Meta·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Apr 2026

Summary

Meta SWE coding round, one question about sorting a nearly-sorted array. Pretty focused session, no fluff.

Questions Asked (1)

Given an array where every element is at most K positions away from its correct sorted position, sort the array efficiently.

Algorithms & Data Structures

Author's notes

Classic heap problem once you see it, but I stared at it for a bit before the min-heap idea clicked.

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AI HintsAI Generated

Suggested Approach

Recognize that the array is nearly sorted with each element at most K positions from its correct position. Use a min-heap of size K+1 to efficiently extract the smallest element and place it in the correct position, achieving O(N log K) time. Alternatively, use insertion sort which is O(NK) but may be simpler; however, the heap approach is optimal for large N and small K.

Pro tip: Mention that for K=1 (almost sorted), insertion sort is O(N) and simpler, but for general K, the heap approach is better. Also, note that if K is large (close to N), just use a standard O(N log N) sort.

1. Understand the problem and constraints

Clarify that each element is at most K positions away from its sorted position. Discuss the implications: the array is 'nearly sorted', and we can exploit this for efficiency.

2. Choose the right algorithm

Decide between insertion sort (O(NK)) and min-heap (O(N log K)). For large N and small K, heap is better. Explain why heap works: the smallest element among the first K+1 elements must be the global minimum.

3. Implement the heap approach

Initialize a min-heap with the first K+1 elements. Then, for each subsequent element, extract the minimum from the heap and place it in the array, then add the new element to the heap. Finally, extract remaining elements.

4. Analyze complexity and edge cases

Time complexity: O(N log K). Space: O(K). Handle edge cases: K=0 (already sorted), K>=N (just sort normally), and ensure heap size does not exceed array bounds.

5. Test with examples

Walk through a small example (e.g., arr = [2,1,4,3], K=1) to verify correctness. Discuss potential pitfalls like off-by-one errors in heap size.

Key Points to Mention

The array is nearly sorted, so we can use a min-heap of size K+1 to efficiently find the next smallest element.
Time complexity: O(N log K) using heap, which is optimal for this problem. Space complexity: O(K).
Insertion sort is a simpler alternative with O(NK) time, which is better when K is very small (e.g., K=1).
The heap approach works because the smallest element among the first K+1 elements must be the global minimum.
Edge cases: K=0 (already sorted), K>=N (use standard sort), and handling the end of the array when the heap has remaining elements.
Comparison with other sorting algorithms: why not use quicksort or mergesort? Because we can do better by exploiting the near-sorted property.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.