约瑟夫环问题 Python3实现
Python学习笔记
尝试用Python3实现约瑟夫环问题。
约瑟夫环问题的描述：
约瑟夫斯问题（有时也称为约瑟夫斯置换），是一个出现在计算机科学和数学中的问题。在计算机编程的算法中，类似问题又称为约瑟夫环。
有 n个囚犯站成一个圆圈，准备处决。首先从一个人开始，越过 k-2个人（因为第一个人已经被越过），并杀掉第k个人。接着，再越过 k-1个人，并杀掉第k个人。这个过程沿着圆圈一直进行，直到最终只剩下一个人留下，这个人就可以继续活着。
问题是，给定了n和 k，一开始要站在什么地方才能避免被处决？
假定n=100;k=3。
则正确的答案是：
总共有100个人，每3个人必须被处死一个，则整个被处死的队列是：
3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 81 84 87 90 93 96 99 2 7 11 16 20 25 29 34 38 43 47 52 56 61 65 70 74 79 83 88 92 97 1 8 14 22 28 35 41 49 55 62 68 76 82 89 95 4 13 23 32 44 53 64 73 85 94 5 19 37 50 67 80 98 17 40 59 86 10 46 77 26 71 31 100 58 91
如果最后一个可以存活，那么你应该站在第91个的位置。
现在自己做个程序来验证：
1 #!/usr/local/bin/python3
2 #! version 3.0.7
3 #! encode utf-8
4 n = 100
5 survive_person = list(range(1,n+1))
6 count = 3
7 temp = 1
8 round = 0
9 kill_person = []
10 while(round < 10):
11 for i in survive_person :
12 print('now it\'s:',i,'turn',end='\n')
13 if temp == count :
14 kill_person.append(i)
15 survive_person.remove(i)
16 temp = 1
17 print('kill person:',i,'lenth of survive:',len(survive_person),end='\n')
18 temp += 1
19 print('the first turn is ',i,end='\n')
20 round += 1
21 print(kill_person)
22 print(survive_person) 但是答案不对：
$./josephloop.py
now it's: 1 turn
the first turn is 1
now it's: 2 turn
the first turn is 2
now it's: 3 turn
kill person: 3 lenth of survive: 99
the first turn is 3
now it's: 5 turn
the first turn is 5
now it's: 6 turn
kill person: 6 lenth of survive: 98
the first turn is 6
now it's: 8 turn
the first turn is 8
now it's: 9 turn
kill person: 9 lenth of survive: 97
the first turn is 9
now it's: 11 turn
the first turn is 11
now it's: 12 turn
kill person: 12 lenth of survive: 96
the first turn is 12
now it's: 14 turn
the first turn is 14
now it's: 15 turn
kill person: 15 lenth of survive: 95
the first turn is 15
now it's: 17 turn
the first turn is 17
now it's: 18 turn
kill person: 18 lenth of survive: 94
the first turn is 18
now it's: 20 turn
the first turn is 20
now it's: 21 turn
kill person: 21 lenth of survive: 93
the first turn is 21
now it's: 23 turn
the first turn is 23
now it's: 24 turn
kill person: 24 lenth of survive: 92
the first turn is 24
now it's: 26 turn
the first turn is 26
now it's: 27 turn
kill person: 27 lenth of survive: 91
the first turn is 27
now it's: 29 turn
the first turn is 29
now it's: 30 turn
kill person: 30 lenth of survive: 90
the first turn is 30
now it's: 32 turn
the first turn is 32
now it's: 33 turn
kill person: 33 lenth of survive: 89
the first turn is 33
now it's: 35 turn
the first turn is 35
now it's: 36 turn
kill person: 36 lenth of survive: 88
the first turn is 36
now it's: 38 turn
the first turn is 38
now it's: 39 turn
kill person: 39 lenth of survive: 87
the first turn is 39
now it's: 41 turn
the first turn is 41
now it's: 42 turn
kill person: 42 lenth of survive: 86
the first turn is 42
now it's: 44 turn
the first turn is 44
now it's: 45 turn
kill person: 45 lenth of survive: 85
the first turn is 45
now it's: 47 turn
the first turn is 47
now it's: 48 turn
kill person: 48 lenth of survive: 84
the first turn is 48
now it's: 50 turn
the first turn is 50
now it's: 51 turn
kill person: 51 lenth of survive: 83
the first turn is 51
now it's: 53 turn
the first turn is 53
now it's: 54 turn
kill person: 54 lenth of survive: 82
the first turn is 54
now it's: 56 turn
the first turn is 56
now it's: 57 turn
kill person: 57 lenth of survive: 81
the first turn is 57
now it's: 59 turn
the first turn is 59
now it's: 60 turn
