solution.java

class Solution {
    public int minPathSum(int[][] grid) {
        int row = grid.length;
        int col = grid[0].length;
        
        //dp[i][j] stores the value of minimum path sum at the [i][j]
        int[][] dp = new int[row][col];

        //initilize the value in dp[][]
        dp[0][0] = grid[0][0]; 

        for (int i = 1; i < row; i++)  {
            dp[i][0] = grid[i][0] +  dp[i - 1][0];
        }
        
        for (int j = 1; j < col; j++) {
            dp[0][j] = grid[0][j] + dp[0][j - 1];
        }
        
        //fill in dp[][]
        //bc there are only two ways to reach a cell at [i][j] and we are trying to find the minimum path sum, 
        //we need to choose the smaller path between dp[i - 1][j] and dp[i][j - 1]. 
        for (int i = 1; i < row; i++) {
            for (int j = 1; j < col; j++) {
                dp[i][j] = Math.min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j];
            }
        }
        
        
        return dp[row - 1][col - 1];
    }
}