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.

Solution: Dynamic Programming. Space O(N).

class Solution {
public:
    int minPathSum(vector<vector<int> > &grid) {
        if(grid.empty()) return INT_MIN;
        int M = grid.size();
        int N = grid[0].size();
        int dp[N];
        dp[0] = grid[0][0];
        for(int i = 1; i < N; i++)
            dp[i] = dp[i-1] + grid[0][i];
        
        for(int i = 1; i < M; i++) {
            dp[0] += grid[i][0];
            for(int j = 1; j < N; j++) {
                dp[j] = min(dp[j-1], dp[j]) + grid[i][j];
            }
        }
        return dp[N-1];
    }
};