题目链接
题意：A为一个方阵，则Tr A表示A的迹（就是主对角线上各项的和），现要求Tr(A^k)%9973。
思路：简单的矩阵快速幂
代码：
#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
using namespace std;
//typedef long long ll;
typedef __int64 ll;
const int MOD = 9973;
const int N = 15;
ll k;
int n;
struct mat{
int s[N][N];
mat() {
memset(s, 0, sizeof(s));
}
mat operator * (const mat& c) {
mat ans;
for (int i = 0; i < N; i++)
for (int j = 0; j < N; j++)
for (int k = 0; k < N; k++)
ans.s[i][j] = (ans.s[i][j] + s[i][k] * c.s[k][j]) % MOD;
return ans;
}
};
mat state;
mat pow_mod(ll k) {
if (k == 1)
return state;
mat a = pow_mod(k / 2);
mat ans = a * a;
if (k % 2)
ans = ans * state;
return ans;
}
int main() {
int cas;
scanf("%d", &cas);
while (cas--) {
scanf("%d%I64d", &n, &k);
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
scanf("%d", &state.s[i][j]);
mat c = pow_mod(k);
int ans = 0;
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
if (i == j)
ans += c.s[i][j];
printf("%d
", ans % MOD);
}
return 0;
}
题目链接