x
def __rmul__(self, x):
data = x.data if self.__class__ == x.__class__ else x
return self.__class__(data * self.data)
def __neg__(self):
return neg(self)
def __abs__(self):
return abs(self.data)
'''
@ -49,42 +57,49 @@ class obj():
def data(self,s):
self.data = s
'''
def norm(self,n=0):
def norm(self, n=0):
'''the default is +oo norm'''
absolute = abs(self.data)
if n < 1 :return max(absolute)
if n < 1:
return max(absolute)
return (sum(absolute**n))**(1/n)
def hasNorm(self):
'''check norm's three necessary conditions:
1. not neg
2. homogenious (qici)
3. triangle inequlity
there is much probably wrong
'''
bl = reduce(and_,[self.norm(i)>=0 for i in range(3)])
bl = reduce(and_, [self.norm(i) >= 0 for i in range(3)])
if bl:
n = randint(2,100)
bl = reduce(and_,[n*(self.norm(i))==(n*self).norm(i) for i in range(3)])
n = randint(2, 100)
bl = reduce(and_, [n*(self.norm(i)) == (n*self).norm(i)
for i in range(3)])
if bl:
another = self*randint(2,10)-randint(1,100)
return reduce(and_,[(another+self).norm(i)<=another.norm(i)+self.norm(i) for i in range(3)])
another = self*randint(2, 10)-randint(1, 100)
return reduce(and_, [(another+self).norm(i) <= another.norm(i)+self.norm(i) for i in range(3)])
return False
class vector(obj):
def __init__(self,arr):
def __init__(self, arr):
''' arr: iterable'''
self.data =np.array(arr)
def innerProduct(self,x):
self.data = np.array(arr)
def innerProduct(self, x):
return sum(self.data*x)
def outerProduct(self,x):
def outerProduct(self, x):
pass
class matrix(obj):
def __init__(self,s):
def __init__(self, s):
'''s is a list of lists'''
self.data=np.mat(s)
self.data = np.mat(s)
self.T = None
self. I = None
'''
@ -104,31 +119,38 @@ class matrix(obj):
def I(self,s):
self.I = s
'''
def E(self,n=None):
if n is None: n = self.data.shape[0]
def E(self, n=None):
if n is None:
n = self.data.shape[0]
return np.eye(n)
def norm(self,n=0):
absolute = abs(self.data)
def norm(self, n=0):
absolute = abs(self.data)
if n < 1:
# max of one row sum
return max([sum(i) for i in absolute])
if n==1:return self.norm1()
elif n==2:return self.norm2()
if n == 1:
return self.norm1()
elif n == 2:
return self.norm2()
def norm1(self):
''' max of sum of cols'''
absolute = abs(self.data)
return max(absolute.sum(axis=0))
return max(absolute.sum(axis=0))
def norm2(self):
''' max of sum of rows'''
absolute = abs(self.data)
return max(absolute.sum(axis=1))
def norm_f(self):
return sum((self.data**2).sum(axis=1))**0.5
if __name__ =='__main__':
v1 = vector([1,-2,3,4])
v2 = vector([0,2,0,5])
m1 = matrix([v1,v2,v2,v1])
if __name__ == '__main__':
v1 = vector([1, -2, 3, 4])
v2 = vector([0, 2, 0, 5])
m1 = matrix([v1, v2, v2, v1])
print([v1.norm(i) for i in range(3)])

56
math/permute/permute_cantor.c
View File

@ -12,56 +12,64 @@
#include<stdio.h>
//使用康托展开计算全排列, 下面存储的是0!,1!,2!...(n-1)!
long long int fac[100]={};
long long int fac[100] = {};
void calFac(int n)
{
int i;
fac[0]=1;
for(i=1;i<=n;i++){
fac[i]=i*fac[i-1];
fac[0] = 1;
for (i = 1; i <= n; i++) {
fac[i] = i * fac[i - 1];
}
}
void permute(int *arr,int n,int sum)
void permute(int *arr, int n, int sum)
{
/*sum表示全排列由小到大排序后的名次,从0 开始计数, 由名次求出 n位的排列存储到 arr 中*/
int i,j,ct=0,k, ct2;
int i, j, ct = 0, k, ct2;
int flag[n];
for(i=0;i<n;i++)flag[i]=1;
for(i=n-1;i>=0;i--){
for(j=i;j>=0;j--){
if(j*fac[i]<=sum){
ct2=0;
for(k=0;k<n;++k){
for (i = 0; i < n; i++)flag[i] = 1;
for (i = n - 1; i >= 0; i--) {
for (j = i; j >= 0; j--) {
if (j * fac[i] <= sum) {
ct2 = 0;
for (k = 0; k < n; ++k) {
//printf("i%d j%d k%d\n",i,j,k);
if(flag[k]==1)ct2++;
if(ct2>j)break;
if (flag[k] == 1)ct2++;
if (ct2 > j)break;
}
arr[ct++] = k;
flag[k]=0;
sum -=j*fac[i];
flag[k] = 0;
sum -= j * fac[i];
break;
}
}
}
}
void printArr(int *p,int n)
void printArr(int *p, int n)
{
for(int i=0;i<n;++i)printf("%d, ",p[i]);
for (int i = 0; i < n; ++i)printf("%d, ", p[i]);
printf("\n");
}
int main()
{
int n = 5,arr[n];
int n = 5, arr[n];
calFac(n);
for(int i=0;i<5;++i)arr[i]=i;
for(int i=0;i<fac[n];++i){
printArr(arr,n);
permute(arr,n,i);
for (int i = 0; i < 5; ++i)arr[i] = i;
for (int i = 0; i < fac[n]; ++i) {
printArr(arr, n);
permute(arr, n, i);
}
return 0;
}

