64最短路径

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.
Example:
Input:
[
[1,3,1],
[1,5,1],
[4,2,1]
]
Output: 7
Explanation: Because the path 1→3→1→1→1 minimizes the sum.

动态规划思想。
利用每格保存之前走过的最短路径，最后得到最末的值即为最短路径。

class Solution {
    public int minPathSum(int[][] grid) {
        int column=grid[0].length;
        int row=grid.length;
        for(int i=0;i<row;i++){
            for(int j=0;j<column;j++){
                if(i==0&&j==0){
                    continue;
                }else if(i==0&&j!=0){
                    grid[i][j]=grid[i][j]+grid[i][j-1];
                }else if(i!=0&&j==0){
                    grid[i][j]=grid[i-1][j]+grid[i][j];
                }else{
                    grid[i][j]=grid[i][j]+Math.min(grid[i-1][j],grid[i][j-1]);
                }
            }
        }
        return grid[row-1][column-1];
    }
}