The solution involved building, traversing, and balancing trees. I wanted to create a Node class to build out the tree, but the interviewer was insistent that I use a hashmap of child->parent relationships. This added so much unnecessary complexity. When refining a final, optimized version, you would come to this as a slightly better solution in terms of space complexity, but a healthy engineering process does not have you jump straight from an unknown problem into a final, all-corners-cut solution.