Interval List Intersections

I dedicated a whole page to this problem.

This was asked at of me at an interview and I flubbed it. I attempted this problem a month after the interview and I still didn't fully get it, and made numerous mistakes which I want to analyze.

Here is the algorithm I came up with:

Here is the code that I wrote:

vector<vector<int>> intervalIntersection(vector<vector<int>>& A, vector<vector<int>>& B) {
 
    int pa = 0, pb = 0;
 
    vector<vector<int>> out;
    vector<int> last = {-1, -1};
    vector<int> cur;
 
    while(pa < A.size() || pb < B.size() )
    {   // get next interval
        // deal with pointers going out of bounds
        if      ( pa >= A.size()  )         { cur = B[pb++];   }
        else if ( pb >= B.size()  )         { cur = A[pa++];   }
        else if ( A[pa][0] <= B[pb][0] )    { cur = A[pa++];   }
        else                                { cur = B[pb++];   }
 
        // check if next intersects with last
        int min_end   = min(last[1], cur[1]);
        int max_start = max(last[0], cur[0]);
 
        if(min_end >= max_start)
        {
            out.push_back({max_start, min_end});
        }
        last = cur;
    }
  return out; 
}