2018-10-02 21:24:06 +08:00
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''' mbinary
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#########################################################################
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# File : bTree.py
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# Author: mbinary
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# Mail: zhuheqin1@gmail.com
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# Blog: https://mbinary.coding.me
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# Github: https://github.com/mbinary
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# Created Time: 2018-08-29 12:49
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# Description:
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#########################################################################
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'''
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2018-08-29 15:52:02 +08:00
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class node:
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def __init__(self,keys=None,isLeaf = True,children=None):
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if keys is None:keys=[]
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if children is None: children =[]
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self.keys = keys
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self.isLeaf = isLeaf
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self.children = []
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def __getitem__(self,i):
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return self.keys[i]
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def __delitem__(self,i):
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del self.keys[i]
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def __setitem__(self,i,k):
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self.keys[i] = k
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def __len__(self):
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return len(self.keys)
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def __repr__(self):
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return str(self.keys)
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def __str__(self):
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children = ','.join([str(nd.keys) for nd in self.children])
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return f'keys: {self.keys}\nchildren: {children}\nisLeaf: {self.isLeaf}'
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def getChd(self,i):
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return self.children[i]
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def delChd(self,i):
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del self.children[i]
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def setChd(self,i,chd):
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self.children[i] = chd
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def getChildren(self,begin=0,end=None):
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if end is None:return self.children[begin:]
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return self.children[begin:end]
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def findKey(self,key):
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for i,k in enumerate(self.keys):
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if k>=key:
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return i
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return len(self)
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def update(self,keys=None,isLeaf=None,children=None):
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if keys is not None:self.keys = keys
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if children is not None:self.children = children
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if isLeaf is not None: self.isLeaf = isLeaf
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def insert(self,i,key=None,nd=None):
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if key is not None:self.keys.insert(i,key)
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if not self.isLeaf and nd is not None: self.children.insert(i,nd)
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def isLeafNode(self):return self.isLeaf
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def split(self,prt,t):
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# form new two nodes
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k = self[t-1]
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nd1 = node()
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nd2 = node()
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nd1.keys,nd2.keys = self[:t-1], self[t:] # note that t is 1 bigger than key index
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nd1.isLeaf = nd2.isLeaf = self.isLeaf
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if not self.isLeaf:
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# note that children index is one bigger than key index, and all children included
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nd1.children, nd2.children = self.children[0:t], self.children[t:]
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# connect them to parent
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idx = prt.findKey(k)
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if prt.children !=[]: prt.children.remove(self) # remove the original node
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prt.insert(idx,k,nd2)
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prt.insert(idx,nd = nd1)
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return prt
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class bTree:
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def __init__(self,degree=2):
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self.root = node()
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self.degree=degree
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self.nodeNum = 1
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self.keyNum = 0
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def search(self,key,withpath=False):
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nd = self.root
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fathers = []
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while True:
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i = nd.findKey(key)
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if i==len(nd): fathers.append((nd,i-1,i))
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else: fathers.append((nd,i,i))
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if i<len(nd) and nd[i]==key:
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if withpath:return nd,i,fathers
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else:return nd,i
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if nd.isLeafNode():
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if withpath:return None,None,None
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else:return None,None
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nd = nd.getChd(i)
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def insert(self,key):
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if len(self.root)== self.degree*2-1:
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self.root = self.root.split(node(isLeaf=False),self.degree)
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self.nodeNum +=2
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nd = self.root
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while True:
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idx = nd.findKey(key)
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if idx<len(nd) and nd[idx] == key:return
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if nd.isLeafNode():
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nd.insert(idx,key)
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self.keyNum+=1
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return
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else:
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chd = nd.getChd(idx)
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if len(chd)== self.degree*2-1: #ensure its keys won't excess when its chd split and u
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nd = chd.split(nd,self.degree)
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self.nodeNum +=1
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else:
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nd = chd