kill person: 60 lenth of survive: 80
the first turn is 60
now it's: 62 turn
the first turn is 62
now it's: 63 turn
kill person: 63 lenth of survive: 79
the first turn is 63
now it's: 65 turn
the first turn is 65
now it's: 66 turn
kill person: 66 lenth of survive: 78
the first turn is 66
now it's: 68 turn
the first turn is 68
now it's: 69 turn
kill person: 69 lenth of survive: 77
the first turn is 69
now it's: 71 turn
the first turn is 71
now it's: 72 turn
kill person: 72 lenth of survive: 76
the first turn is 72
now it's: 74 turn
the first turn is 74
now it's: 75 turn
kill person: 75 lenth of survive: 75
the first turn is 75
now it's: 77 turn
the first turn is 77
now it's: 78 turn
kill person: 78 lenth of survive: 74
the first turn is 78
now it's: 80 turn
the first turn is 80
now it's: 81 turn
kill person: 81 lenth of survive: 73
the first turn is 81
now it's: 83 turn
the first turn is 83
now it's: 84 turn
kill person: 84 lenth of survive: 72
the first turn is 84
now it's: 86 turn
the first turn is 86
now it's: 87 turn
kill person: 87 lenth of survive: 71
the first turn is 87
now it's: 89 turn
the first turn is 89
now it's: 90 turn
kill person: 90 lenth of survive: 70
the first turn is 90
now it's: 92 turn
the first turn is 92
now it's: 93 turn
kill person: 93 lenth of survive: 69
the first turn is 93
now it's: 95 turn
the first turn is 95
now it's: 96 turn
kill person: 96 lenth of survive: 68
the first turn is 96
now it's: 98 turn
the first turn is 98
now it's: 99 turn
kill person: 99 lenth of survive: 67
the first turn is 99
now it's: 1 turn
the first turn is 1
now it's: 2 turn
kill person: 2 lenth of survive: 66
the first turn is 2
now it's: 5 turn
the first turn is 5
now it's: 7 turn
kill person: 7 lenth of survive: 65
the first turn is 7
now it's: 10 turn
the first turn is 10
now it's: 11 turn
kill person: 11 lenth of survive: 64
the first turn is 11
now it's: 14 turn
the first turn is 14
now it's: 16 turn
kill person: 16 lenth of survive: 63
the first turn is 16
now it's: 19 turn
the first turn is 19
now it's: 20 turn
kill person: 20 lenth of survive: 62
the first turn is 20
now it's: 23 turn
the first turn is 23
now it's: 25 turn
kill person: 25 lenth of survive: 61
the first turn is 25
now it's: 28 turn
the first turn is 28
now it's: 29 turn
kill person: 29 lenth of survive: 60
the first turn is 29
now it's: 32 turn
the first turn is 32
now it's: 34 turn
kill person: 34 lenth of survive: 59
the first turn is 34
now it's: 37 turn
the first turn is 37
now it's: 38 turn
kill person: 38 lenth of survive: 58
the first turn is 38
now it's: 41 turn
the first turn is 41
now it's: 43 turn
kill person: 43 lenth of survive: 57
the first turn is 43
now it's: 46 turn
the first turn is 46
now it's: 47 turn
kill person: 47 lenth of survive: 56
the first turn is 47
now it's: 50 turn
the first turn is 50
now it's: 52 turn
kill person: 52 lenth of survive: 55
the first turn is 52
now it's: 55 turn
the first turn is 55
now it's: 56 turn
kill person: 56 lenth of survive: 54
the first turn is 56
now it's: 59 turn
the first turn is 59
now it's: 61 turn
kill person: 61 lenth of survive: 53
the first turn is 61
now it's: 64 turn
the first turn is 64
now it's: 65 turn
kill person: 65 lenth of survive: 52
the first turn is 65
now it's: 68 turn
the first turn is 68
now it's: 70 turn
kill person: 70 lenth of survive: 51
the first turn is 70
now it's: 73 turn
the first turn is 73
now it's: 74 turn
kill person: 74 lenth of survive: 50
the first turn is 74
