【模板】矩阵快速幂

单位矩阵相当于普通乘法算术中的单位元。

代码如下

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

struct matrix {
	LL mat[maxn][maxn];
	int n, m;
	matrix(int n, int m) : n(n), m(m) {
		memset(mat, 0, sizeof(mat));
	}
	LL *operator[](int x) {
		return mat[x];
	}
	friend matrix operator*(matrix &x, matrix &y) {
		matrix z(x.n, y.m);
		for (int i = 1; i <= x.n; i++) {
			for (int j = 1; j <= y.m; j++) {
				for (int k = 1; k <= x.m; k++) {
					z[i][j] = (z[i][j] + x[i][k] * y[k][j] % mod) % mod;
				}
			}
		}
		return z;
	}
};

int n; LL K;

int main() {
	scanf("%d %lld", &n, &K);
	matrix a(n, n), id(n, n);
	for (int i = 1; i <= n; i++) {
		for (int j = 1; j <= n; j++) {
			scanf("%lld", &a[i][j]);
		}
	}
	for (int i = 1; i <= n; i++) {
		id[i][i] = 1;
	}
	for (; K; K >>= 1, a = a * a) {
		if (K & 1) {
			id = id * a;
		}
	}
	for (int i = 1; i <= n; i++) {
		for (int j = 1; j <= n; j++) {
			printf("%lld ", id[i][j]);
		}
		printf("
");
	}
	return 0;
}