Minimum Path Sum

Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right which minimizes the sum of all numbers along its path.

Note: You can only move either down or right at any point in time.

Similar to unique paths problem, we just need to choose which previous path has the minimum path sum.

public int minPathSum(int[][] grid) {
        if (grid==null||grid.length==0) {
            return 0;
        }

        int m = grid.length;
        int n = grid[0].length;

        int[][] results = new int[m][n];

        /*
         * [1  2  3  4
         *  5  6  7  8
         *  9 10 11 12
         * ]
         * 
         * look at grid[2][3]=12, it can come from grid[1][3]=8 or grid[2][2]=11, so we pick the minimum one plus 12
         * 
         */

        for(int i=0; i<m; i++) {
            for(int j=0; j<n; j++) {               
                if(i==0&&j==0) {
                    results[0][0]=grid[0][0];
                //on first column
                } else if (j==0) {
                    results[i][0]=results[i-1][0]+grid[i][0];
                //on first row
                } else if(i==0) {
                    results[0][j]=results[0][j-1]+grid[0][j];
                //always compare previous path find the smaller one add the current node value
                } else {
                    results[i][j]=Math.min(results[i-1][j],results[i][j-1])+grid[i][j];
                }
            }
        }
        return results[m-1][n-1];  
    }