HDU-置换群

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问题及代码：
/*  *Copyright (c)2014,烟台大学计算机与控制工程学院  *All rights reserved.  *文件名称：HDU.cpp  *作    者：单昕昕  *完成日期：2015年1月27日  *版 本 号：v1.0  *问题描述：As a unicorn, the ability of using magic is the distinguishing feature among other kind of pony. Being familiar with composition and decomposition is the fundamental course for a young unicorn. Twilight Sparkle is interested in the decomposition of permutations. A permutation of a set S = {1, 2, ..., n} is a bijection from S to itself. In the great magician —— Cauchy's two-line notation, one lists the elements of set S in the first row, and then for each element, writes its image under the permutation below it in the second row. For instance, a permutation of set {1, 2, 3, 4, 5} σ can be written as:<img src="http://img.blog.csdn.net/20150127221620625?watermark/2/text/aHR0cDovL2Jsb2cuY3Nkbi5uZXQvTUlLQVNBMw==/font/5a6L5L2T/fontsize/400/fill/I0JBQkFCMA==/dissolve/70/gravity/Center" alt="" />Here σ(1) = 2, σ(2) = 5, σ(3) = 4, σ(4) = 3, and σ(5) = 1.Twilight Sparkle is going to decompose the permutation into some disjoint cycles. For instance, the above permutation can be rewritten as:<img src="http://img.blog.csdn.net/20150127221734621?watermark/2/text/aHR0cDovL2Jsb2cuY3Nkbi5uZXQvTUlLQVNBMw==/font/5a6L5L2T/fontsize/400/fill/I0JBQkFCMA==/dissolve/70/gravity/Center" alt="" />Help Twilight Sparkle find the lexicographic smallest solution. (Only considering numbers). *程序输入：Input contains multiple test cases (less than 10). For each test case, the first line contains one number n (1<=n<=10^5). The second line contains n numbers which the i-th of them(start from 1) is σ(i). *程序输出：For each case, output the corresponding result. Sample Input52 5 4 3 131 2 3Sample Output(1 2 5)(3 4)(1)(2)(3)*/#include<cstdio>#include<cstring>#include<iostream>using namespace std;const int MAX=100000;int main(){    std::ios::sync_with_stdio(false);    int n,i,j,k;    int a[MAX];    while(cin>>n)    {        for(i=1; i<=n; i++)            cin>>a[i];        for(i=1; i<=n; i++)        {            while(a[i])            {                cout<<"("<<i;                j=a[i];                a[i]=0;                while(a[j])                {                    cout<<" "<<j;                    k=a[j];                    a[j]=0;                    j=k;                }                cout<<")";            }        }        puts("");    }    return 0;}
运行结果：
知识点总结：
置换群。
学习心得：
就是按规律置换。
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