矩阵快速幂

原理

见《进阶指南》第156页。

模板题

洛谷-P3390-【模板】矩阵快速幂

#include <iostream>
#include <cstring>
using namespace std;

typedef long long LL;
const int N = 110, M = 1e9 + 7;
LL n, k;
int a[N][N], res[N][N];

void mul (int a[N][N], int b[N][N], int c[N][N]) {
    int res[N][N];
    memset(res, 0, sizeof(res));
    for (int i = 0; i < N; ++ i)
        for (int k = 0; k < N; ++ k)
            for (int j = 0; j < N; ++ j)
                res[i][j] = (res[i][j] + (LL)a[i][k] * b[k][j]) % M;
    memcpy(c, res, sizeof(res));
}

int main () {
    cin >> n >> k;
    for (int i = 0; i < n; ++ i)
        for (int j = 0; j < n; ++ j)
            cin >> a[i][j];
    
    for (int i = 0; i < n; ++ i) res[i][i] = 1;
    while (k > 0) {
        if (k & 1) mul(res, a, res);
        mul(a, a, a);
        k /= 2;
    }

    for (int i = 0; i < n; ++ i) {
        for (int j = 0; j < n; ++ j)
            cout << res[i][j] << ' ';
        cout << endl;
    }
    return 0;
}