约瑟环的python实现（举例说明）

2019-11-08 02:29:59

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来源：转载

供稿：网友

题目是： N个人围成一圈报数，报到某一个数m的就出局，问你最后剩下来的人的号码？

网上通用约瑟夫环的算法是：

//函数接收n和m，返回最后出圈的是第几个人 /*e.g. yuesefu(5,2)=3 yuesefu(2,100)=1*/ int yuesefu(int n,int m) { int i,r=0; for (i=2;i <=n;i++) r=(r+m)%i; return r+1; }

用python实现上面算法为：

def yuesefu2(n, m): # 网上常见方法，答案准确 # yuesefu2(50, 5)=19 i = 0 r = 0 for i in range(2, n + 1): r = (r + m) % i return r + 1

用python模拟报数出局的方法为：

def yuesefu3(n, m): a = range(1, n + 1) b = [] i = 0 # 指针 while n > 1: i = i + m if i > n: i = i % n b.append(a.pop(i - 1)) # PRint a.pop(i-1) n = n - 1 i = i - 1 if i == n or i == -1: # 特别处理，如果正好弹出最后一个，i值归0 i = 0 b.append(a[0]) return bif __name__ == '__main__': n = 60 m = 99 print u'约瑟环2:' + str(yuesefu2(n, m)) print u'约瑟环3:' + str(yuesefu3(n, m))

50人报5出局答案，及出局顺序为：约瑟环2:19 约瑟环3:[5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 6, 12, 18, 24, 31, 37, 43, 49, 7, 14, 22, 29, 38, 46, 3, 13, 23, 33, 42, 2, 16, 27, 39, 1, 17, 32, 47, 11, 34, 4, 26, 48, 28, 9, 44, 41, 8, 21, 36, 19]

30人报3出局答案，及出局顺序为：约瑟环2:29 约瑟环3:[3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 4, 8, 13, 17, 22, 26, 1, 7, 14, 20, 28, 5, 16, 25, 10, 23, 11, 2, 19, 29]

60人报99出局答案，及出局顺序为：约瑟环2:55 约瑟环3:[39, 19, 1, 45, 30, 17, 7, 58, 52, 48, 46, 47, 51, 57, 6, 16, 29, 44, 10, 32, 2, 31, 9, 43, 28, 21, 14, 13, 20, 27, 42, 8, 38, 22, 4, 60, 11, 26, 54, 36, 34, 41, 12, 56, 5, 40, 49, 23, 33, 25, 18, 15, 37, 50, 59, 53, 24, 3, 35, 55]

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