poj 1721 CARDS（置换）_cardsalice and bob have a set of n cards labelled -优快云博客

本文链接：https://blog.youkuaiyun.com/clover_hxy/article/details/51468748

本文介绍了一种基于逆向思维的算法挑战，玩家需根据最终卡片排列及操作次数推算初始状态。通过分析循环特性，文章提供了一种高效求解策略。

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CARDS

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 1776		Accepted: 916

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

Sample Output

Source

CEOI 1998

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题目大意：给你目标状态和置换的次数，请你求出初始状态。

题解：置换。

通过找规律可以发现，这个序列是存在循环节的，即置换多少次后就会又变回原来的状态。

那么我们可以用置换次数%循环节，然后在置换t-m%t次即为答案。（m为置换次数，t为循环节）

#include<iostream>  
#include<cstdio>  
#include<cstring>  
#include<algorithm>  
#include<cmath>  
#define N 1003   
using namespace std;  
int n,m;  
int cnt[N],a[N],ans[N],l[N],use[N],b[N];  
int main()  
{  
    //freopen("a.in","r",stdin);
    //freopen("my.out","w",stdout);
    scanf("%d%d",&n,&m);  
    int maxn=0;  
    for (int i=1;i<=n;i++)  
     scanf("%d",&a[i]),cnt[i]=a[i];
    bool flag=1;  int t=0;
    while (1){
    	t++;
    	for (int i=1;i<=n;i++)  b[i]=a[a[i]];
    	for (int i=1;i<=n;i++)
    	 if (cnt[i]!=b[i]) {
    	 	flag=false;
    	 	break;
    	 }
    	if (flag)  break;
    	flag=true;
    	for (int i=1;i<=n;i++) a[i]=b[i];
    }
    for (int i=1;i<=n;i++) a[i]=b[i];
    t=t-m%t;
    for (int i=1;i<=t;i++){
    	for (int j=1;j<=n;j++)  b[j]=a[a[j]];
    	for (int j=1;j<=n;j++)  a[j]=b[j];
    }
    for (int i=1;i<=n;i++)  
      printf("%d\n",a[i]);  
}