Minimum Path Sum

Problem:

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.

动态规划：

F(i,j)表示从左上角到(i,j)单元的最小路径和。

F(0,0)=grid[0][0];

对任意j>0，F(0,j)=F(0,j-1)+grid[0][j];

对任意i>0，F(i,0)=F(i-1,0)+grid[i][0];

对任意i>0，j>0，F(i,j)=min(F(i-1,j),F(i,j-1))+grid[i][j]。

public class Solution {
    public int minPathSum(int[][] grid) {
        if(grid==null||grid.length==0)
             return -1;
        for(int i=0;i<grid.length;i++)
             for(int j=0;j<grid[0].length;j++)
             {
                 if(i==0)
                     grid[0][j] += j>0?grid[0][j-1]:0;
                 else if(j==0)
                     grid[i][0] += grid[i-1][0];
                 else
                     grid[i][j] += Math.min(grid[i-1][j], grid[i][j-1]);
             }
        return grid[grid.length-1][grid[0].length-1];
    }
}