$f(i, j)=f(i-1, j)+f(i, j-1)$

class Solution {
public:
    int uniquePaths(int n, int m) {
        vector<vector<int>> f(n, vector<int>(m));
        for (int i = 0; i < n; i++) f[i][0] = 1;
        for (int j = 0; j < m; j++) f[0][j] = 1;
        for (int i = 1; i < n; i++) {
            for (int j = 1; j < m; j++) {
                f[i][j] = f[i - 1][j] + f[i][j - 1];
            }
        }

        /*
        for (auto x : f) {
            for (auto y : x) cout << y << " ";
            cout << endl;
        }
        */
        return f[n - 1][m - 1];
    }
};

April 12, 2024

class Solution {
public:
    int uniquePaths(int n, int m) {
        vector<vector<int>> f(n + 1, vector<int>(m + 1));
        for (int i = 1; i <= n; i++) {
            for (int j = 1; j <= m; j++) {
                if (i == 1 && j == 1) f[i][j] = 1;
                else f[i][j] = f[i - 1][j] + f[i][j - 1];
            }
        }
        return f[n][m];
    }
};