HDU 2256 Problem of Precision (矩阵快速幂)

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=2256

最重要的是构建递推式，下面的图是盗来的。貌似这种叫共轭数。

#include <iostream>
#include <cstdio>
#include <cmath>
#include <cstring>
#include <algorithm>
using namespace std;
const int mod = 1024;
struct data {
    int mat[3][3];
    data() {}
    data(int x, int y, int z1 = 0, int z2 = 0) {
        mat[1][1] = x, mat[1][2] = y;
        mat[2][1] = z1, mat[2][2] = z2;
    }
};

data operator* (data a, data b) {
    data ans;
    for(int i = 1; i <= 2; ++i) {
        for(int j = 1; j <= 2; ++j) {
            ans.mat[i][j] = 0;
            for(int k = 1; k <= 2; ++k)
                ans.mat[i][j] = (ans.mat[i][j] + a.mat[i][k] * b.mat[k][j] % mod) % mod;
        }
    }
    return ans;
}

data operator^ (data a, int n) {
    data ans;
    for(int i = 1; i <= 2; ++i) {
        for(int j = 1; j <= 2; ++j) {
            ans.mat[i][j] = (i == j);
        }
    }
    while(n) {
        if(n & 1)
            ans = ans * a;
        a = a * a;
        n >>= 1;
    }
    return ans;
}

int main()
{
    int t, n;
    scanf("%d", &t);
    while(t--) {
        scanf("%d", &n);
        data ans(5, 2);
        data a(5, 2, 12, 5);
        a = a ^ (n - 1);
        ans = ans * a;
        printf("%d\n", (ans.mat[1][1] * 2 - 1 + mod) % mod);
    }
    return 0;
}