125
search/8Astar.py → search/Astar.py
View File

@ -1,6 +1,6 @@
''' mbinary
#########################################################################
# File : 8Astar.py
# File : Astar.py
# Author: mbinary
# Mail: zhuheqin1@gmail.com
# Blog: https://mbinary.xyz
@ -10,53 +10,62 @@
#########################################################################
'''
isVisited = [0]*362880 # 0 for not visited,1 for occured,2 for visited
fac = [1,1,2,6,24,120,720,5040,40320]
from random import shuffle
isVisited = [0]*362880 # 0 for not visited,1 for occured,2 for visited
fac = [1, 1, 2, 6, 24, 120, 720, 5040, 40320]
lf = len(fac)
h = [[0,1,2,1,2,3,2,3,4],
[1,0,1,2,1,2,3,2,3],
[2,1,0,3,2,1,4,3,2],
[1,2,3,0,1,2,1,2,3],
[2,1,2,1,0,1,2,1,2],
[3,2,1,2,1,0,3,2,1],
[2,3,4,1,2,3,0,1,2],
[3,2,3,2,1,2,1,0,1],
[4,3,2,3,2,1,2,1,0]]
h = [[0, 1, 2, 1, 2, 3, 2, 3, 4],
[1, 0, 1, 2, 1, 2, 3, 2, 3],
[2, 1, 0, 3, 2, 1, 4, 3, 2],
[1, 2, 3, 0, 1, 2, 1, 2, 3],
[2, 1, 2, 1, 0, 1, 2, 1, 2],
[3, 2, 1, 2, 1, 0, 3, 2, 1],
[2, 3, 4, 1, 2, 3, 0, 1, 2],
[3, 2, 3, 2, 1, 2, 1, 0, 1],
[4, 3, 2, 3, 2, 1, 2, 1, 0]]
def cantor(s):
sum = 0
ls = len(s)
for i in range(ls):
count = 0
for j in range(i+1,ls):
if s[i] > s[j]: count +=1
for j in range(i+1, ls):
if s[i] > s[j]:
count += 1
sum += count*fac[lf-i-1]
return sum
que = []
dir = {-3:'u',1:'r',3:'d',-1:'l'}
dir = {-3: 'u', 1: 'r', 3: 'd', -1: 'l'}
class state:
flag = True
def __init__(self,s,x,f,step=0,last=0):
def __init__(self, s, x, f, step=0, last=0):
self.x = x
self.s = list(s)
self.step = step
self.path = []
self.last = last
self.f = f
def can(self):
cans = [-1,1,3,-3]
if self.last in cans :
cans = [-1, 1, 3, -3]
if self.last in cans:
cans.remove(-self.last)
if self.x<3:
if self.x < 3:
cans.remove(-3)
if self.x>5:
if self.x > 5:
cans.remove(3)
if self.x%3 is 0:
if self.x % 3 is 0:
cans.remove(-1)
if self.x%3 is 2:
if self.x % 3 is 2:
cans.remove(1)
return cans
def move(self):
cans = self.can()
for i in cans:
@ -65,36 +74,46 @@ class state:
s[self.x] = s[tmp]
s[tmp] = '9'
ct = cantor(s)
if isVisited[ct] != 2 :
if isVisited[ct] != 2:
val = int(s[self.x])
f = h[8][tmp] +h[val-1][self.x]-h[8][self.x]-h[val-1][tmp]+self.step+1
new = state(s,tmp,f,self.step +1,i)
f = h[8][tmp] + h[val-1][self.x] - \
h[8][self.x]-h[val-1][tmp]+self.step+1
new = state(s, tmp, f, self.step + 1, i)
new.path = self.path + [dir[i]]
if isVisited[ct] == 1:
for i,node in enumerate(que):
for i, node in enumerate(que):
if mew.s == node.s:
del que[i]
break
else:isVisited[ct] = 1
else:
isVisited[ct] = 1
if que == []:
que.append(new)
continue
for i,node in enumerate(que):
if new.f<=node.f:
que.insert(i,new)
for i, node in enumerate(que):
if new.f <= node.f:
que.insert(i, new)
def solvable(s):
reverse = 0
for i in range(8):
if s[i] is '9':continue
for j in range(i+1,9):
if s[i]>s[j]:reverse +=1
if reverse % 2 is 0:return True
else:return False
def getPath(s,index):
if s[i] is '9':
continue
for j in range(i+1, 9):
if s[i] > s[j]:
reverse += 1
if reverse % 2 is 0:
return True
else:
return False
def getPath(s, index):
f = 0
for i,j in enumerate(s):
f+=h[int(j)-1][i]
que.append(state(s,index,f,0,0))
for i, j in enumerate(s):
f += h[int(j)-1][i]
que.append(state(s, index, f, 0, 0))
while que != []:
cur = que.pop(0)
ct = cantor(cur.s)
@ -102,28 +121,34 @@ def getPath(s,index):
if ct is 0:
return cur.path
cur.move()
def info():
print('input a 3x3 matrix in one line')
print('from left to right,from up to down')
print('from left to right,from up to down')
print('such as 56831247x represent matrix as follow')
print('5 6 8\n3 1 2\n4 7 x')
print('then, if it has, I will print the path of moving x to reach state as follows')
print('1 2 3\n4 5 6\n7 8 x')
print('print q to quit')
from random import shuffle
case = list('12345678x')
def genCase():
tmp = case.copy()
shuffle(tmp)
print(f'Using random data: {tmp}')
index = -1
for i,j in enumerate(tmp):
if j=='x':
for i, j in enumerate(tmp):
if j == 'x':
index = i
break
tmp[index] = '9'
return tmp,index
return tmp, index
def isValid(li):
for i in '123456789':
if not i in li:
@ -131,12 +156,13 @@ def isValid(li):
return False
return True
def run():
while 1:
print('\n\n'+'-'*10+'Game Begins'+ '-'*10)
print('\n\n'+'-'*10+'Game Begins' + '-'*10)
info()
s=input('input: ')
if s=='q' or s=='Q' or s=='quit':
s = input('input: ')
if s == 'q' or s == 'Q' or s == 'quit':
break
index = s.find('x')
li = list(s)
@ -145,8 +171,9 @@ def run():
if not isValid(li):
li, index = genCase()
if solvable(li):
print(''.join(getPath(li,index)))
else:print('unsolvable')
print(''.join(getPath(li, index)))
else:
print('unsolvable')
if __name__ == '__main__':

21
search/bloomFilter.py
View File

@ -13,22 +13,27 @@ from bitarray import bitarray
import mmh3
class bloomFilter(set):
def __init__(self,size,hash_count):
super(bloomFilter,self).__init__()
def __init__(self, size, hash_count):
super(bloomFilter, self).__init__()
self.bits = bitarray(size)
self.bits.setall(0)
self.size = size
self.hash_count = hash_count
def __len__(self):
return self.size
def __iter__(self):
return iter(self.bits)
def add(self,item):
def add(self, item):
for i in range(self.hash_count):
idx = mmh3.hash(item,i) % self.size
self.bits[idx]=1
idx = mmh3.hash(item, i) % self.size
self.bits[idx] = 1
return self
def __contains__(self,item):
idxs = [mmh3.hash(item,i)%self.size for i in range(self.hash_count)]
return all([self.bits[i]==1 for i in idxs])
def __contains__(self, item):
idxs = [mmh3.hash(item, i) % self.size for i in range(self.hash_count)]
return all([self.bits[i] == 1 for i in idxs])

