python实现求解列表中元素的排列和组合问题
求解列表中元素的排列和组合问题这个问题之前就遇到过几次没有太留意，最近在做题的时候遇上挺多的排列组合问题的，想来有必要温习一下了，今天花点时间写一下，之前都是手工写的，后来知道可以直接使用python的内置模块就可以完成这个工作了，今天就使用python的itertools模块来完成这个工作，一共解决四个问题：
1.生成排列，列表中元素不允许重复出现
2.生成排列，列表中元素可以重复出现
3.生成组合,不限元素个数，列表中元素不允许重复出现
4.生成组合,不限元素个数，列表中元素可以重复出现
因为大家都有排列组合的知识这里就不累赘了，问题很简单，下面看具体的实现：
#!usr/bin/env python
#encoding:utf-8
'''''
__Author__:沂水寒城
功能：求解列表中元素的排列和组合问题
'''
from itertools import product
from itertools import combinations
import itertools
def test_func1(num_list):
'''''
生成排列
列表中元素不允许重复出现
排列数计算为：n！，其中n为num_list列表中元素个数
'''
tmp_list = itertools.permutations(num_list)
res_list=[]
for one in tmp_list:
res_list.append(one)
print res_list
print '元素不允许重复出现排列总数为:', len(res_list)
def test_func11(num_list):
'''''
生成排列
列表中元素可以重复出现
排列总数计算为：(n*n*n...*n)，一共n个n相乘
'''
num=len(num_list)
res_list=list(product(num_list,repeat=num))
print res_list
print '元素可以重复出现排列总数为:', len(res_list)
def test_func2(num_list):
'''''
生成组合,不限元素个数
列表中元素不允许重复出现
组合数计算为：2^n，其中n为num_list列表中元素个数
'''
res_list=[]
for i in range(len(num_list)+1):
res_list+=list(combinations(num_list, i))
print res_list
print '元素不允许重复出现组合总数为:', len(res_list)
def test_func22(num_list):
'''''
生成组合,不限元素个数
列表中元素可以重复出现
'''
res_list=[]
num_list1=[str(i) for i in num_list]
for i in range(0,len(num_list)+1):
res_list+=[''.join(x) for x in itertools.product(*[num_list1] * i)]
print res_list
print '元素可以重复出现组合总数为:', len(res_list)
if __name__ == '__main__':
num_list=[1,2,3,4]
test_func1(num_list)
print '-------------------------------------'
test_func11(num_list)
print '-------------------------------------'
test_func2(num_list)
print '-------------------------------------'
test_func22(num_list)
结果如下：
[(1, 2, 3, 4), (1, 2, 4, 3), (1, 3, 2, 4), (1, 3, 4, 2), (1, 4, 2, 3), (1, 4, 3, 2), (2, 1, 3, 4), (2, 1, 4, 3), (2, 3, 1, 4), (2, 3, 4, 1), (2, 4, 1, 3), (2, 4, 3, 1), (3, 1, 2, 4), (3, 1, 4, 2), (3, 2, 1, 4), (3, 2, 4, 1), (3, 4, 1, 2), (3, 4, 2, 1), (4, 1, 2, 3), (4, 1, 3, 2), (4, 2, 1, 3), (4, 2, 3, 1), (4, 3, 1, 2), (4, 3, 2, 1)]
元素不允许重复出现排列总数为: 24
-------------------------------------
[(1, 1, 1, 1), (1, 1, 1, 2), (1, 1, 1, 3), (1, 1, 1, 4), (1, 1, 2, 1), (1, 1, 2, 2), (1, 1, 2, 3), (1, 1, 2, 4), (1, 1, 3, 1), (1, 1, 3, 2), (1, 1, 3, 3), (1, 1, 3, 4), (1, 1, 4, 1), (1, 1, 4, 2), (1, 1, 4, 3), (1, 1, 4, 4), (1, 2, 1, 1), (1, 2, 1, 2), (1, 2, 1, 3), (1, 2, 1, 4), (1, 2, 2, 1), (1, 2, 2, 2), (1, 2, 2, 3), (1, 2, 2, 4), (1, 2, 3, 1), (1, 2, 3, 2), (1, 2, 3, 3), (1, 2, 3, 4), (1, 2, 4, 1), (1, 2, 4, 2), (1, 2, 4, 3), (1, 2, 4, 4), (1, 3, 1, 1), (1, 3, 1, 2), (1, 3, 1, 3), (1, 3, 1, 4), (1, 3, 2, 1), (1, 3, 2, 2), (1, 3, 2, 3), (1, 3, 2, 4), (1, 3, 3, 1), (1, 3, 3, 2), (1, 3, 3, 3), (1, 3, 3, 4), (1, 3, 4, 1), (1, 3, 4, 2), (1, 3, 4, 3), (1, 3, 4, 4), (1, 4, 1, 1), (1, 4, 1, 2), (1, 4, 1, 3), (1, 4, 1, 4), (1, 4, 2, 1), (1, 4, 2, 2), (1, 4, 2, 3), (1, 4, 2, 4), (1, 4, 