Author: zyy
Date: 20250709
tag: 矩阵乘法
link: https://www.luogu.com.cn/problem/P3390

题目描述

link

分析

矩阵乘法具有结合律，因此矩阵可以进行快速幂

代码实现

#include<bits/stdc++.h>
using namespace std;
const int N = 110;
const int Mod = 1e9 + 7;
typedef long long LL;

LL n, k;
LL a[N][N], ans[N][N];

inline void mul(LL a[N][N], LL b[N][N]) {
    LL c[N][N] = {0};// k > 1 c数组一定要清空
    for (int i = 1; i <= n; i++)
        for (int j = 1; j <= n; j++)
            for (int k = 1; k <= n; k++)
                c[i][j] = (c[i][j] + a[i][k] * b[k][j]) % Mod;
    memcpy(a, c, sizeof c);
}

inline void qmi(LL k) {
    // 初始化ans为单位矩阵
    for (int i = 1; i <= n; i++)
        ans[i][i] = 1;
    
    while (k) {
        if (k & 1) mul(ans, a);
        mul(a, a);
        k >>= 1;
    }
}

int main() {
    cin >> n >> k;
    for (int i = 1; i <= n; i++)
        for (int j = 1; j <= n; j++)
            cin >> a[i][j];
    
    qmi(k);
    
    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= n; j++)
            cout << ans[i][j] << " ";
        cout << endl;
    }
    return 0;
}