Minimum Path Sum

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;

}