!!!Python 組合せと順列の計算
[Python]{{category アルゴリズム}}
!!組合せと順列を計算してみる
::サンプル
 # -*- encoding:utf-8 -*-
 import copy
 
 def combination(elem):
     '''組合せ'''
     for i,v in enumerate(elem):
         for v2 in elem[i+1:]:
             print (v, v2)
 
 def permutation(slot,elem, size):
     '''順列'''
     if len(elem) == 1:
         slot[size - 1] = elem[0]
         print slot
     else:
         for i,v in enumerate(elem):
             slot[size - len(elem)] = v
             e2 = copy.copy(elem)
             e2.remove(v)
             permutation(slot, e2, size)
     return
 
 if  __name__ == '__main__':
     elem = range(4)
     slot = [-1 for x in elem]
 
     combination(elem)
     permutation(slot, elem, len(elem))
     
::結果
 (0, 1)
 (0, 2)
 (0, 3)
 (1, 2)
 (1, 3)
 (2, 3)
 [0, 1, 2, 3]
 [0, 1, 3, 2]
 [0, 2, 1, 3]
 [0, 2, 3, 1]
 [0, 3, 1, 2]
 [0, 3, 2, 1]
 [1, 0, 2, 3]
 [1, 0, 3, 2]
 [1, 2, 0, 3]
 [1, 2, 3, 0]
 [1, 3, 0, 2]
 [1, 3, 2, 0]
 [2, 0, 1, 3]
 [2, 0, 3, 1]
 [2, 1, 0, 3]
 [2, 1, 3, 0]
 [2, 3, 0, 1]
 [2, 3, 1, 0]
 [3, 0, 1, 2]
 [3, 0, 2, 1]
 [3, 1, 0, 2]
 [3, 1, 2, 0]
 [3, 2, 0, 1]
 [3, 2, 1, 0]

!!組み合わせの数
 def combi(n ,r):
     p = 1
     for i in range(1, r+1):
         p = p * (n - i + 1) / i
     return p
 
 if __name__ == "__main__":
     print combi(4, 2)
::
 6

!1行
*Pytho3.x では、functioolsのimportが必要、2.7xでは不要
 >>> from functools import reduce
 >>> cmb = lambda n,r:reduce(lambda x,y:x*y,range(n,n-r,-1))/reduce(lambda x,y:x*y,range(r,1,-1))
 >>> cmb(7,3)
 35.0