解題區/解題區 - UVa

UVa 12792 - Shuffled Deck

contents

  1. 1. Problem
  2. 2. Sample Input
  3. 3. Sample Output
  4. 4. Solution

Problem

給定一種洗牌方式，請問重複多少次之後會復原到原本一開始的排列。

Sample Input

1
2
3
4
4
6
2
100002

Sample Output

1
2
3
4
4
3
2
100002

Solution

一道置換群的題目，將置換的方式找出，接著找一組一組循環置換集合，找到最小公倍數即可。

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#include <stdio.h>
#include <algorithm>
using namespace std;
int A[1<<21], used[1<<21] = {};
int testcase = 0;
long long gcd(long long x, long long y) {
    long long t;
    while (x%y)
        t = x, x = y, y = t%y;
    return y;
}
int main() {
    int n;
    while (scanf("%d", &n) == 1) {
        for (int i = 0; i < n; i++) {
            if (i&1)
                A[i] = i/2;
            else
                A[i] = i/2 + n/2;
        }
        
        testcase++;
        long long lcm = 1;
        for (int i = 0; i < n; i++) {
            if (A[i] != i && used[i] != testcase) {
                int ss = 0;
                for (int j = i; used[j] != testcase; j = A[j])
                    used[j] = testcase, ss++;
                lcm = lcm / gcd(lcm, ss) * ss;
            }
        }
        printf("%d\n", lcm);
    }
    return 0;
}
/*
4
6
2
100002
*/