102
search/schedule.py
View File

@ -15,89 +15,105 @@
设有n个任务由k个可并行工作的机器来完成，完成任务i需要时间为 。试设计一个算法找出完成这n个任务的最佳调度，使完成全部任务的时间最早。
'''
from time import time
from functools import total_ordering
@total_ordering
class record:
def __init__(self,nums=None):
def __init__(self, nums=None):
if nums is None:
nums=[]
self.nums=nums
nums = []
self.nums = nums
self.sum = sum(nums)
def append(self,x):
def append(self, x):
self.nums.append(x)
self.sum+=x
self.sum += x
def pop(self):
x = self.nums.pop()
self.sum-=x
self.sum -= x
return x
def __repr__(self):
return repr(self.nums)
def __lt__(self,r):
return self.sum<r.sum
def __eq__(self,r):
return self.sum==r.sum
def __lt__(self, r):
return self.sum < r.sum
def __eq__(self, r):
return self.sum == r.sum
def tolist(self):
return self.nums.copy()
def __hash__(self):
return self.sum
def schedule(works,k):
def backtrackSearch(i,lsts):
nonlocal best,rst
if i==n:
cost = max(r.sum for r in lsts )
if best>cost:
best= cost
def schedule(works, k):
def backtrackSearch(i, lsts):
nonlocal best, rst
if i == n:
cost = max(r.sum for r in lsts)
if best > cost:
best = cost
rst = [st.tolist() for st in lsts]
else:
for cur in set(lsts):
if best>cur.sum+works[i]:
if best > cur.sum+works[i]:
cur.append(works[i])
backtrackSearch(i+1,lsts)
backtrackSearch(i+1, lsts)
cur.pop()
def findInitial(i,lst):
def findInitial(i, lst):
nonlocal best
if i==n:
if i == n:
cost = max(lst)
if best>cost:best = cost
if best > cost:
best = cost
else:
mn = lst[0]
idx = 0
visited=set()
for j,cur in enumerate(lst):
visited = set()
for j, cur in enumerate(lst):
if cur not in visited:
visited.add(cur)
if mn>cur:
if mn > cur:
mn = cur
idx = j
lst[idx]+=works[i]
findInitial(i+1,lst)
lst[idx]-=works[i]
lst[idx] += works[i]
findInitial(i+1, lst)
lst[idx] -= works[i]
n = len(works)
print()
print('machine Num:',n)
print('works :',works)
rst = None
works.sort(reverse=True) # key step
print('machine Num:', n)
print('works :', works)
rst = None
works.sort(reverse=True) # key step
best = sum(works[:n-k+1])
t = time()
findInitial(0,[0]*k) # key step
findInitial(0, [0]*k) # key step
t1 = time()-t
print('init solution: {} cost time {:.6f}s'.format(best,t1))
print('init solution: {} cost time {:.6f}s'.format(best, t1))
t = time()
backtrackSearch(0,[record() for i in range(k)])
backtrackSearch(0, [record() for i in range(k)])
t2 = time()-t
print('final solution: {} cost time {:.6f}s'.format(best,t2))
print('schedule plan:',rst)
return best,rst
print('final solution: {} cost time {:.6f}s'.format(best, t2))
print('schedule plan:', rst)
return best, rst
if __name__=='__main__':
if __name__ == '__main__':
from random import randint
schedule([47,20,28,44,21,45,30,39,28,33],3)
schedule([98,84,50,23,32,99,22,76,72,61,81,39,76,54,37],5)
schedule([39,39,23,45,100,69,21,81,39,55,20,86,34,53,58,99,36,45,46],8)
schedule([47, 20, 28, 44, 21, 45, 30, 39, 28, 33], 3)
schedule([98, 84, 50, 23, 32, 99, 22, 76, 72, 61, 81, 39, 76, 54, 37], 5)
schedule([39, 39, 23, 45, 100, 69, 21, 81, 39, 55,
20, 86, 34, 53, 58, 99, 36, 45, 46], 8)
'''
machine Num: 19

36
search/work_dispatch.py
View File

@ -12,37 +12,39 @@
'''
设有n件工作要分配给n个人去完成，将工作i分配给第j个人所需费用为c_ij 。试设计一个算法，为每个人分配1件不同的工作，并使总费用达到最小。
'''
import random
def dispatch(mat):
'''mat: matrix of c_ij'''
def _util(i,arrange,cost):
def _util(i, arrange, cost):
''' for i-th work'''
nonlocal total,used,rst
if i==n:
total=cost
rst = arrange.copy() # copy is needed
nonlocal total, used, rst
if i == n:
total = cost
rst = arrange.copy() # copy is needed
else:
for j in range(n):
if not used[j] and( total is None or cost+mat[i][j]<total):
used[j]=True
if not used[j] and(total is None or cost+mat[i][j] < total):
used[j] = True
arrange[i] = j
_util(i+1,arrange,cost+mat[i][j])
used[j]=False
_util(i+1, arrange, cost+mat[i][j])
used[j] = False
total = None
rst = None
n = len(mat)
used = [False for i in range(n)]
_util(0,[-1]*n,0)
return total,rst
_util(0, [-1]*n, 0)
return total, rst
import random
if __name__=='__main__':
if __name__ == '__main__':
n = 10
mat = [[random.randint(1,100) for i in range(n)] for i in range(n)]
mat = [[random.randint(1, 100) for i in range(n)] for i in range(n)]
print('work matrix: c_ij: work_i and person_j')
for i in range(n):
print(mat[i])
print('result: ',end='')
print('result: ', end='')
print(dispatch(mat))

70
sort/binaryTree.py
View File

@ -12,57 +12,69 @@
from functools import total_ordering
@total_ordering
class node:
def __init__(self,val,left=None,right=None):
self.val=val
def __init__(self, val, left=None, right=None):
self.val = val
self.frequency = 1
self.left=left
self.right=right
def __lt__(self,x):
return self.val<x.val
def __eq__(self,x):
return self.val==x.val
self.left = left
self.right = right
def __lt__(self, x):
return self.val < x.val
def __eq__(self, x):
return self.val == x.val
def inc(self):
self.val+=1
self.val += 1
def dec(self):
self.val-=1
self.val -= 1
def incFreq(self):
self.frequency +=1
self.frequency += 1
def decFreq(self):
self.frequency -=1
self.frequency -= 1
class binaryTree:
def __init__(self,reverse = True):
def __init__(self, reverse=True):
self.reverse = reverse
self.data=None
def cmp(self,n1,n2):
ret=0
if n1 < n2: ret=-1
if n1 > n2: ret= 1
self.data = None
def cmp(self, n1, n2):
ret = 0
if n1 < n2:
ret = -1
if n1 > n2:
ret = 1
return ret * -1 if self.reverse else ret
def addNode(self,nd):
def _add(prt,chd):
if self.cmp(prt,chd)==0:
def addNode(self, nd):
def _add(prt, chd):
if self.cmp(prt, chd) == 0:
prt.incFreq()
return
if self.cmp(prt,chd)<0:
if self.cmp(prt, chd) < 0:
if not isinstance(nd,node):nd=node(nd)
if not self.root :
self.root=node(val)
if not isinstance(nd, node):
nd = node(nd)
if not self.root:
self.root = node(val)
else:
if self.root == val:
self.root.incfreq()
else:
cur = self.root
def build(self,lst):
def build(self, lst):
dic = {}
for i in lst:
if i in dic:
dic[i].incFreq()
else:
dic[i] = node(i)
self.data =list( dic.values())
self.data = list(dic.values())

