Triangle

Given a triangle, find the minimum path sum from top to bottom. Each step you may move to adjacent numbers on the row below.

For example, given the following triangle

[
     [2],
    [3,4],
   [6,5,7],
  [4,1,8,3]
]

 

The minimum path sum from top to bottom is 11 (i.e., 2 + 3 + 5 + 1 = 11).

Note:
Bonus point if you are able to do this using only O(n) extra space, where n is the total number of rows in the triangle.

 

Analyse: DP. From bottom to up, compute the shortest path from next level to this level's elements. 

class Solution {
public:
    int minimumTotal(vector<vector<int>>& triangle) {
        if(triangle.empty() || triangle[0].empty()) return 0;
        
        vector<int> dp = triangle.back();
        for(int i = triangle.size() - 2; i >= 0; i--) {
            for(int j = 0; j <= i; j++)
                dp[j] = triangle[i][j] + min(dp[j], dp[j + 1]);
        }
        
        return dp[0];
    }
};