Reconstruct Queue (Alternative Sort)
You are asked to reconstruct a queue of people based on their height and the number of people in front of them who are taller. Use a greedy approach with a non-standard sort.
Why Interviewers Ask This
Meta asks this problem to evaluate a candidate's ability to handle complex sorting logic and greedy algorithm design. It tests whether you can recognize that standard sorting fails here, requiring a custom comparator strategy. Interviewers specifically look for your capacity to transform a seemingly chaotic reconstruction task into an ordered process by prioritizing height and count constraints efficiently.
How to Answer This Question
1. Clarify the input format and constraints, ensuring you understand that 'k' represents taller people in front. 2. Propose a greedy strategy: sort the array primarily by height in descending order, and secondarily by k in ascending order. This ensures taller people are placed first without disturbing existing positions of other tall individuals. 3. Initialize an empty list or dynamic array to build the reconstructed queue. 4. Iterate through the sorted list; for each person, insert them at index equal to their k value. Since taller people are already placed, inserting a shorter person at index k guarantees exactly k taller people precede them. 5. Analyze time complexity (O(N^2) due to insertion) versus space complexity, discussing optimizations if N is large. 6. Walk through a concrete example like [[7,0],[4,4],[7,1],[5,0]] to validate the logic step-by-step before coding.
Key Points to Cover
- Recognize that standard sorting is insufficient and requires a custom comparator.
- Understand that processing taller people first allows simpler insertion logic for shorter people.
- Correctly implement the secondary sort key (ascending k) for equal heights.
- Demonstrate understanding of how insertion at index k satisfies the constraint dynamically.
- Clearly articulate the trade-off between O(N^2) insertion time and code simplicity.
Sample Answer
To solve the Reconstruct Queue problem, I would start by analyzing the constraints. The core challenge is that inserting a person affects the relative order of others. A brute-force approach checking every permutation wo…
Common Mistakes to Avoid
- Sorting only by height in ascending order, which makes it impossible to determine correct positions for shorter people later.
- Ignoring the secondary sort condition for equal heights, leading to incorrect placement when multiple people share the same height.
- Attempting to use a static array without resizing, failing to account for shifting elements during insertion.
- Overcomplicating the solution with data structures like Segment Trees when a simple greedy insertion suffices.
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