64. Minimum Path Sum (Graph; DP)

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) {
        if(grid.empty()) return 0;

        vector<vector<int>> dp(grid.size(), vector<int>(grid[0].size(), 0));
        dp[0][0] = grid[0][0];
        for(int i = 1; i< grid[0].size(); i++)
        {
            dp[0][i] = dp[0][i-1] + grid[0][i];
        }
        for(int i = 1; i< grid.size(); i++)
        {
            dp[i][0] = dp[i-1][0] + grid[i][0];
        }

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