now it's: 77 turn
the first turn is 77
now it's: 79 turn
kill person: 79 lenth of survive: 49
the first turn is 79
now it's: 82 turn
the first turn is 82
now it's: 83 turn
kill person: 83 lenth of survive: 48
the first turn is 83
now it's: 86 turn
the first turn is 86
now it's: 88 turn
kill person: 88 lenth of survive: 47
the first turn is 88
now it's: 91 turn
the first turn is 91
now it's: 92 turn
kill person: 92 lenth of survive: 46
the first turn is 92
now it's: 95 turn
the first turn is 95
now it's: 97 turn
kill person: 97 lenth of survive: 45
the first turn is 97
now it's: 100 turn
the first turn is 100
now it's: 1 turn
kill person: 1 lenth of survive: 44
the first turn is 1
now it's: 5 turn
the first turn is 5
now it's: 8 turn
kill person: 8 lenth of survive: 43
the first turn is 8
now it's: 13 turn
the first turn is 13
now it's: 14 turn
kill person: 14 lenth of survive: 42
the first turn is 14
now it's: 19 turn
the first turn is 19
now it's: 22 turn
kill person: 22 lenth of survive: 41
the first turn is 22
now it's: 26 turn
the first turn is 26
now it's: 28 turn
kill person: 28 lenth of survive: 40
the first turn is 28
now it's: 32 turn
the first turn is 32
now it's: 35 turn
kill person: 35 lenth of survive: 39
the first turn is 35
now it's: 40 turn
the first turn is 40
now it's: 41 turn
kill person: 41 lenth of survive: 38
the first turn is 41
now it's: 46 turn
the first turn is 46
now it's: 49 turn
kill person: 49 lenth of survive: 37
the first turn is 49
now it's: 53 turn
the first turn is 53
now it's: 55 turn
kill person: 55 lenth of survive: 36
the first turn is 55
now it's: 59 turn
the first turn is 59
now it's: 62 turn
kill person: 62 lenth of survive: 35
the first turn is 62
now it's: 67 turn
the first turn is 67
now it's: 68 turn
kill person: 68 lenth of survive: 34
the first turn is 68
now it's: 73 turn
the first turn is 73
now it's: 76 turn
kill person: 76 lenth of survive: 33
the first turn is 76
now it's: 80 turn
the first turn is 80
now it's: 82 turn
kill person: 82 lenth of survive: 32
the first turn is 82
now it's: 86 turn
the first turn is 86
now it's: 89 turn
kill person: 89 lenth of survive: 31
the first turn is 89
now it's: 94 turn
the first turn is 94
now it's: 95 turn
kill person: 95 lenth of survive: 30
the first turn is 95
now it's: 100 turn
the first turn is 100
now it's: 4 turn
kill person: 4 lenth of survive: 29
the first turn is 4
now it's: 10 turn
the first turn is 10
now it's: 13 turn
kill person: 13 lenth of survive: 28
the first turn is 13
now it's: 19 turn
the first turn is 19
now it's: 23 turn
kill person: 23 lenth of survive: 27
the first turn is 23
now it's: 31 turn
the first turn is 31
now it's: 32 turn
kill person: 32 lenth of survive: 26
the first turn is 32
now it's: 40 turn
the first turn is 40
now it's: 44 turn
kill person: 44 lenth of survive: 25
the first turn is 44
now it's: 50 turn
the first turn is 50
now it's: 53 turn
kill person: 53 lenth of survive: 24
the first turn is 53
now it's: 59 turn
the first turn is 59
now it's: 64 turn
kill person: 64 lenth of survive: 23
the first turn is 64
now it's: 71 turn
the first turn is 71
now it's: 73 turn
kill person: 73 lenth of survive: 22
the first turn is 73
now it's: 80 turn
the first turn is 80
now it's: 85 turn
kill person: 85 lenth of survive: 21
the first turn is 85
now it's: 91 turn
the first turn is 91
now it's: 94 turn
kill person: 94 lenth of survive: 20
the first turn is 94
now it's: 100 turn