62
sort/heapSort.py
View File

@ -11,62 +11,76 @@
'''
from functools import partial
class heap:
def __init__(self,lst,reverse = False):
self.data= heapify(lst,reverse)
self.cmp = partial(lambda i,j,r:cmp(self.data[i],self.data[j],r),r= reverse)
def __init__(self, lst, reverse=False):
self.data = heapify(lst, reverse)
self.cmp = partial(lambda i, j, r: cmp(
self.data[i], self.data[j], r), r=reverse)
def getTop(self):
return self.data[0]
def __getitem__(self,idx):
def __getitem__(self, idx):
return self.data[idx]
def __bool__(self):
return self.data != []
def popTop(self):
ret = self.data[0]
n = len(self.data)
cur = 1
while cur * 2<=n:
while cur * 2 <= n:
chd = cur-1
r_idx = cur*2
l_idx = r_idx-1
if r_idx==n:
if r_idx == n:
self.data[chd] = self.data[l_idx]
break
j = l_idx if self.cmp(l_idx,r_idx)<0 else r_idx
j = l_idx if self.cmp(l_idx, r_idx) < 0 else r_idx
self.data[chd] = self.data[j]
cur = j+1
self.data[cur-1] = self.data[-1]
self.data.pop()
return ret
def addNode(self,val):
def addNode(self, val):
self.data.append(val)
self.data = one_heapify(len(self.data)-1)
def cmp(n1,n2,reverse=False):
def cmp(n1, n2, reverse=False):
fac = -1 if reverse else 1
if n1 < n2: return -fac
elif n1 > n2: return fac
if n1 < n2:
return -fac
elif n1 > n2:
return fac
return 0
def heapify(lst,reverse = False):
def heapify(lst, reverse=False):
for i in range(len(lst)):
lst = one_heapify(lst,i,reverse)
lst = one_heapify(lst, i, reverse)
return lst
def one_heapify(lst,cur,reverse = False):
cur +=1
while cur>1:
def one_heapify(lst, cur, reverse=False):
cur += 1
while cur > 1:
chd = cur-1
prt = cur//2-1
if cmp(lst[prt],lst[chd],reverse)<0:
if cmp(lst[prt], lst[chd], reverse) < 0:
break
lst[prt],lst[chd] = lst[chd], lst[prt]
lst[prt], lst[chd] = lst[chd], lst[prt]
cur = prt+1
return lst
def heapSort(lst,reverse = False):
def heapSort(lst, reverse=False):
lst = lst.copy()
hp = heap(lst,reverse)
hp = heap(lst, reverse)
ret = []
while hp:
ret.append(hp.popTop())
@ -75,10 +89,10 @@ def heapSort(lst,reverse = False):
if __name__ == '__main__':
from random import randint
n = randint(10,20)
lst = [randint(0,100) for i in range(n)]
n = randint(10, 20)
lst = [randint(0, 100) for i in range(n)]
print('random : ', lst)
print('small-heap: ', heapify(lst))
print('big-heap : ', heapify(lst,True))
print('big-heap : ', heapify(lst, True))
print('ascend : ', heapSort(lst))
print('descend : ', heapSort(lst,True))
print('descend : ', heapSort(lst, True))

31
sort/quickSort.c
View File

@ -9,23 +9,28 @@
# Description:
#########################################################################
*/
int partition(int *arr,int i,int j)
int partition(int *arr, int i, int j)
{
int pivot = arr[j],p=i,q=j;
while(p<q){
while(p<q && arr[p]<=pivot)++p;
if(p<q)arr[q--]=arr[p];
while(p<q && arr[q]>pivot)--q;
if(p<q)arr[p++]=arr[q];
int pivot = arr[j], p = i, q = j;
while (p < q) {
while (p < q && arr[p] <= pivot)++p;
if (p < q)arr[q--] = arr[p];
while (p < q && arr[q] > pivot)--q;
if (p < q)arr[p++] = arr[q];
}
arr[p]=pivot;
arr[p] = pivot;
return p;
}
void quickSort(int *arr,int i,int j)
void quickSort(int *arr, int i, int j)
{
if(i<j){
int p = partition(arr,i,j);
quickSort(arr,i,p-1);
quickSort(arr,p+1,j);
if (i < j) {
int p = partition(arr, i, j);
quickSort(arr, i, p - 1);
quickSort(arr, p + 1, j);
}
}

18
sort/quickSort.py
View File

@ -11,6 +11,9 @@
'''
from time import time
def quickSort(lst):
'''A optimized version of Hoare partition'''
@ -31,7 +34,8 @@ def quickSort(lst):
return a
def _sort(a, b):
if a >= b: return
if a >= b:
return
mid = (a + b) // 2
# 三数取中值置于第一个作为 pivot
if (lst[a] < lst[mid]) ^ (lst[b] < lst[mid]):
@ -55,12 +59,14 @@ def quickSort2(lst):
for i in range(a, b):
if lst[i] <= pivot:
j += 1
if i != j: lst[i], lst[j] = lst[j], lst[i]
if i != j:
lst[i], lst[j] = lst[j], lst[i]
lst[j + 1], lst[b] = lst[b], lst[j + 1]
return j + 1
def _sort(a, b):
if a >= b: return
if a >= b:
return
mid = (a + b) // 2
# 三数取中值置于第一个作为 pivot
if (lst[a] < lst[mid]) ^ (lst[b] < lst[mid]):
@ -84,7 +90,8 @@ def quickSort3(lst):
for i in range(a, b):
if lst[i] <= pivot:
j += 1
if i != j: lst[i], lst[j] = lst[j], lst[i]
if i != j:
lst[i], lst[j] = lst[j], lst[i]
lst[j + 1], lst[b] = lst[b], lst[j + 1]
return j + 1
@ -104,9 +111,6 @@ def quickSort3(lst):
return lst
from time import time
def timer(func, lst, n=100):
t = time()
for i in range(n):