3, 1), (1, 4, 3, 2), (1, 4, 3, 3), (1, 4, 3, 4), (1, 4, 4, 1), (1, 4, 4, 2), (1, 4, 4, 3), (1, 4, 4, 4), (2, 1, 1, 1), (2, 1, 1, 2), (2, 1, 1, 3), (2, 1, 1, 4), (2, 1, 2, 1), (2, 1, 2, 2), (2, 1, 2, 3), (2, 1, 2, 4), (2, 1, 3, 1), (2, 1, 3, 2), (2, 1, 3, 3), (2, 1, 3, 4), (2, 1, 4, 1), (2, 1, 4, 2), (2, 1, 4, 3), (2, 1, 4, 4), (2, 2, 1, 1), (2, 2, 1, 2), (2, 2, 1, 3), (2, 2, 1, 4), (2, 2, 2, 1), (2, 2, 2, 2), (2, 2, 2, 3), (2, 2, 2, 4), (2, 2, 3, 1), (2, 2, 3, 2), (2, 2, 3, 3), (2, 2, 3, 4), (2, 2, 4, 1), (2, 2, 4, 2), (2, 2, 4, 3), (2, 2, 4, 4), (2, 3, 1, 1), (2, 3, 1, 2), (2, 3, 1, 3), (2, 3, 1, 4), (2, 3, 2, 1), (2, 3, 2, 2), (2, 3, 2, 3), (2, 3, 2, 4), (2, 3, 3, 1), (2, 3, 3, 2), (2, 3, 3, 3), (2, 3, 3, 4), (2, 3, 4, 1), (2, 3, 4, 2), (2, 3, 4, 3), (2, 3, 4, 4), (2, 4, 1, 1), (2, 4, 1, 2), (2, 4, 1, 3), (2, 4, 1, 4), (2, 4, 2, 1), (2, 4, 2, 2), (2, 4, 2, 3), (2, 4, 2, 4), (2, 4, 3, 1), (2, 4, 3, 2), (2, 4, 3, 3), (2, 4, 3, 4), (2, 4, 4, 1), (2, 4, 4, 2), (2, 4, 4, 3), (2, 4, 4, 4), (3, 1, 1, 1), (3, 1, 1, 2), (3, 1, 1, 3), (3, 1, 1, 4), (3, 1, 2, 1), (3, 1, 2, 2), (3, 1, 2, 3), (3, 1, 2, 4), (3, 1, 3, 1), (3, 1, 3, 2), (3, 1, 3, 3), (3, 1, 3, 4), (3, 1, 4, 1), (3, 1, 4, 2), (3, 1, 4, 3), (3, 1, 4, 4), (3, 2, 1, 1), (3, 2, 1, 2), (3, 2, 1, 3), (3, 2, 1, 4), (3, 2, 2, 1), (3, 2, 2, 2), (3, 2, 2, 3), (3, 2, 2, 4), (3, 2, 3, 1), (3, 2, 3, 2), (3, 2, 3, 3), (3, 2, 3, 4), (3, 2, 4, 1), (3, 2, 4, 2), (3, 2, 4, 3), (3, 2, 4, 4), (3, 3, 1, 1), (3, 3, 1, 2), (3, 3, 1, 3), (3, 3, 1, 4), (3, 3, 2, 1), (3, 3, 2, 2), (3, 3, 2, 3), (3, 3, 2, 4), (3, 3, 3, 1), (3, 3, 3, 2), (3, 3, 3, 3), (3, 3, 3, 4), (3, 3, 4, 1), (3, 3, 4, 2), (3, 3, 4, 3), (3, 3, 4, 4), (3, 4, 1, 1), (3, 4, 1, 2), (3, 4, 1, 3), (3, 4, 1, 4), (3, 4, 2, 1), (3, 4, 2, 2), (3, 4, 2, 3), (3, 4, 2, 4), (3, 4, 3, 1), (3, 4, 3, 2), (3, 4, 3, 3), (3, 4, 3, 4), (3, 4, 4, 1), (3, 4, 4, 2), (3, 4, 4, 3), (3, 4, 4, 4), (4, 1, 1, 1), (4, 1, 1, 2), (4, 1, 1, 3), (4, 1, 1, 4), (4, 1, 2, 1), (4, 1, 2, 2), (4, 1, 2, 3), (4, 1, 2, 4), (4, 1, 3, 1), (4, 1, 3, 2), (4, 1, 3, 3), (4, 1, 3, 4), (4, 1, 4, 1), (4, 1, 4, 2), (4, 1, 4, 3), (4, 1, 4, 4), (4, 2, 1, 1), (4, 2, 1, 2), (4, 2, 1, 3), (4, 2, 1, 4), (4, 2, 2, 1), (4, 2, 2, 2), (4, 2, 2, 3), (4, 2, 2, 4), (4, 2, 3, 1), (4, 2, 3, 2), (4, 2, 3, 3), (4, 2, 3, 4), (4, 2, 4, 1), (4, 2, 4, 2), (4, 2, 4, 3), (4, 2, 4, 4), (4, 3, 1, 1), (4, 3, 1, 2), (4, 3, 1, 3), (4, 3, 1, 4), (4, 3, 2, 1), (4, 3, 2, 2), (4, 3, 2, 3), (4, 3, 2, 4), (4, 3, 3, 1), (4, 3, 3, 2), (4, 3, 3, 3), (4, 3, 3, 4), (4, 3, 4, 1), (4, 3, 4, 2), (4, 3, 4, 3), (4, 3, 4, 4), (4, 4, 1, 1), (4, 4, 1, 2), (4, 4, 1, 3), (4, 4, 1, 4), (4, 4, 2, 1), (4, 4, 2, 2), (4, 4, 2, 3), (4, 4, 2, 4), (4, 4, 3, 1), (4, 4, 3, 2), (4, 4, 3, 3), (4, 4, 3, 4), (4, 4, 4, 1), (4, 4, 4, 2), (4, 4, 4, 3), (4, 4, 4, 4)]
元素可以重复出现排列总数为: 256
-------------------------------------
