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.

 

本题和triangle比较相似，只不过从三角形变成了矩形，但是方法还是一样的，同样是用dp解决，代码如下：

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