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.
 

給出一個包含非負元素的二維陣列，只能往右邊和下邊走，讓求出從左上到右下的最小路徑和，跟leetcode63很相似。還是動態規劃。

程式碼：

class Solution {
    public int minPathSum(int[][] grid) {
        int [][]dp=new int [grid.length][grid[0].length];
        dp[0][0]=grid[0][0];
        for(int i=1;i<grid.length;i++){
            dp[i][0]=dp[i-1][0]+grid[i]
 
[0];
        }
        for(int j=1;j<grid[0].length;j++){
            dp[0][j]=dp[0][j-1]+grid[0][j];
        }
        for(int i=1;i<grid.length;i++){
            for(int j=1;j<grid[0].length;j++){
                dp[i][j]=(dp[i-1][j]<dp[i][j-1]?dp[i-1][j]:dp[i][j-1])+grid[i][j];
            }
 

        }
        return dp[grid.length-1][grid[0].length-1];
    }
}