[Lintcode]Minimum Path Sum

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.

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Example

 

Note

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

 

public class Solution {
    /**
     * @param grid: a list of lists of integers.
     * @return: An integer, minimizes the sum of all numbers along its path
     */
    public int minPathSum(int[][] grid) {
        // write your code here
        if(grid.length==0 || grid[0].length==0) return 0;
        int m=grid.length;
        int n=grid[0].length;
     
        int[][] sum=new int[m][n];
        int minSum;
        

        for(int i=0;i<m;i++)
        {
           for(int j=0;j<n;j++)
            {
                if(i==0&&j==0)
                {
                    minSum=0;
                }
                else if(i==0) {minSum=sum[0][j-1];}
                else if(j==0) {minSum=sum[i-1][0];}
                else
                {
                  minSum=Math.min(sum[i-1][j],sum[i][j-1]);
                }
                
                sum[i][j]=minSum+grid[i][j];
            }
        }
        
        return sum[m-1][n-1];
    }
}