Minimum Path Sum

最新推荐文章于 2019-10-26 15:10:44 发布

brucehb

最新推荐文章于 2019-10-26 15:10:44 发布

阅读量342

点赞数

CC 4.0 BY-SA版权

分类专栏：算法

本文链接：https://blog.youkuaiyun.com/brucehb/article/details/45104467

算法专栏收录该内容

636 篇文章

订阅专栏

本文介绍了一个算法问题：在一个非负数构成的网格中寻找从左上角到右下角的路径，使得路径上的数字之和最小。文章提供了一种解决方案，通过动态规划的方法逐步计算出每个格子达到该位置的最小路径和。

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.

class Solution {
public:
    int minPathSum(vector<vector<int> > &grid) {
        int result = 0;
	    int m = grid.size();
	    if (m < 1)
	    {
		    return result;
	    }
	    int n = grid[0].size();

	    int buf[m][n];
	    buf[0][0] = grid[0][0];
	    for (int i = 1; i < n; i++)
	    {
		    buf[0][i] = buf[0][i-1] + grid[0][i];
	    }

	    for (int j = 1; j < m; j++)
	    {
		    buf[j][0] = buf[j-1][0] + grid[j][0];
	    }

	    for (int i = 1; i < m; i++)
	    {
		    for (int j = 1; j < n; j++)
		    {
			    buf[i][j] = min(buf[i-1][j], buf[i][j-1]) + grid[i][j];
		    }
	    }

	    return buf[m-1][n-1]; 
    }
};