Minimum Path Sum

最新推荐文章于 2025-09-12 18:45:12 发布

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最新推荐文章于 2025-09-12 18:45:12 发布

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CC 4.0 BY-SA版权

文章标签： c/c++

原文链接：http://www.cnblogs.com/wuchanming/p/4110384.html

本文介绍了一个经典的动态规划问题——给定一个填充了非负数的矩阵，寻找从左上角到右下角路径中数字之和最小的路径。文章详细讲解了仅允许向下或向右移动时的解决方案，并提供了C++实现代码。

Dynamic Programming

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.

C++实现代码：

#include<iostream>
#include<vector>
using namespace std;

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

int main()
{
    Solution s;
    vector<vector<int> > vec={{1,8,3},{4,5,6},{7,8,9}};
    cout<<s.minPathSum(vec)<<endl;
}