64
sort/radixSort.py
View File

@ -10,43 +10,47 @@
#########################################################################
'''
def radixSort(lst,radix=10):
ls = [[] for i in range(radix)]
mx = max(lst)
weight = 1
while mx >= weight:
for i in lst:
ls[(i // weight)%radix].append(i)
weight *= radix
lst = sum(ls,[])
ls = [[] for i in range(radix)]
return lst
def countSort(lst,mn,mx):
mark = [0]*(mx-mn+1)
for i in lst:
mark[i-mn]+=1
ret =[]
for n,i in enumerate(mark):
ret +=[n+mn]*i
return ret
from random import randint
from quickSort import quickSort
from time import time
from random import randint
def timer(funcs,span,num=1000000):
lst = [randint(0,span) for i in range(num)]
print('range({}), {} items'.format(span,num))
def radixSort(lst, radix=10):
ls = [[] for i in range(radix)]
mx = max(lst)
weight = 1
while mx >= weight:
for i in lst:
ls[(i // weight) % radix].append(i)
weight *= radix
lst = sum(ls, [])
ls = [[] for i in range(radix)]
return lst
def countSort(lst, mn, mx):
mark = [0]*(mx-mn+1)
for i in lst:
mark[i-mn] += 1
ret = []
for n, i in enumerate(mark):
ret += [n+mn]*i
return ret
def timer(funcs, span, num=1000000):
lst = [randint(0, span) for i in range(num)]
print('range({}), {} items'.format(span, num))
for func in funcs:
data = lst.copy()
t = time()
func(data)
t = time()-t
print('{}: {}s'.format(func.__name__,t))
print('{}: {}s'.format(func.__name__, t))
if __name__ == '__main__':
timer([quickSort,radixSort,sorted],1000000000000,1000)
timer([quickSort,radixSort,sorted],10000,100000)
lst = [randint(0,100) for i in range(1000)]
print(countSort(lst,0,100)==sorted(lst))
timer([quickSort, radixSort, sorted], 1000000000000, 1000)
timer([quickSort, radixSort, sorted], 10000, 100000)
lst = [randint(0, 100) for i in range(1000)]
print(countSort(lst, 0, 100) == sorted(lst))

58
sort/select.py
View File

@ -11,39 +11,47 @@
'''
from random import randint
def select(lst,i):
def select(lst, i):
lst = lst.copy()
def partition(a,b):
def partition(a, b):
pivot = lst[a]
while a<b:
while a<b and lst[b]>pivot: b-=1
if a<b:
while a < b:
while a < b and lst[b] > pivot:
b -= 1
if a < b:
lst[a] = lst[b]
a+=1
while a<b and lst[a]<pivot: a+=1
if a<b:
a += 1
while a < b and lst[a] < pivot:
a += 1
if a < b:
lst[b] = lst[a]
b-=1
lst[a]= pivot
b -= 1
lst[a] = pivot
return a
def _select(a,b):
if a>=b: return lst[a]
def _select(a, b):
if a >= b:
return lst[a]
# randomized select
n = randint(a,b)
lst[a],lst[n] = lst[n],lst[a]
pos = partition(a,b)
if pos>i:
return _select(a,pos-1)
elif pos<i:
return _select(pos+1,b)
else:return lst[pos]
return _select(0,len(lst)-1)
n = randint(a, b)
lst[a], lst[n] = lst[n], lst[a]
pos = partition(a, b)
if pos > i:
return _select(a, pos-1)
elif pos < i:
return _select(pos+1, b)
else:
return lst[pos]
return _select(0, len(lst)-1)
if __name__ =='__main__':
lst = [randint(0,1000) for i in range(100)]
if __name__ == '__main__':
lst = [randint(0, 1000) for i in range(100)]
st = sorted(lst)
for i in range(10):
n = randint(0,99)
print('select {}th: \nexpect: {}\ngot: {}'.format(n,st[n],select(lst,n)))
n = randint(0, 99)
print('select {}th: \nexpect: {}\ngot: {}'.format(
n, st[n], select(lst, n)))

18
sort/shellSort.py
View File

@ -10,26 +10,28 @@
#########################################################################
'''
def shellSort(s,gaps=None):
def shellSort(s, gaps=None):
if gaps is None:
gaps = [127,63,31,15,7,3,1]
gaps = [127, 63, 31, 15, 7, 3, 1]
n = len(s)
for gap in gaps:
for j in range(gap,n):
for j in range(gap, n):
cur = j
num = s[j]
while cur>=gap and num < s[cur-gap]:
while cur >= gap and num < s[cur-gap]:
s[cur] = s[cur-gap]
cur-=gap
cur -= gap
s[cur] = num
return s
if __name__=='__main__':
if __name__ == '__main__':
from random import randint
import sys
n = 20
if len(sys.argv)>1:
if len(sys.argv) > 1:
n = int(sys.argv[1])
nums = [randint(1,100) for i in range(n)]
nums = [randint(1, 100) for i in range(n)]
print(nums)
print(shellSort(nums))

59
string/KMP.py
View File

@ -11,48 +11,55 @@
#########################################################################
'''
def getPrefixFunc(s):
'''return the list of prefix function of s'''
length = 0
i = 1
n = len(s)
ret = [0]
while i<n:
if s[i]==s[length]:
length +=1
while i < n:
if s[i] == s[length]:
length += 1
ret.append(length)
i+=1
i += 1
else:
if length==0:
if length == 0:
ret.append(0)
i+=1
i += 1
else:
length = ret[length-1]
return ret
def findAll(s,p):
pre = getPrefixFunc(p)
i = j =0
n,m = len(s),len(p)
ret = []
while i<n:
if s[i]==p[j]:
i+=1
j+=1
if j==m:
ret.append(i-j)
j=pre[j-1]
else:
if j==0: i+=1
else: j = pre[j-1]
return ret
def randStr(n=3):
return [randint(ord('a'),ord('z')) for i in range(n)]
if __name__ =='__main__':
def findAll(s, p):
pre = getPrefixFunc(p)
i = j = 0
n, m = len(s), len(p)
ret = []
while i < n:
if s[i] == p[j]:
i += 1
j += 1
if j == m:
ret.append(i-j)
j = pre[j-1]
else:
if j == 0:
i += 1
else:
j = pre[j-1]
return ret
def randStr(n=3):
return [randint(ord('a'), ord('z')) for i in range(n)]
if __name__ == '__main__':
from random import randint
s = randStr(50)
p = randStr(1)
print(s)
print(p)
print(findAll(s,p))
print(findAll(s, p))

32
string/manacher.py
View File

@ -10,6 +10,7 @@
#########################################################################
'''
class Solution:
def longestPalindrome(self, s):
"""
@ -17,22 +18,23 @@ class Solution:
:rtype: str
"""
n = len(s)
s2='$#'+'#'.join(s)+'#@'
ct =[0]*(2*n+4)
mid=1
for cur in range(1,2*n+2):
if cur<mid+ct[mid]:
ct[cur] = min(ct[2*mid-cur],mid+ct[mid]-cur)
s2 = '$#'+'#'.join(s)+'#@'
ct = [0]*(2*n+4)
mid = 1
for cur in range(1, 2*n+2):
if cur < mid+ct[mid]:
ct[cur] = min(ct[2*mid-cur], mid+ct[mid]-cur)
else:
ct[cur]=1
while s2[cur-ct[cur]]==s2[cur+ct[cur]]:
ct[cur]+=1
if cur+ct[cur] > mid+ct[mid]:mid = cur
ct[cur] = 1
while s2[cur-ct[cur]] == s2[cur+ct[cur]]:
ct[cur] += 1
if cur+ct[cur] > mid+ct[mid]:
mid = cur
mx = max(ct)
idxs = [i for i,j in enumerate(ct) if j == mx]
idxs = [i for i, j in enumerate(ct) if j == mx]
p = idxs[0]
for i in idxs:
if s2[i]=='#':p = i
rst =s2[p-mx+1:p+mx].replace('#','')
return rst
if s2[i] == '#':
p = i
rst = s2[p-mx+1:p+mx].replace('#', '')
return rst

