hdu 1575 矩阵幂对角线和_杭电对角线矩阵java-优快云博客

本文链接：https://blog.youkuaiyun.com/ADjky/article/details/52746507

本文提供了一种使用C++实现的矩阵快速幂算法来解决HDU1575问题的方法。该算法通过构造特定的矩阵并利用快速幂运算，有效地计算了给定矩阵的高次幂，特别适用于解决与矩阵有关的问题。

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矩阵裸题，直接上代码.

code:

/*
adrui's submission 
Language : C++
Result : Accepted
Love : ll
Favorite : Dragon Balls

Standing in the Hall of Fame
*/



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

#define debug 0
#define LL long long
#define mod 9973
#define M(a, b) memset(a, b, sizeof(a))

const int maxn(15);
int n, k;

struct Matrix {
	int mat[maxn][maxn];
	void init() {
		M(mat, 0);
		for (int i = 0; i < n; i++)
			mat[i][i] = 1;
	}
};

Matrix operator * (Matrix a, Matrix t) {				//矩阵乘法
	Matrix c;
	M(c.mat, 0);

	for (int i = 0; i < n; i++)
		for (int j = 0; j < n; j++)
		{
			for (int k = 0; k < n; k++)
				c.mat[i][j] += (a.mat[i][k] * t.mat[k][j]) % mod;
			c.mat[i][j] %= mod;
		}

	return c;
}
Matrix operator ^ (Matrix tmp, int b) {					//快速幂
	Matrix res;
	res.init();

	while (b) {
		if (b & 1) res = res * tmp;
		tmp = tmp * tmp;
		b >>= 1;
	}

	return res;
}
int main() {
#if debug
	freopen("in.txt", "r", stdin);
#endif //debug
	
	int t;
	scanf("%d", &t);
	while (t--) {
		scanf("%d%d", &n, &k);
		Matrix tmp;
		M(tmp.mat, 0);										//构造底数矩阵
		for (int i = 0; i < n; i++)
			for (int j = 0; j < n; j++)
				scanf("%d", &tmp.mat[i][j]);

		Matrix res = tmp ^ k;								//快速幂
		int ans = 0;
		for (int i = 0; i < n; i++)
			ans = (ans + res.mat[i][i]) % mod;				//对角线
		printf("%d\n", ans);								//ans
	}
	return 0;
}</span>