f(x, y) = f(x - 1, y) + f(x, y - 1)

f-x-y-recursion

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

class Solution {
public:
    int f(int x, int y) {
        vec.resize(x + 1);
        for (int i = 0; i < x + 1; ++i) {
            vec[i] = vector<int>(y + 1, 0);
            vec[i][0] = 2;
        }
        for (int i = 0; i < y + 1; ++i) {
            vec[0][i] = 2;
        }
        return cal(x, y);
    }
    
    int g(int x, int y) {
        if (x == 0 || y == 0) {
            return 2;
        }
        return g(x - 1, y) + g(x, y - 1);
    }
    
private:
    int cal(int x, int y) {
        if (vec[x][y] != 0) {
            return vec[x][y];
        }
        vec[x][y] = cal(x - 1, y) + cal(x, y - 1);
        return vec[x][y];
    }
    
private:
    vector<vector<int> > vec;
};

int main() {
    cout << Solution().f(20, 20) << endl;
    cout << Solution().g(15, 15) << endl;
    return 0;
}