120 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.

Solution:

class Solution {
public:
    int minimumTotal(vector<vector<int>>& triangle) {
        int n = triangle.size();
        if ( n == 0 ) return 0;
        if ( n == 1 ) return triangle[0][0];
        vector<int> tmp1 = triangle[n-1];
        for ( int i = n-2; i >= 0; i-- ) {
            vector<int> tmp2;
            for ( int j = 0; j <= i; j++ ) tmp2.push_back(triangle[i][j] + min(tmp1[j], tmp1[j+1]));
            tmp1 = tmp2;
        }
        return tmp1[0];
    }
};

[
     [2],
    [3,4],
   [6,5,7],
  [4,1,8,3]
]
[4,1,8,3] --> [1+6, 1+5, 7+3] -->[6+3, 6+4] --> [9+2]