leetcode: Minimum Path Sum

最新推荐文章于 2018-09-23 20:06:35 发布

martin_liang

最新推荐文章于 2018-09-23 20:06:35 发布

阅读量366

点赞数

CC 4.0 BY-SA版权

分类专栏：算法 leetcode C++/C

本文链接：https://blog.youkuaiyun.com/martin_liang/article/details/34958185

算法同时被 3 个专栏收录

537 篇文章

订阅专栏

C++/C

504 篇文章

订阅专栏

leetcode

230 篇文章

订阅专栏

本文探讨了如何使用动态规划算法解决在给定的m x n网格中找到从左上角到右下角的最小路径和的问题。通过构建辅助网格并应用递推公式，我们能够有效地求解最小路径和。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

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 {
private:
    int min(int &a, int &b)
    {
        if (a <= b)
            return a;
        return b;
    }
    
public:
    int minPathSum(vector<vector<int> > &grid) {
        
        int m = grid.size();
        int n = grid[0].size();
        vector<vector<int> > helperGrid(m, vector<int>(n));
        
        helperGrid[0][0] = grid[0][0];
        for (int j=1; j<n; j++)
        {
            helperGrid[0][j] = helperGrid[0][j-1]+grid[0][j];
        }
        
        for (int i=1; i<m; i++)
        {
            helperGrid[i][0] = helperGrid[i-1][0]+grid[i][0];
        }
        
        for (int i=1; i<m; i++)
        {
            for (int j=1; j<n; j++)
            {
                helperGrid[i][j] = min(helperGrid[i-1][j], helperGrid[i][j-1]) + grid[i][j];
            }
        }
        
        return helperGrid[m-1][n-1];
    }
};