64. Minimum Path Sum

Recursive Solution

int getMinPath(vector <vector <int>> &grid, int i, int j) {
        if (i == 0 && j == 0) {
            return grid[i][j];
        }
        int m = INT_MAX;
        if (j > 0) {
            m = grid[i][j] + getMinPath(grid, i, j - 1);
        }
        if (i > 0) {
            int s = grid[i][j] + getMinPath(grid, i - 1, j);
            m = min(m, s);
        }
        return m;
    }
    


Top Down DP - Memoization

int getMinPath(vector <vector <int>> &grid, int i, int j, vector <vector<int>> dp) {
        if (i == 0 && j == 0) {
            return grid[i][j];
        }
        if (dp[i][j] != -1) {
            return dp[i][j];
        }
        
        int m = INT_MAX;
        if (j > 0) {
            m = grid[i][j] + getMinPath(grid, i, j - 1, dp);
        }
        if (i > 0) {
            int s = grid[i][j] + getMinPath(grid, i - 1, j, dp);
            m = min(m, s);
        }
        
        dp[i][j] = m;
        return dp[i][j];
    }


Bottom Up DP - Table Filling

int getMinPath(vector <vector <int>> &grid) {
        int r = grid.size();
        int c = grid[0].size();

        vector <vector <int>> dp(r, vector <int>(c, 0));
        dp[0][0] = grid[0][0];
        
        for (int i = 1; i < c; i++) {
            dp[0][i] = grid[0][i] + dp[0][i - 1];
        }
        
        for (int i = 1; i < r; i++) {
            dp[i][0] = grid[i][0] + dp[i - 1][0];
        }

        for (int i = 1; i < r; i++) {
            for (int j = 1; j < c; j++) {
                dp[i][j] = grid[i][j] + min(dp[i - 1][j], dp[i][j - 1]);
            }
        }
         
        return dp[r - 1][c - 1];
    }