the first turn is 100
now it's: 5 turn
kill person: 5 lenth of survive: 19
the first turn is 5
now it's: 17 turn
the first turn is 17
now it's: 19 turn
kill person: 19 lenth of survive: 18
the first turn is 19
now it's: 31 turn
the first turn is 31
now it's: 37 turn
kill person: 37 lenth of survive: 17
the first turn is 37
now it's: 46 turn
the first turn is 46
now it's: 50 turn
kill person: 50 lenth of survive: 16
the first turn is 50
now it's: 59 turn
the first turn is 59
now it's: 67 turn
kill person: 67 lenth of survive: 15
the first turn is 67
now it's: 77 turn
the first turn is 77
now it's: 80 turn
kill person: 80 lenth of survive: 14
the first turn is 80
now it's: 91 turn
the first turn is 91
now it's: 98 turn
kill person: 98 lenth of survive: 13
the first turn is 98
now it's: 10 turn
the first turn is 10
now it's: 17 turn
kill person: 17 lenth of survive: 12
the first turn is 17
now it's: 31 turn
the first turn is 31
now it's: 40 turn
kill person: 40 lenth of survive: 11
the first turn is 40
now it's: 58 turn
the first turn is 58
now it's: 59 turn
kill person: 59 lenth of survive: 10
the first turn is 59
now it's: 77 turn
the first turn is 77
now it's: 86 turn
kill person: 86 lenth of survive: 9
the first turn is 86
now it's: 100 turn
the first turn is 100
now it's: 10 turn
kill person: 10 lenth of survive: 8
the first turn is 10
now it's: 31 turn
the first turn is 31
now it's: 46 turn
kill person: 46 lenth of survive: 7
the first turn is 46
now it's: 71 turn
the first turn is 71
now it's: 77 turn
kill person: 77 lenth of survive: 6
the first turn is 77
now it's: 100 turn
the first turn is 100
now it's: 26 turn
kill person: 26 lenth of survive: 5
the first turn is 26
now it's: 58 turn
the first turn is 58
now it's: 71 turn
kill person: 71 lenth of survive: 4
the first turn is 71
now it's: 100 turn
the first turn is 100
now it's: 31 turn
kill person: 31 lenth of survive: 3
the first turn is 31
now it's: 91 turn
the first turn is 91
now it's: 100 turn
kill person: 100 lenth of survive: 2
the first turn is 100
now it's: 58 turn
the first turn is 58
now it's: 91 turn
kill person: 91 lenth of survive: 1
the first turn is 91
[3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 2, 7, 11, 16, 20, 25, 29, 34, 38, 43, 47, 52, 56, 61, 65, 70, 74, 79, 83, 88, 92, 97, 1, 8, 14, 22, 28, 35, 41, 49, 55, 62, 68, 76, 82, 89, 95, 4, 13, 23, 32, 44, 53, 64, 73, 85, 94, 5, 19, 37, 50, 67, 80, 98, 17, 40, 59, 86, 10, 46, 77, 26, 71, 31, 100, 91]
[58]
程序应该逻辑上是正确的。但是第一次Kill了3以后，4就不显示了呢？
排查下发现survive_person.remove(i)这个动作导致了问题。CSDN还是有大神的，https://blog.csdn.net/guan666/article/details/71511948 就描述了这个问题。
重新修改如下：
1 #!/usr/local/bin/python3
2 #! version 3.0.7
3 #! encode utf-8
4 import copy
5 import sys
6 def joseph(n,count):
7 n = 100
8 survive_person = list(range(1,n+1))
9 count = 3
10 temp = 1
11 round = 0
12 kill_person = []
13 while len(survive_person)>1 :
14 for i in survive_person :
15 print('now it\'s:',i,'turn','count is ',temp,end='\n')
16 if temp == count :
17 print('kill person:',i,'lenth of survive:',len(survive_person)-1,end='\n')
18 print('the first turn is ',i,end='\n')
19 kill_person.append(i)
20 cache = copy.deepcopy(survive_person)
21 cache.remove(i)
22 survive_person = copy.deepcopy(cache)
23 cache = []
24 temp = 0
25 temp += 1
26 round += 1
27 print(kill_person)
28 print(survive_person)
29 if __name__ == '__main__':
30 amount=input('please input amount:')
31 step=input('please input step:')
32 joseph(amount,step)
完美解决！！！