Update shellSort, Add fibnacci computation method of matrix power

math/fibonacci/fibonacci.hs

@@ -0,0 +1,29 @@
+:{
+''' mbinary
+#######################################################################
+# File : fibonacci.hs
+# Author: mbinary
+# Mail: zhuheqin1@gmail.com
+# Blog: https://mbinary.github.io
+# Github: https://github.com/mbinary
+# Created Time: 2019-02-03  19:42
+# Description: matrix pow and fast pow:
+    calculate big number fibonacci item. for negative item, use f(n) = f(n+2)-f(n+1)
+#######################################################################
+:}
+module Fibonacci where
+
+fib :: Integer -> Integer
+fib  n = let p =  if n>0 then n-2 else 2-n
+             mat = if n>0 then [1,1,1,0] else [0,1,1,-1]
+             m = matrix_pow mat p
+          in m!!0+m!!1
+          
+          
+matrix_pow mat n = if n<=0 then [1,0,0,1]
+                   else let v = if (mod n 2==0) then [1,0,0,1] else mat
+                            m2 = matrix_mul mat mat
+                            remain = matrix_pow m2  (div n 2)
+                         in matrix_mul v remain          
+                   
+matrix_mul a b = [ 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]                   

math/fibonacci/fibonacci.py

@@ -0,0 +1,37 @@
+#coding: utf-8
+''' mbinary
+#######################################################################
+# File : fibonacci.py
+# Author: mbinary
+# Mail: zhuheqin1@gmail.com
+# Blog: https://mbinary.github.io
+# Github: https://github.com/mbinary
+# Created Time: 2019-02-03  19:10
+# Description: use matrix and fast pow to calculate big numbr fibonacci value.
+#######################################################################
+'''
+
+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)
+    return ans
+
+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]
+
+
+if __name__=='__main__':
+    for i in range(-5,5):
+        print(i,fib(i))

math/fibonacci/test.hs

@@ -0,0 +1,22 @@
+module Fibonacci.Test where
+import Fibonacci
+import Test.QuickCheck
+import Test.QuickCheck.All
+
+
+prop_fib :: Int -> Bool
+prop_fib  x =  fib n == 2
+main = $(quickCheckAll)
+
+:{
+prop_fib 0 = fib 0 == 0
+prop_fib 1 = fib 1 == 1
+prop_fib 2 = fib 2 == 1
+prop_fib 3 = fib 3 == 2
+prop_fib 5 = fib 5 == 5
+prop_fib 5 = fib 5 == 5
+prop_fib -6 = fib -6 == -8
+prop_fib -96 = fib -96 == -51680708854858323072
+prop_fib 2000 = fib 2000 ==  4224696333392304878706725602341482782579852840250681098010280137314308584370130707224123599639141511088446087538909603607640194711643596029271983312598737326253555802606991585915229492453904998722256795316982874482472992263901833716778060607011615497886719879858311468870876264597369086722884023654422295243347964480139515349562972087652656069529806499841977448720155612802665404554171717881930324025204312082516817125
+:}
+

math/numberTheory/isPrime.py

@@ -88,7 +88,21 @@ class primeSieve:
                     if i%j==0:break
                 else:lst.append(i)
             self.primes+=lst
-        return twoDivideFind(x,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)

sort/shellSort.py

@@ -10,15 +10,26 @@
 #########################################################################
 '''
 
-def shellSort(s,inc=None):
-    if inc is None:inc = [1,3,5,7,11,13,17,19]
-    num = len(s)
-    inc.sort(reverse=True)
-    for i in inc:
-        for j in range(i,num):
+def shellSort(s,gaps=None):
+    if gaps is None:
+        gaps = [127,63,31,15,7,3,1]
+    n = len(s)
+    for gap in gaps:
+        for j in range(gap,n):
             cur = j
-            while cur>=i and s[j] > s[cur-i]:
-                s[cur] = s[cur-i]
-                cur-=i
-            s[cur] = s[j]
+            num = s[j]
+            while cur>=gap and num < s[cur-gap]:
+                s[cur] = s[cur-gap]
+                cur-=gap
+            s[cur] = num
     return s
+
+if __name__=='__main__':
+    from random import randint
+    import sys
+    n = 20
+    if len(sys.argv)>1:
+        n = int(sys.argv[1])
+    nums = [randint(1,100) for i in range(n)]
+    print(nums)
+    print(shellSort(nums))

utils/config.py

@@ -6,6 +6,7 @@ README = r'''
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 >Notes and codes for learning algorithm and data structures :smiley: