[LeetCode]Minimum Path Sum

Minimum Path Sum

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.

 

DP，递推公式f[i][j]=min(f[i-1][j],f[i][j-1])+grid[i][j]。

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