88
string/markov.py
View File

@ -15,44 +15,50 @@ import re
class markov:
def __init__(self,txt):
self.words= self.clean(txt)
self.dic = self.getDic(self.words)
def clean(self,text):
text = text.replace("\n", " ");
text = text.replace("\"", "");
# 保证每个标点符号都和前面的单词在一起
# 这样不会被剔除，保留在马尔可夫链中
punctuation = [',', '.', ';',':']
for symbol in punctuation:
text = text.replace(symbol, symbol+" ");
return re.split(' +',text)
def getDic(self,words):
dic = {}
end = len(words)
for i in range(1,end):
if words[i-1] not in dic:
dic[words[i-1]] = {words[i]:1}
elif words[i] not in dic[words[i-1]]:
dic[words[i-1]][words[i]] = 1
else: dic[words[i-1]][words[i]] +=1
return dic
def getSum(self,dic):
if '%size' not in dic:
dic['%size'] = sum(list(dic.values()))
return dic['%size']
def nextWord(self,word):
k = randint(1,self.getSum(self.dic[word]))
for i,j in self.dic[word].items():
k-=j
if k<=0:return i
def genSentence(self,begin = 'I',length = 30):
li = [begin]
nextWord= begin
for i in range(1,length):
nextWord= self.nextWord(nextWord)
li.append(nextWord)
return ' '.join(li)
def __init__(self, txt):
self.words = self.clean(txt)
self.dic = self.getDic(self.words)
def clean(self, text):
text = text.replace("\n", " ")
text = text.replace("\"", "")
# 保证每个标点符号都和前面的单词在一起
# 这样不会被剔除，保留在马尔可夫链中
punctuation = [',', '.', ';', ':']
for symbol in punctuation:
text = text.replace(symbol, symbol+" ")
return re.split(' +', text)
def getDic(self, words):
dic = {}
end = len(words)
for i in range(1, end):
if words[i-1] not in dic:
dic[words[i-1]] = {words[i]: 1}
elif words[i] not in dic[words[i-1]]:
dic[words[i-1]][words[i]] = 1
else:
dic[words[i-1]][words[i]] += 1
return dic
def getSum(self, dic):
if '%size' not in dic:
dic['%size'] = sum(list(dic.values()))
return dic['%size']
def nextWord(self, word):
k = randint(1, self.getSum(self.dic[word]))
for i, j in self.dic[word].items():
k -= j
if k <= 0:
return i
def genSentence(self, begin='I', length=30):
li = [begin]
nextWord = begin
for i in range(1, length):
nextWord = self.nextWord(nextWord)
li.append(nextWord)
return ' '.join(li)

45
string/min-window-substring.py
View File

@ -27,34 +27,37 @@ When the window is no longer valid, start expanding again using the right pointe
'''
from collections import defaultdict
class Solution:
def minWindow(self, s: str, t: str) -> str:
def expand(j,lacked,dic):
while j<n and lacked:
def expand(j, lacked, dic):
while j < n and lacked:
if s[j] in lacked:
lacked[s[j]]-=1
if lacked[s[j]]==0:
lacked[s[j]] -= 1
if lacked[s[j]] == 0:
del lacked[s[j]]
dic[s[j]]+=1
j+=1
dic[s[j]] += 1
j += 1
return j
def contract(left,right):
for i in range(left,right):
dic[s[i]]-=1
if dic[s[i]]==0:
def contract(left, right):
for i in range(left, right):
dic[s[i]] -= 1
if dic[s[i]] == 0:
del dic[s[i]]
if s[i] in chars and (s[i] not in dic or dic[s[i]]<chars[s[i]]):
return i+1,{s[i]:1}
n ,i, j= len(s),0,0
if s[i] in chars and (s[i] not in dic or dic[s[i]] < chars[s[i]]):
return i+1, {s[i]: 1}
n, i, j = len(s), 0, 0
ans = ''
dic,lacked = defaultdict(int), defaultdict(int)
dic, lacked = defaultdict(int), defaultdict(int)
for c in t:
lacked[c]+=1
lacked[c] += 1
chars = lacked.copy()
while j<n and lacked:
j = expand(j,lacked,dic)
if not lacked:
i,lacked=contract(i,j)
if ans=='' or len(ans)>j-i+1:
while j < n and lacked:
j = expand(j, lacked, dic)
if not lacked:
i, lacked = contract(i, j)
if ans == '' or len(ans) > j-i+1:
ans = s[i-1:j]
return ans
return ans

54
string/rabin_karp.py
View File

@ -11,50 +11,62 @@
#########################################################################
'''
def isPrime(x):
for i in range(2,int(x**0.5)+1):
if x%i==0:return False
for i in range(2, int(x**0.5)+1):
if x % i == 0:
return False
return True
def getPrime(x):
'''return a prime which is bigger than x'''
for i in range(x,2*x):
if isPrime(i):return i
def findAll(s,p):
for i in range(x, 2*x):
if isPrime(i):
return i
def findAll(s, p):
'''s: string p: pattern'''
dic={}
n,m = len(s),len(p)
d=0 #radix
dic = {}
n, m = len(s), len(p)
d = 0 # radix
for c in s:
if c not in dic:
dic[c]=d
d+=1
dic[c] = d
d += 1
sm = 0
for c in p:
if c not in dic:return []
if c not in dic:
return []
sm = sm*d+dic[c]
ret = []
cur = 0
for i in range(m): cur=cur*d + dic[s[i]]
if cur==sm:ret.append(0)
for i in range(m):
cur = cur*d + dic[s[i]]
if cur == sm:
ret.append(0)
tmp = n-m
q = getPrime(m)
cur = cur%q
sm = sm%q
cur = cur % q
sm = sm % q
exp = d**(m-1) % q
for i in range(m,n):
for i in range(m, n):
cur = ((cur-dic[s[i-m]]*exp)*d+dic[s[i]]) % q
if cur == sm and p==s[i-m+1:i+1]:
if cur == sm and p == s[i-m+1:i+1]:
ret.append(i-m+1)
return ret
def randStr(n=3):
return [randint(ord('a'),ord('z')) for i in range(n)]
if __name__ =='__main__':
def randStr(n=3):
return [randint(ord('a'), ord('z')) for i in range(n)]
if __name__ == '__main__':
from random import randint
s = randStr(50)
p = randStr(1)
print(s)
print(p)
print(findAll(s,p))
print(findAll(s, p))

