LeetCode OJ 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) {
        vector<vector<int> > dp(grid.size());
        for (int i = 0; i < dp.size(); i++) dp[i].resize(grid[i].size());
        dp[0][0] = grid[0][0];
        for (int i = 1; i < dp[0].size(); i++) {
            dp[0][i] = dp[0][i - 1] + grid[0][i];
        }
        for (int i = 1; i < dp.size(); i++) {
            dp[i][0] = dp[i - 1][0] + grid[i][0];
        }
        for (int i = 1; i < dp.size(); i++) {
            for (int j = 1; j < dp[i].size(); j++) {
                dp[i][j] = min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j];
            }
        }
        return dp[dp.size() - 1][dp[dp.size() - 1].size() - 1];
    }
};