Minimum Path Sum

题目描述：

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.

代码如下：

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