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def delete(self,key):#to do
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'''search the key, delete it , and form down to up to rebalance it '''
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nd,idx ,fathers= self.search(key,withpath=True)
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if nd is None : return
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del nd[idx]
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self.keyNum-=1
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if not nd.isLeafNode():
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chd = nd.getChd(idx) # find the predecessor key
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while not chd.isLeafNode():
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fathers.append((chd,len(chd)-1,len(chd)))
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chd = chd.getChd(-1)
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fathers.append((chd,len(chd)-1,len(chd)))
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nd.insert(idx,chd[-1])
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del chd[-1]
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if len(fathers)>1:self.rebalance(fathers)
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def rebalance(self,fathers):
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nd,keyIdx,chdIdx = fathers.pop()
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while len(nd)<self.degree-1: # rebalance tree from down to up
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prt,keyIdx,chdIdx = fathers[-1]
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lbro = [] if chdIdx==0 else prt.getChd(chdIdx-1)
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rbro = [] if chdIdx==len(prt) else prt.getChd(chdIdx+1)
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if len(lbro)<self.degree and len(rbro)<self.degree: # merge two deficient nodes
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beforeNode,afterNode = None,None
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if lbro ==[]:
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keyIdx = chdIdx
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beforeNode,afterNode = nd,rbro
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else:
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beforeNode,afterNode = lbro,nd
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keyIdx = chdIdx-1 # important, when choosing
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keys = beforeNode[:]+[prt[keyIdx]]+afterNode[:]
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children = beforeNode.getChildren() + afterNode.getChildren()
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isLeaf = beforeNode.isLeafNode()
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prt.delChd(keyIdx+1)
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del prt[keyIdx]
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nd.update(keys,isLeaf,children)
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prt.children[keyIdx]=nd
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self.nodeNum -=1
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elif len(lbro)>=self.degree: # rotate when only one sibling is deficient
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keyIdx = chdIdx-1
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nd.insert(0,prt[keyIdx]) # rotate keys
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prt[keyIdx] = lbro[-1]
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del lbro[-1]
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if not nd.isLeafNode(): # if not leaf, move children
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nd.insert(0,nd=lbro.getChd(-1))
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lbro.delChd(-1)
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else:
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keyIdx = chdIdx
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nd.insert(len(nd),prt[keyIdx]) # rotate keys
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prt[keyIdx] = rbro[0]
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del rbro[0]
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if not nd.isLeafNode(): # if not leaf, move children
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#note that insert(-1,ele) will make the ele be the last second one
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nd.insert(len(nd),nd=rbro.getChd(0))
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rbro.delChd(0)
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if len(fathers)==1:
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if len(self.root)==0:
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self.root = nd
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self.nodeNum -=1
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break
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nd,i,j = fathers.pop()
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def __str__(self):
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head= '\n'+'-'*30+'B Tree'+'-'*30
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tail= '-'*30+'the end'+'-'*30+'\n'
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lst = [[head],[f'node num: {self.nodeNum}, key num: {self.keyNum}']]
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cur = []
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ndNum =0
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ndTotal= 1
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que = [self.root]
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while que!=[]:
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nd = que.pop(0)
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cur.append(repr(nd))
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ndNum+=1
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que+=nd.getChildren()
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if ndNum==ndTotal:
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lst.append(cur)
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cur = []
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ndNum = 0
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ndTotal =len(que)
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lst.append([tail])
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lst = [','.join(li) for li in lst]
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return '\n'.join(lst)
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def __iter__(self,nd = None):
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if nd is None: nd = self.root
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que = [nd]
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while que !=[]:
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nd = que.pop(0)
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yield nd
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if nd.isLeafNode():continue
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for i in range(len(nd)+1):
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que.append(nd.getChd(i))
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if __name__ =='__main__':
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bt = bTree()
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from random import shuffle,sample
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n = 20
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lst = [i for i in range(n)]
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shuffle(lst)
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test= sample(lst,len(lst)//4)
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print(f'building b-tree with {lst}')
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for i in lst:
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bt.insert(i)
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#print(f'inserting {i})
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#print(bt)
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print(bt)
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print(f'serching {test}')
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for i in test:
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nd,idx = bt.search(i)
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print(f'node: {repr(nd)}[{idx}]== {i}')
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for i in test:
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print(f'deleting {i}')
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bt.delete(i)
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print(bt)
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