链接:http://poj.org/problem?id=1286 http://poj.org/problem?id=2409 #include <cstdio> #include <iostream> #include <cstring> #include <cmath> #include <algorithm> using namespace std; typedef long long LL; LL P_M( LL a, LL b ) {…

http://poj.org/problem?id=1286 题意:有红.绿.蓝三种颜色的n个珠子.要把它们构成一个项链,问有多少种不同的方法.旋转和翻转后同样的属于同一种方法. polya计数. 搜了一篇论文Pólya原理及其应用看了看polya究竟是什么东东.它主要计算所有互异的组合的个数.对置换群还是似懂略懂.用polya定理解决这个问题的关键是找出置换群的个数及哪些置换群,每种置换的循环节数.像这样的不同颜色的珠子构成项链的问题能够把N个珠子看成正N边形. Polya定理:(1)设G是p…

Necklace of Beads Time Limit: 1000MS   Memory Limit: 10000K Total Submissions: 7763   Accepted: 3247 Description Beads of red, blue or green colors are connected together into a circular necklace of n beads ( n < 24 ). If the repetitions that are pro…

Necklace of Beads Time Limit: 1000MS   Memory Limit: 10000K Total Submissions: 7874   Accepted: 3290 Description Beads of red, blue or green colors are connected together into a circular necklace of n beads ( n < 24 ). If the repetitions that are pro…

Necklace of Beads 大意:3种颜色的珠子,n个串在一起,旋转变换跟反转变换假设同样就算是同一种,问会有多少种不同的组合. 思路:正规学Polya的第一道题,在楠神的带领下,理解的还算挺快的.代码没什么好说的,裸的Polya.也不须要优化. /************************************************************************* > File Name: POJ1286.cpp > Author: GLSilence &…

题目:http://poj.org/problem?id=2409 题意:用k种不同的颜色给长度为n的项链染色 网上大神的题解: 1.旋转置换:一个有n个旋转置换,依次为旋转0,1,2,```n-1.对每一个旋转置换,它循环分解之后得到的循环因子个数为gcd(n,i). 2.翻转置换:分奇偶讨论. 奇数的时候 翻转轴 = (顶点+对边终点的连线),一共有n个顶点,故有n个置换,且每个置换分解之后的因子个数为n/2+1; 偶数的时候 翻转轴 = (顶点+顶点的连线),一共有n个顶点,故有n/2个置…

和poj 2409差不多,就是k变成3了,详见 还有不一样的地方是记得特判n==0的情况不然会RE #include<iostream> #include<cstdio> using namespace std; long long n,ans; long long ksm(long long a,long long b) { long long r=1; while(b) { if(b&1) r=r*a; a=a*a; b>>=1; } return r; }…

Description Beads of red, blue or green colors are connected together into a circular necklace of n beads ( n < 24 ). If the repetitions that are produced by rotation around the center of the circular necklace or reflection to the axis of symmetry ar…

  Description Beads of red, blue or green colors are connected together into a circular necklace of n beads ( n < ). If the repetitions that are produced by rotation around the center of the circular necklace or reflection to the axis of symmetry are…

这是做的第一道群论题,自然要很水又很裸.注意用long long. 就是用到了两个定理 burnside :不等价方案数=每个置换的不动置换方案数的和 / 置换个数 polya: 一个置换的不动置换方案数=k^(这个置换的循环个数) 先看第一个博客再看第二个 http://cxjyxx.me/?p=198 http://endlesscount.blog.163.com/blog/static/82119787201221324524202/ 这两个蛮好的,上代码: #include <cstd…