[LeetCode] 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，f[i][j] = min(f[i-1][j], f[i][j-1]) + a[i][j]

class Solution {
private:
    int f[1000][1000];
public:
    int minPathSum(vector<vector<int> > &grid) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        if (grid.size() == 0 || grid[0].size() == 0)
            return 0;
            
        f[0][0] = grid[0][0];
        
        for(int i = 1; i < grid.size(); i++)
            f[i][0] = f[i-1][0] + grid[i][0];
            
        for(int i = 1; i < grid[0].size(); i++)
            f[0][i] = f[0][i-1] + grid[0][i];
            
        for(int i = 1; i < grid.size(); i++)
            for(int j = 1; j < grid[0].size(); j++)
                f[i][j] = min(f[i-1][j], f[i][j-1]) + grid[i][j];
                
        return f[grid.size()-1][grid[0].size()-1];
    }
};