64. Minimum Path Sum

题目：

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.

 

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  Array Dynamic Programming

 

链接： http://leetcode.com/problems/minimum-path-sum/

题解：

DP，可以in-place，也可以使用滚动数组。

Time Complexity - O(mn)， Space Complexity - O(1)。

public class Solution {

    public int minPathSum(int[][] grid) {

        if(grid == null || grid.length == 0)

            return 0;

            

        for(int i = 1; i < grid.length; i ++){

            grid[i][0] += grid[i - 1][0]; 

        }

        

        for(int j = 1; j < grid[0].length; j ++){

            grid[0][j] += grid[0][j - 1];

        }

        

        for(int i = 1; i < grid.length; i ++){

            for(int j = 1; j < grid[0].length; j ++){

                grid[i][j] += Math.min(grid[i][j - 1], grid[i - 1][j]);

            }

        }

        

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

    }

}

 

测试：