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Find Kth Largest and Tree Ancestors

MetaSoftware Engineer · Technical Screen
MediumSoftware EngineerTechnical ScreenCoding & Algorithms

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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.

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.