[dynamic programming] leetcode 688 Knight Probability in Chessboard

problem: https://leetcode.com/problems/knight-probability-in-chessboard/

         This is an easy problem using dfs.

class Solution {
public:
    vector<int> dx{1,2,2,1,-1,-2,-2,-1};
    vector<int> dy{2,1,-1,-2,-2,-1,1,2};
    vector<vector<vector<double>>> dp;
    double knightProbability(int N, int K, int r, int c) {
        double res = 0.0;
        if(K == 0) return 1.0;
        if(dp.empty())
        {
            dp.resize(K + 1, vector<vector<double>>(N, vector<double>(N, -1)));
        }
        if(dp[K][r][c] != -1) return dp[K][r][c];
        for(int k = 0;k < 8 ;k++)
        {
            int x = r + dx[k];
            int y = c + dy[k];
            if(x >= 0 && x < N && y >= 0 && y < N)
            {
                res += knightProbability(N, K - 1, x, y) * 0.125;
            }
        }
        return dp[K][r][c] = res;
    }
};