poj3233 Matrix Power Series

思路：

递推 + 快速幂优化。

实现：

#include <iostream>
#include <vector>
using namespace std;

typedef vector<vector<int> > matrix;

matrix multiply(matrix & a, matrix & b, int MOD)
{
    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, int n, int m)
{
    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, m);
        a = multiply(a, a, m);
        n >>= 1;
    }
    return res;
}

int main()
{
    int n, k, m;
    cin >> n >> k >> m;
    matrix a(n * 2, vector<int>(n, 0)), b(n * 2, vector<int>(n * 2, 0));
    for (int i = 0; i < n; i++)
    {
        for (int j = 0; j < n; j++)
        {
            cin >> b[i][j];
        }
    }
    for (int i = 0; i < n; i++)
    {
        a[i][i] = b[n + i][i] = b[n + i][n + i] = 1;
    }
    matrix b_k = pow(b, k + 1, m);
    matrix ans = multiply(b_k, a, m);
    for (int i = 0; i < n; i++)
    {
        for (int j = 0; j < n; j++)
        {
            int tmp = ans[n + i][j];
            if (i == j) tmp = (tmp - 1 + m) % m;
            cout << tmp << " ";
        }
        cout << endl;
    }
    return 0;
}