《置换群》

离散数学都快还给老师了。。

对于一个置换群P，它的一阶等于他本身。

那么这里我们求P的二阶，应该是对P * P，P对P轮换。

$\begin{pmatrix}1 & 2 & 3\\ a1 & a2 & a3\end{pmatrix} * \begin{pmatrix}1 & 2 & 3\\ b1 & b2 & b3\end{pmatrix} =\begin{pmatrix}1 & 2 & 3\\ b(a1) & b(a2) & b(a3) \end{pmatrix}$

注意三阶应该是P的二阶对P的一阶置换。一开始算的时候一直拿P的二阶对P的二阶置换结果陷入了循环中。。

 性质：https://blog.csdn.net/qq_36102055/article/details/107726401

POJ-1721:

#include<iostream>
#include<stdio.h>
#include<queue>
#include<algorithm>
#include<math.h>
#include<stack>
#include<map>
#include<limits.h>
#include<vector>
#include<string.h>
#include<string>
using namespace std;
typedef long long LL;
typedef pair<LL,int> pii;
const int N = 1e3 + 5;
const int M = 1e5 + 5;
const LL Mod = 199999;
#define pi acos(-1)
#define INF 1e9
#define dbg(ax) cout << "now this num is " << ax << endl;
namespace FASTIO{
    inline LL read(){
        LL x = 0,f = 1;char c = getchar();
        while(c < '0' || c > '9'){if(c == '-') f = -1;c = getchar();}
        while(c >= '0' && c <= '9'){x = (x<<1)+(x<<3)+(c^48);c = getchar();}
        return x*f;
    }
    void print(int x){
        if(x < 0){x = -x;putchar('-');}
        if(x > 9) print(x/10);
        putchar(x%10+'0');
    }
}
using namespace FASTIO;

int n,s,a[N],pp[N],p[N];
bool solve() {
    for(int i = 1;i <= n;++i) {
        pp[i] = p[p[i]];
    }
    for(int i = 1;i <= n;++i) p[i] = pp[i];
    for(int i = 1;i <= n;++i) {
        if(p[i] != a[i]) return false;
    }
    return true;
}
void solve2() {
    for(int i = 1;i <= n;++i) pp[i] = p[p[i]];
    for(int i = 1;i <= n;++i) p[i] = pp[i];
}
int main() {
    while(cin >> n >> s) {
        for(int i = 1;i <= n;++i) a[i] = read(),p[i] = a[i];
        int len = 0;
        while(1) {
            ++len;
            if(solve()) break;
        }
        int ch = len - s % len;
        for(int i = 1;i <= n;++i) p[i] = a[i];
        while(ch--) solve2();
        for(int i = 1;i <= n;++i) printf("%d\n",p[i]);
    }

    system("pause");
    return 0;
}