poj3734 Blocks

思路：

递推 + 快速幂优化。

实现：

#include <iostream>
#include <cstdio>
#include <vector> 
using namespace std;
typedef vector<vector<int> > matrix;

const int MOD = 10007;

matrix multiply(matrix & a, matrix & b)
{
    matrix c(a.size(), vector<int>(b[0].size()));
    for (int i = 0; i < a.size(); i++)
    {
        for (int k = 0; k < a[0].size(); k++)
        {
            for (int j = 0; j < b[0].size(); j++)
            {
                c[i][j] = (c[i][j] + a[i][k] * b[k][j]) % MOD;
            }
        }
    }
    return c;
}

matrix pow(matrix & a, long long n)
{
    matrix res(a.size(), vector<int>(a[0].size()));
    for (int i = 0; i < a.size(); i++)
    {
        res[i][i] = 1;
    }
    while (n > 0)
    {
        if (n & 1)
            res = multiply(res, a);
        a = multiply(a, a);
        n >>= 1;
    }
    return res;
}
int main()
{
    int t;
    long long n;
    cin >> t;
    while (t--)
    {
        scanf("%lld", &n);
        matrix a(3, vector<int>(3));
        a[0][0] = 2; a[0][1] = 1; 
        a[1][0] = 2; a[1][1] = 2; a[1][2] = 2;
                     a[2][1] = 1; a[2][2] = 2;
        a = pow(a, n);
        matrix b(3, vector<int>(1));
        b[0][0] = 1;
        b[1][0] = 0;
        b[2][0] = 0;
        a = multiply(a, b);
        cout << a[0][0] << endl;
    }
    return 0;    
}