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 ;

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

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