64. 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. 
Note: You can only move either down or right at any point in time.

利用DP的思想，因为只能向下或者是向右，所以不用考虑其他。

一般:
d[i][j]=min{dp[i-1][j],dp[i][j-1]}+grid[i][j];
边缘：
d[0][j]=dp[0][j-1]+grid[0][j];
d[i][0]=dp[i-1][0]+grid[i][0];不需要额外的空间，直接使用grid即可

public class Solution {
public int minPathSum(int[][] grid) {
if(grid==null || grid.length==0){
return 0;
}
int m=grid.length,n=grid[0].length;//m行n列
for(int j=1;j<n;j++){
grid[0][j]=grid[0][j-1]+grid[0][j];
}
for(int i=1;i<m;i++){
grid[i][0]=grid[i-1][0]+grid[i][0];
}
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])+grid[i][j];
}
}
m = m==0?m=0:m-1;
n = n==0?n=0:n-1;
return grid[m]
;
}
}