Find Kth Largest and Tree Ancestors
Company: Meta
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: medium
Interview Round: Technical Screen
In a technical phone interview, the candidate was asked two coding problems in the same round:
1. **K-th largest element in an array**
Given an unsorted integer array `nums` and an integer `k`, return the `k`-th largest element in the array. You should discuss the expected time and space complexity of your approach, and whether it can be solved without fully sorting the array.
2. **Lowest common ancestor in a tree**
Given the root of a binary tree and two distinct nodes `p` and `q` in the tree, return their lowest common ancestor.
The interviewer then asked several follow-up variants:
- How would you optimize the solution if the tree is a **binary search tree**?
- How would you solve it if each node has a **parent pointer**?
- How would you approach the problem if the tree is **too large to fit into memory**?
For each problem, explain the core idea, edge cases, and the most efficient implementation you would choose in an interview.
Quick Answer: This question evaluates algorithmic problem-solving and data-structure competencies, focusing on selection algorithms and time/space complexity reasoning for the k-th largest element and tree traversal, lowest common ancestor discovery with attention to BST properties, parent pointers, and external-memory constraints.