矩阵快速幂

先看看快速幂

const int mod = 1e9 + 7;
typedef long long ll;

ll ksm(ll a, ll n)
{
	ll ans = 1;
	while(n)
	{
		if(n & 1)
			ans = ans * a % mod;
		n >>= 1;
		a = a * a % mod;
	}
	return ans % mod;
}

快速幂的原理就不解释了， 矩阵快速幂就是把快速幂里整数相乘部分转化为矩阵相乘，本质一样。快速幂掌握之后，矩阵快速幂也能很快掌握。
代码见下：

#include <iostream>
#include <algorithm>
#include <cmath>
#include <cstring>
#include <cstdio>
#define mem(a, b) memset(a, b, sizeof(a))
using namespace std;

const int maxn = 1e2 + 10;
const int mod = 1e9 + 7;
typedef long long ll;
struct matrix{
	ll m[maxn][maxn];
}a, ans;

matrix multi(matrix x, matrix y, int n)
{
	matrix tem;
	for(int i = 1; i <= n; i++)
		for(int j = 1; j <= n; j++)
			tem.m[i][j] = 0;
	for(int i = 1; i <= n; i++)
		for(int j = 1; j <= n; j++)
			for(int k = 1; k <= n; k++)
				(tem.m[i][j] += x.m[i][k] * y.m[k][j] % mod) %= mod;
	return tem;
}

void quick(int n, ll k)
{
	for(int i = 1; i <= n; i++)
		for(int j = 1; j <= n; j++)
			if(i == j)
				ans.m[i][j] = 1;
			else
				ans.m[i][j] = 0;
	while(k)
	{	
		if(k & 1)
			ans = multi(ans, a, n);
		a = multi(a, a, n);
		k >>= 1;
	}
}

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