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.

class Solution {

public:
    int minPathSum(vector<vector<int> > &grid) {
        int rows = grid.size();
        int cols = grid[0].size();
        vector<int> temp(cols, 0);
        vector<vector<int> > dp(rows, temp);
        
        dp[0][0] = grid[0][0];
        for (int i=1;i<rows;i++)
            dp[i][0] = grid[i][0] + dp[i-1][0];
        for (int j=1;j<cols;j++)
            dp[0][j] = grid[0][j] + dp[0][j-1];
        for (int i=1;i<rows;i++){
            for (int j=1;j<cols;j++){
                dp[i][j] = min(dp[i-1][j] + grid[i][j],
                                dp[i][j-1] + grid[i][j]);
            } 
        }
        
        return dp[rows-1][cols-1];
    }
};