[(), (1,), (2,), (3,), (4,), (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4), (1, 2, 3), (1, 2, 4), (1, 3, 4), (2, 3, 4), (1, 2, 3, 4)]
元素不允许重复出现组合总数为: 16
-------------------------------------
['', '1', '2', '3', '4', '11', '12', '13', '14', '21', '22', '23', '24', '31', '32', '33', '34', '41', '42', '43', '44', '111', '112', '113', '114', '121', '122', '123', '124', '131', '132', '133', '134', '141', '142', '143', '144', '211', '212', '213', '214', '221', '222', '223', '224', '231', '232', '233', '234', '241', '242', '243', '244', '311', '312', '313', '314', '321', '322', '323', '324', '331', '332', '333', '334', '341', '342', '343', '344', '411', '412', '413', '414', '421', '422', '423', '424', '431', '432', '433', '434', '441', '442', '443', '444', '1111', '1112', '1113', '1114', '1121', '1122', '1123', '1124', '1131', '1132', '1133', '1134', '1141', '1142', '1143', '1144', '1211', '1212', '1213', '1214', '1221', '1222', '1223', '1224', '1231', '1232', '1233', '1234', '1241', '1242', '1243', '1244', '1311', '1312', '1313', '1314', '1321', '1322', '1323', '1324', '1331', '1332', '1333', '1334', '1341', '1342', '1343', '1344', '1411', '1412', '1413', '1414', '1421', '1422', '1423', '1424', '1431', '1432', '1433', '1434', '1441', '1442', '1443', '1444', '2111', '2112', '2113', '2114', '2121', '2122', '2123', '2124', '2131', '2132', '2133', '2134', '2141', '2142', '2143', '2144', '2211', '2212', '2213', '2214', '2221', '2222', '2223', '2224', '2231', '2232', '2233', '2234', '2241', '2242', '2243', '2244', '2311', '2312', '2313', '2314', '2321', '2322', '2323', '2324', '2331', '2332', '2333', '2334', '2341', '2342', '2343', '2344', '2411', '2412', '2413', '2414', '2421', '2422', '2423', '2424', '2431', '2432', '2433', '2434', '2441', '2442', '2443', '2444', '3111', '3112', '3113', '3114', '3121', '3122', '3123', '3124', '3131', '3132', '3133', '3134', '3141', '3142', '3143', '3144', '3211', '3212', '3213', '3214', '3221', '3222', '3223', '3224', '3231', '3232', '3233', '3234', '3241', '3242', '3243', '3244', '3311', '3312', '3313', '3314', '3321', '3322', '3323', '3324', '3331', '3332', '3333', '3334', '3341', '3342', '3343', '3344', '3411', '3412', '3413', '3414', '3421', '3422', '3423', '3424', '3431', '3432', '3433', '3434', '3441', '3442', '3443', '3444', '4111', '4112', '4113', '4114', '4121', '4122', '4123', '4124', '4131', '4132', '4133', '4134', '4141', '4142', '4143', '4144', '4211', '4212', '4213', '4214', '4221', '4222', '4223', '4224', '4231', '4232', '4233', '4234', '4241', '4242', '4243', '4244', '4311', '4312', '4313', '4314', '4321', '4322', '4323', '4324', '4331', '4332', '4333', '4334', '4341', '4342', '4343', '4344', '4411', '4412', '4413', '4414', '4421', '4422', '4423', '4424', '4431', '4432', '4433', '4434', '4441', '4442', '4443', '4444']
元素可以重复出现组合总数为: 341
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