Minimum Path Sum Java

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.

 Key to solve: DP
    This a classical DP problem, same as Unique Paths 
    beside there is value in each grid and we need to find path
    with min sum. We can minimum the sum base on value of previous
    column and above row
    Thus, formula: gird[i][j]=min(gird[i][j-1],gird[i-1][j-1])

public class Solution {    public int minPathSum(int[][] grid) {         int m=grid.length;        int n=grid[0].length;        //minimum the row value        for(int i=1;i<m;i++){            grid[i][0]+=grid[i-1][0];        }        //minimum the column value        for(int j=1;j<n;j++){            grid[0][j]+=grid[0][j-1];        }        for(int i=1;i<m;i++){            for(int j=1;j<n;j++){                grid[i][j]+=Math.min(grid[i-1][j],grid[i][j-1]);            }        }        return grid[m-1][n-1];    }}