矩阵快速幂及应用

luogu 模板： https://www.luogu.com.cn/problem/P3390

矩阵快速幂

#include <bits/stdc++.h>
using namespace std;
#define LL long long
const int N = 110, mod = 1e9 + 7;
LL n, k, a[N][N], b[N][N], t[N][N];
void matrixQp(LL y){
	while (y){
		if (y & 1){
			memset(t, 0, sizeof t);
			for (int i = 1; i <= n; i ++ )
				for (int j = 1; j <= n; j ++ )
					for (int k = 1; k <= n; k ++ )
						t[i][j] = ( t[i][j] + (a[i][k] * b[k][j]) % mod ) % mod;
			memcpy(b, t, sizeof t);
		}
		y >>= 1;
		memset(t, 0, sizeof t);
		for (int i = 1; i <= n; i ++ )
			for (int j = 1; j <= n; j ++ )
				for (int k = 1; k <= n; k ++ )
					t[i][j] = ( t[i][j] + (a[i][k] * a[k][j]) % mod ) % mod;
		memcpy(a, t, sizeof t);
	}
}
int main(){
	cin >> n >> k;
	for (int i = 1; i <= n; i ++ )
		for (int j = 1; j <= n; j ++ ){
			cin >> b[i][j];
			a[i][j] = b[i][j];
		}
	matrixQp(k - 1);
	for (int i = 1; i <= n; i ++ )
		for (int j = 1; j <= n; j ++ )
			cout << b[i][j] << " \n"[j == n];
	return 0;
}

https://www.luogu.com.cn/problem/P1939

矩阵加速

#include <bits/stdc++.h>
using namespace std;
#define LL long long
const int mod = 1e9 + 7;
LL T, n, t[5][5], a[5][5], b[5][5];
void matrixQp(LL y){
	while (y){
		if (y & 1){
			memset(t, 0, sizeof t);
			for (int i = 1; i <= 3; i ++ )
				for (int j = 1; j <= 1; j ++ )
					for (int k = 1; k <= 3; k ++ )
						t[i][j] = ( t[i][j] + (a[i][k] * b[k][j]) % mod ) % mod;
			memcpy(b, t, sizeof t);
		}
		y >>= 1;
		memset(t, 0, sizeof t);
		for (int i = 1; i <= 3; i ++ )
			for (int j = 1; j <= 3; j ++ )
				for (int k = 1; k <= 3; k ++ )
					t[i][j] = ( t[i][j] + (a[i][k] * a[k][j]) % mod ) % mod;
		memcpy(a, t, sizeof t);
	}
}
void init(){
	b[1][1] = b[2][1] = b[3][1] = 1;
	memset(a, 0, sizeof a);
	a[1][1] = a[2][1] = a[1][3] = a[3][2] = 1;
}
void solve(){
	cin >> n;
	if (n <= 3) cout << "1\n";
	else{
		init();
		matrixQp(n - 3);
		cout << b[1][1] << "\n";
	}
}
int main(){
	cin >> T;
	while ( T -- )
		solve();
	return 0;
}