62.Unique-Paths.cpp

// Top Down Solution (Recursive)
class Solution {
public:
    int solve(int i, int j, int &m, int &n, vector<vector<int>> &dp){
        if(i >= m || j >= n) return 0;
        if(i == m - 1 && j == n - 1) return 1;
        if(dp[i][j] != -1) return dp[i][j];
        return dp[i][j] = solve(i + 1, j, m, n, dp) + solve(i, j + 1, m, n, dp);
    }
    int uniquePaths(int m, int n) {
        vector<vector<int>> dp(m, vector<int>(n, -1));
        return solve(0, 0, m, n, dp);
    }
};

// Bottom Up Solution (Iterative)
class Solution {
public:
    int uniquePaths(int m, int n) {
        vector<vector<int>> dp(m, vector<int>(n));
        for(int i = 0; i < m; i++) dp[i][0] = 1;
        for(int i = 0; i < n; i++) dp[0][i] = 1;
        for(int i = 1; i < m; i++){
            for(int j = 1; j < n; j++){
                dp[i][j] = dp[i][j - 1] + dp[i - 1][j];
            }
        }
        return dp[m - 1][n - 1];
    }
};