Minimum Path Sum leetcode java

题目：

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.

题解：

这道题跟Unique Path系列是思路一样的。具体思路看代码就很清楚了

代码如下：

 1     public int minPathSum(int[][] grid) {
 2         int m = grid.length;
 3         int n = grid[0].length;
 4         
 5         if(m==0||n==0)
 6             return 0;
 7             
 8         int[][] dp = new int[m][n];
 9         
         dp[0][0]=grid[0][0];
         
         //a row
         for (int i = 1; i < n; i++) 
             dp[0][i] = dp[0][i - 1] + grid[0][i];  
 
         //a column
         for (int j = 1; j < m; j++)   
             dp[j][0] = dp[j - 1][0] + grid[j][0];  
         
         for (int i=1; i<m; i++){  
                 for (int j=1; j<n; j++){  
                     if(dp[i-1][j]<dp[i][j-1])
                         dp[i][j]=dp[i-1][j]+grid[i][j];
                     else
                         dp[i][j]=dp[i][j-1]+grid[i][j];
                 }  
             }  
             return dp[m-1][n-1];  
     }