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: result[i][j] = min(result[i - 1][j - 1], result[i - 1][j]) + triangle[i][j];

Runtime: 8ms.

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