【POJ 1721】CARDS（置换群）

CARDS Time Limit: 1000MS   Memory Limit: 10000K Total Submissions: 1779   Accepted: 917 Description Alice and Bob have a set of N cards labelled with numbers 1 ... N (so that no two cards have the same label) and a shuffle machine. We assume that N is an odd integer.  The shuffle machine accepts the set of cards arranged in an arbitrary order and performs the following operation of double shuffle : for all positions i, 1 <= i <= N, if the card at the position i is j and the card at the position j is k, then after the completion of the operation of double shuffle, position i will hold the card k.  Alice and Bob play a game. Alice first writes down all the numbers from 1 to N in some random order: a1, a2, ..., aN. Then she arranges the cards so that the position ai holds the card numbered a i+1, for every 1 <= i <= N-1, while the position aN holds the card numbered a1.  This way, cards are put in some order x1, x2, ..., xN, where xi is the card at the i th position.  Now she sequentially performs S double shuffles using the shuffle machine described above. After that, the cards are arranged in some final order p1, p2, ..., pN which Alice reveals to Bob, together with the number S. Bob's task is to guess the order x1, x2, ..., xN in which Alice originally put the cards just before giving them to the shuffle machine.  Input The first line of the input contains two integers separated by a single blank character : the odd integer N, 1 <= N <= 1000, the number of cards, and the integer S, 1 <= S <= 1000, the number of double shuffle operations.  The following N lines describe the final order of cards after all the double shuffles have been performed such that for each i, 1 <= i <= N, the (i+1) st line of the input file contains pi (the card at the position i after all double shuffles).  Output The output should contain N lines which describe the order of cards just before they were given to the shuffle machine.  For each i, 1 <= i <= N, the ith line of the output file should contain xi (the card at the position i before the double shuffles).  Sample Input 7 4 6 3 1 2 4 7 5 Sample Output 4 7 5 6 1 2 3 Source CEOI 1998

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[题意][给出末状态和置换次数，求初状态]

【题解】【置换群】

【然而，只会暴力模拟呵，因为每次置换都是b[i]=a[a[i]]，所以求出用t次回到原位置，所以t次为一个循环，因为是m次变成当前状态，所以只要再转t-m%t次即可回到原位置，数据很弱，模拟即可】

#include
#include
#include
using namespace std;
int a[1010],cnt[1010],b[1010],n,m,t;
bool p;
int main()
{
	int i,j;
	scanf("%d%d",&n,&m);
	for(i=1;i<=n;++i) scanf("%d",&a[i]),cnt[i]=a[i];
	p=true;
	while(1)
	 {
	    t++;
		for(i=1;i<=n;++i) b[i]=a[a[i]];
		for(i=1;i<=n;++i)
		 if(cnt[i]!=b[i]) 
		  {p=false; break;} 
		if(p) break;
		p=true;
		for(i=1;i<=n;++i) a[i]=b[i];
	  } 
	for(i=1;i<=n;++i) a[i]=b[i];
	t=t-m%t;
	for(i=1;i<=t;++i) 
	 {
	 	for(j=1;j<=n;++j) b[j]=a[a[j]];
	 	for(j=1;j<=n;++j) a[j]=b[j];
	 }
	for(i=1;i<=n;++i) printf("%d\n",a[i]);
	return 0; 
}

转载于:https://www.cnblogs.com/lris-searching/p/9403140.html