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         
10         dp[0][0]=grid[0][0];
11         
12          // a row
13           for ( int i = 1; i < n; i++) 
14             dp[0][i] = dp[0][i - 1] + grid[0][i];  
15 
16          // a column
17           for ( int j = 1; j < m; j++)   
18             dp[j][0] = dp[j - 1][0] + grid[j][0];  
19         
20          for ( int i=1; i<m; i++){  
21                  for ( int j=1; j<n; j++){  
22                      if(dp[i-1][j]<dp[i][j-1])
23                         dp[i][j]=dp[i-1][j]+grid[i][j];
24                      else
25                         dp[i][j]=dp[i][j-1]+grid[i][j];
26                 }  
27             }  
28              return dp[m-1][n-1];  
29     }