python中的combinations和permutations

排列和组合是数论中的基本概念。在python中，实现了组合函数combinations 和 排列函数permutations。两个函数都在itertools包中。举例如下：

from itertools import combinations, permutations
data = [1,2,3,4]
from itertools import combinations, permutations
data=[1,2,3,4]
for combination in combinations(data,2):
    print(combination)

(1, 2)
(1, 3)
(1, 4)
(2, 3)
(2, 4)
(3, 4)
for permutation in permutations(data,2):
    print(permutation)

(1, 2)
(1, 3)
(1, 4)
(2, 1)
(2, 3)
(2, 4)
(3, 1)
(3, 2)
(3, 4)
(4, 1)
(4, 2)
(4, 3)

组合的个数为$C_{4}^{2} = 6$，排列的个数为$A_{4}^{2} = 12$。
这两个函数都是基于下标的，而不是基于值的，也就是说，如果有重复，结果中不会去重。举例如下：

from itertools import combinations, permutations
data = [1,1,1,2]
for combination in combinations(data,2):
    print(combination)

(1, 1)
(1, 1)
(1, 2)
(1, 1)
(1, 2)
(1, 2)
for permutation in permutations(data,2):
    print(permutation)

(1, 1)
(1, 1)
(1, 2)
(1, 1)
(1, 1)
(1, 2)
(1, 1)
(1, 1)
(1, 2)
(2, 1)
(2, 1)
(2, 1)

结果没有去重。