103
string/rotate.py
View File

@ -17,77 +17,80 @@
#########################################################################
'''
def rotate(s,k,right=False):
def reverse(a,b):
while a<b:
s[a],s[b]=s[b],s[a]
a+=1
b-=1
n=len(s)
k = k%n if not right else n-k%n
reverse(0,k-1)
reverse(k,n-1)
reverse(0,n-1)
def rotate(s, k, right=False):
def reverse(a, b):
while a < b:
s[a], s[b] = s[b], s[a]
a += 1
b -= 1
n = len(s)
k = k % n if not right else n-k % n
reverse(0, k-1)
reverse(k, n-1)
reverse(0, n-1)
return s
def rotate2(s,k,right=False):
def swap(a,b,c):
def rotate2(s, k, right=False):
def swap(a, b, c):
for i in range(c):
s[a+i],s[b+i] = s[b+i],s[a+i]
def _rot(pl,pr):
s[a+i], s[b+i] = s[b+i], s[a+i]
def _rot(pl, pr):
''' swap s[pl,pr) , s[pr:]'''
if pr==n:return
if pr-pl<=n-pr:
swap(pl,pr,pr-pl)
_rot(pr,2*pr-pl)
if pr == n:
return
if pr-pl <= n-pr:
swap(pl, pr, pr-pl)
_rot(pr, 2*pr-pl)
else:
swap(pl,pr,n-pr)
_rot(n-pr+pl,pr)
n=len(s)
k = k%n if not right else n-k%n
_rot(0,k)
swap(pl, pr, n-pr)
_rot(n-pr+pl, pr)
n = len(s)
k = k % n if not right else n-k % n
_rot(0, k)
return s
def rotate3(s, k, right=False):
def gcd(a, b):
if b == 0:
return a
return gcd(b, a % b)
def rotate3(s,k,right=False):
def gcd(a,b):
if b==0:return a
return gcd(b,a%b)
n=len(s)
k = k%n if not right else n-k%n
r=gcd(n,k)
n = len(s)
k = k % n if not right else n-k % n
r = gcd(n, k)
for i in range(r):
tmp = s[i]
j = (i+k)%n
while j!=i:
j = (i+k) % n
while j != i:
s[j-k] = s[j]
j = (j+k)%n
s[(j-k+n)%n] = tmp
j = (j+k) % n
s[(j-k+n) % n] = tmp
return s
def test():
def f(func,*args,right=False):
print(' '.join(['testing:',func.__name__,str(args),'right=',str(right)]))
rst = func(*args,right=right)
print('result',rst)
def f(func, *args, right=False):
print(' '.join(['testing:', func.__name__,
str(args), 'right=', str(right)]))
rst = func(*args, right=right)
print('result', rst)
print()
return f
if __name__=='__main__':
s=[i for i in range(10)]
tester= test()
tester(rotate,s,4,right=True)
tester(rotate,s,4)
tester(rotate2,s,2,right=True)
tester(rotate2,s,2)
tester(rotate3,s,132,right=True)
tester(rotate3,s,132)
if __name__ == '__main__':
s = [i for i in range(10)]
tester = test()
tester(rotate, s, 4, right=True)
tester(rotate, s, 4)
tester(rotate2, s, 2, right=True)
tester(rotate2, s, 2)
tester(rotate3, s, 132, right=True)
tester(rotate3, s, 132)
'''

52
string/sunday.py
View File

@ -12,66 +12,74 @@
'''
def getPos(pattern):
dic = {}
for i,j in enumerate(pattern[::-1]):
for i, j in enumerate(pattern[::-1]):
if j not in dic:
dic[j]= i
dic[j] = i
return dic
def find(s,p):
def find(s, p):
dic = getPos(p)
ps = pp = 0
ns = len(s)
np = len(p)
while ps<ns and pp<np:
while ps < ns and pp < np:
if s[ps] == p[pp]:
ps,pp = ps+1,pp+1
ps, pp = ps+1, pp+1
else:
idx = ps+ np-pp
if idx >=ns:return -1
idx = ps + np-pp
if idx >= ns:
return -1
ch = s[idx]
if ch in dic:
ps += dic[ch]+1-pp
else:
ps = idx+1
pp = 0
if pp==np:return ps-np
if pp == np:
return ps-np
else:
return -1
def findAll(s,p):
def findAll(s, p):
ns = len(s)
np = len(p)
i = 0
ret = []
while s:
print(s,p)
tmp = find(s,p)
if tmp==-1: break
print(s, p)
tmp = find(s, p)
if tmp == -1:
break
ret.append(i+tmp)
end = tmp+np
i +=end
i += end
s = s[end:]
return ret
def randStr(n=3):
return [randint(ord('a'),ord('z')) for i in range(n)]
return [randint(ord('a'), ord('z')) for i in range(n)]
def test(n):
s = randStr(n)
p = randStr(3)
str_s = ''.join((chr(i) for i in s))
str_p = ''.join((chr(i) for i in p))
n1 = find(s,p)
n2 = str_s.find(str_p) # 利用已有的 str find 算法检验
if n1!=n2:
print(n1,n2,str_p,str_s)
n1 = find(s, p)
n2 = str_s.find(str_p) # 利用已有的 str find 算法检验
if n1 != n2:
print(n1, n2, str_p, str_s)
return False
return True
if __name__ =='__main__':
if __name__ == '__main__':
from random import randint
n = 1000
suc = sum(test(n) for i in range(n))
print('test {n} times, success {suc} times'.format(n=n,suc=suc))
print('test {n} times, success {suc} times'.format(n=n, suc=suc))

13
string/wildcard_matching.py
View File

@ -33,25 +33,26 @@ else : dp[j][i] = dp[j-1][i-1] and s[i] == p[j]
# leetcode: q44 https://leetcode.com/problems/wildcard-matching/description/
def isMatch(self, s, p):
"""
:type s: str
:type p: str pattern str including wildcard
:rtype: bool
"""
n,m = len(s),len(p)
last = [False]*(n+1)
n, m = len(s), len(p)
last = [False]*(n+1)
last[0] = True
for j in range(m):
if p[j]=='*':
if p[j] == '*':
for i in range(n):
last[i+1] = last[i+1] or last[i]
elif p[j]=='?':
elif p[j] == '?':
last.pop()
last.insert(0,False)
last.insert(0, False)
else:
li = [False]
for i in range(n):
li.append( last[i] and p[j]==s[i])
li.append(last[i] and p[j] == s[i])
last = li
return last[-1]

