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.

class Solution {
public:
    int minimumTotal(vector<vector<int> > &triangle) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        int n = triangle.size();
        if (!n) return 0;
        
        int *sum = new int[n];
        sum[0] = triangle[0][0];
        
        for (int i = 1; i < n; ++i) {
            for (int j = i; j >= 0; --j) {
                if (j != 0 && j != i) {
                    sum[j] = min(sum[j - 1], sum[j]) + triangle[i][j];
                }
                else if (j == i) {
                    sum[j] = sum[j - 1] + triangle[i][j];
                }
                else {
                    sum[j] = sum[j] + triangle[i][j];
                }
            }
        }
        
        int m = sum[0];
        for (int i = 1; i < n; ++i) if (sum[i] < m) m = sum[i];
        delete[] sum;
        return m;
    }
};