64. Minimum Path Sum

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

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

这是一道动态规划的题目。去年在基因组大数据课上第一次接触动态规划（之前没有学过算法的小白），所以好有点印象，这道题和昨天那道计算有多少条路线的题目区别在于：一个是统计多少条路径，一个是累加value；累加value的时候在左边和上面的格子里取最小值。但是要注意因为会出现i-1和j-1,所以需要进行判断。

public int minPathSum(int[][] grid) {        if(grid==null)            return 0;        int m = grid.length;        int n = grid[0].length;        int[][] res = new int[m][n];                res[0][0]=grid[0][0];        for(int i=0;i<m;i++){            for(int j=0;j<n;j++){                if(i==0&&j>0)                    res[i][j]=res[i][j-1]+grid[i][j];                if(j==0&&i>0)                    res[i][j]=res[i-1][j]+grid[i][j];                else if(i>0&&j>0)                    res[i][j]=Math.min(res[i-1][j],res[i][j-1])+grid[i][j];                            }        }        return res[m-1][n-1];    }