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.

明显的动态管理求解 动态方程 res[i][j]=min(res[i-1][j],res[i][j-1])+grid[i][j] 代码如下：

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