矩阵快速幂,比较赤裸····,最后求出的矩阵,把对角线之和求出来就可以了,现在我比较纠结的是构造矩阵····
#include<iostream>
#include<cstdio>
#include<string.h>
#include<string>
#include<set>
#include<algorithm>
#include<cmath>
#define ll __int64
#define MAX 1000009
using namespace std;
int n;
const int mod = 9973;
struct Matrix
{
int m[12][12];
};
Matrix mul(Matrix a,Matrix b) //¾ØÕó³Ë·¨
{
int i,j,k;
Matrix c;
for (i = 0 ; i < n; i++)
for (j = 0; j < n; j++)
{
c.m[i][j] = 0;
for (k = 0; k < n; k++)
c.m[i][j] += (a.m[i][k] * b.m[k][j])%mod;
c.m[i][j] %= mod;
}
return c;
}
Matrix pow(Matrix a,Matrix b,int x)//µÝ¹éÇó¿ìËÙÃÝ
{
while (x)
{
if (x & 1)
b = mul(b,a);
x = x >> 1;
a = mul(a,a);
}
return b;
}
int main()
{
int k;
int t;
Matrix A,B;
scanf("%d",&t);
while(t--)
{
scanf("%d%d",&n,&k);
for(int i = 0; i<n; i++)
{
for(int j = 0; j<n; j++)
{
scanf("%d",&A.m[i][j]);
B.m[i][j] = A.m[i][j];
}
}
Matrix C = pow(A,B,k-1);
int ans = 0;
for(int i = 0; i<n; i++)
ans = (ans + C.m[i][i])%mod;
printf("%d\n",ans);
}
return 0;
}
本文介绍了一种利用矩阵快速幂算法求解特定矩阵对角线之和的高效方法,适用于复杂矩阵运算场景。
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