32
utils/codecogs.py
View File

@ -14,39 +14,47 @@ import re
import sys
from translate import Translator as TR
FORMULA = re.compile(r'\${1,2}(?P<formula>.+?)\${1,2}',re.DOTALL)
FORMULA = re.compile(r'\${1,2}(?P<formula>.+?)\${1,2}', re.DOTALL)
Chinese = re.compile(u"(?P<chinese>[\u4e00-\u9fa5]+)")
API = 'https://latex.codecogs.com/gif.latex?'
def codecog(f):
if os.path.exists(f) and f.endswith('.md'):
with open(f) as fp:
txt = fp.read()
with open(f,'w') as fp:
fp.write(re.sub(FORMULA,covert,txt))
with open(f, 'w') as fp:
fp.write(re.sub(FORMULA, covert, txt))
else:
s = re.sub(FORMULA,covert,f)
s = re.sub(FORMULA, covert, f)
print(s)
def covert(matched):
s = matched.group('formula').strip('$ ')
s = re.sub(Chinese,zh2en,s)
s = re.sub(r'\r+|\n+|\\n',' ',s)
s = re.sub(' +','&space;',s)
return '![]({})'.format(API+s)
s = re.sub(Chinese, zh2en, s)
s = re.sub(r'\r+|\n+|\\n', ' ', s)
s = re.sub(' +', '&space;', s)
return '![]({})'.format(API+s)
def zh2en(txt):
s = txt.group('chinese').strip()
tran = TR(to_lang='en',from_lang='zh')
tran = TR(to_lang='en', from_lang='zh')
en = tran.translate(s)
return re.sub(' +','-',en)
return re.sub(' +', '-', en)
def handle(path):
if os.path.isdir(path):
for p,ds,fs in os.walk(path):
for p, ds, fs in os.walk(path):
for f in fs:
if f.endswith('.md'):
codecog(os.path.join(p,f))
codecog(os.path.join(p, f))
else:
codecog(path)
if __name__ == '__main__':
args = sys.argv[1:]
if not args:

13
utils/genReadme.py
View File

@ -16,17 +16,18 @@ from config import README
parser = ArgumentParser()
parser.add_argument('-p','--path',default='.',help='path to walk')
parser.add_argument('-f','--fileinclude',action='store_true',default=True,help='if has, list files and dirs, else only dirs')
parser.add_argument('-d','--depth', type = int, default = 2)
#获取参数
parser.add_argument('-p', '--path', default='.', help='path to walk')
parser.add_argument('-f', '--fileinclude', action='store_true',
default=True, help='if has, list files and dirs, else only dirs')
parser.add_argument('-d', '--depth', type=int, default=2)
# 获取参数
args = parser.parse_args()
FILE = args.fileinclude
PATH = args.path
DEPTH = args.depth
idxs = tree(PATH,DEPTH,FILE)
idxs = tree(PATH, DEPTH, FILE)
s = README.format(index='\n'.join(idxs))
with open('README.md','w') as f:
with open('README.md', 'w') as f:
f.write(s)

43
utils/headinfo.py
View File

@ -15,44 +15,55 @@ import sys
import time
from config import HEAD
count = 0
def handleFile(path):
global count
head = getHead(path)
if head =='': return
with open(path,'r',encoding='utf8',errors='ignore') as f:
if head == '':
return
with open(path, 'r', encoding='utf8', errors='ignore') as f:
s = f.read()
if 'mbinary' in s:
return
count +=1
count += 1
name = os.path.basename(path)
print('[{count}]: Adding head info to {name}'.format(count=count,name=name))
with open(path,'w') as f:
print('[{count}]: Adding head info to {name}'.format(count=count, name=name))
with open(path, 'w') as f:
f.write(head+s)
def getHead(path):
name = os.path.basename(path)
# skip self or hidden file
if name == os.path.basename(__file__) or name[0]=='.': return ''
suf = name[name.rfind('.')+1 :]
begin = end =''
if name == os.path.basename(__file__) or name[0] == '.':
return ''
suf = name[name.rfind('.')+1:]
begin = end = ''
if suf == 'py':
begin = end = "'''"
elif suf in ['c','cc','cpp','java']:
begin,end = '/*','*/'
elif suf in ['c', 'cc', 'cpp', 'java']:
begin, end = '/*', '*/'
elif suf == 'sh':
begin = end = '#'
else:return ''
else:
return ''
timeStamp = time.localtime(os.stat(path).st_ctime)
ctime = time.strftime('%Y-%m-%d %H:%M',timeStamp)
return HEAD.format(begin=begin,end=end,ctime=ctime,name = name)
ctime = time.strftime('%Y-%m-%d %H:%M', timeStamp)
return HEAD.format(begin=begin, end=end, ctime=ctime, name=name)
def handleDir(dirPath):
gen = os.walk(dirPath)
for path,dirs,files in gen:
for f in files: handleFile(os.path.join(path,f))
for path, dirs, files in gen:
for f in files:
handleFile(os.path.join(path, f))
if __name__ == '__main__':
works = sys.argv[1:]
if works==[] : works = ['.']
if works == []:
works = ['.']
for one in works:
if not os.path.exists(one):
print('[PathError]: {one} not exists'.format(one=one))

43
utils/tree.py
View File

@ -13,42 +13,51 @@
import os
from argparse import ArgumentParser
#命令行输入参数处理
# 命令行输入参数处理
parser = ArgumentParser()
parser.add_argument('-p','--path',default='.',help='path to walk')
parser.add_argument('-f','--fileinclude',action='store_true',help='if has, list files and dirs, else only dirs')
parser.add_argument('-d','--depth', type = int, default = 2)
#获取参数
parser.add_argument('-p', '--path', default='.', help='path to walk')
parser.add_argument('-f', '--fileinclude', action='store_true',
help='if has, list files and dirs, else only dirs')
parser.add_argument('-d', '--depth', type=int, default=2)
# 获取参数
args = parser.parse_args()
FILE = args.fileinclude
PATH = args.path
DEPTH = args.depth
def mklink(path):
return '* [{name}]({path})'.format(name=os.path.basename(path),path=path)
return '* [{name}]({path})'.format(name=os.path.basename(path), path=path)
def clean(paths):
ret = []
for path in paths:
name = os.path.basename(path)
if not ( name.startswith('.') or name.startswith('__')):
if not (name.startswith('.') or name.startswith('__')):
ret.append(path)
return ret
def tree(path='.',depth=2,showfile=False):
def tree(path='.', depth=2, showfile=False):
li = []
if os.path.isdir(path):li = os.listdir(path)
else:li=[path]
items = [os.path.join(path,i) for i in li if not i.startswith('.')]
if os.path.isdir(path):
li = os.listdir(path)
else:
li = [path]
items = [os.path.join(path, i) for i in li if not i.startswith('.')]
items = clean(items)
items = sorted(items)
if not showfile: items = [i for i in items if os.path.isdir(i)]
if depth==1:
if not showfile:
items = [i for i in items if os.path.isdir(i)]
if depth == 1:
return [mklink(path)] + [' '*4 + mklink(i) for i in items]
else:
uls = [tree(i,depth-1,showfile) for i in items]
uls = [tree(i, depth-1, showfile) for i in items]
ret = [' '*4 + li for ul in uls for li in ul]
return [mklink(path)] + ret
return [mklink(path)] + ret
if __name__ =='__main__':
print('\n'.join(tree(PATH,DEPTH,FILE)))
if __name__ == '__main__':
print('\n'.join(tree(PATH, DEPTH, FILE)))