Capital One·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Apr 2026

Summary

Capital One SWE interview with a coding question that flipped a familiar problem on its head. The twist was subtle but enough to throw me off if you weren't paying attention.

Questions Asked (1)

Given a sequence of deletions applied to an array, after each deletion report the total number of consecutive segments currently in the array.

Algorithms & Data Structures

Author's notes

It's basically the inverse of the classic 'longest consecutive segment after insertions' problem, except instead of tracking the longest segment you're counting all of them, and you're removing elements instead of adding.

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AI HintsAI Generated

Suggested Approach

Clarify that deletions are given as indices and that we need to report the number of contiguous segments after each deletion. Propose an efficient solution using a disjoint-set union (DSU) data structure to track active elements and merge adjacent segments, or a reverse-processing approach where you add elements back and count segments. Explain how each deletion affects the segment count based on the states of neighboring elements.

Pro tip: Mention that processing deletions in reverse (adding elements instead of removing) simplifies the problem because adding an element can only merge existing segments, making the segment count update straightforward. This demonstrates algorithmic maturity and often leads to a cleaner implementation.

1. Clarify the problem

Confirm that the array initially has all elements present, deletions are given as indices, and after each deletion we must report the current number of contiguous segments of remaining elements.

2. Choose an efficient approach

Decide between forward simulation with a balanced BST or DSU, or reverse processing with DSU. Explain why reverse processing is often simpler: start with an empty array and add elements back in reverse order, merging segments.

3. Design the data structure

Use a DSU to maintain connected components of active elements. For reverse processing, maintain a boolean array of active elements and a variable tracking the current number of segments.

4. Define the update rule

When adding an element at index i, check if its left neighbor (i-1) and right neighbor (i+1) are active. If neither is active, a new segment is created (segments++). If exactly one is active, the element joins that segment (segments unchanged). If both are active, two segments merge (segments--).

5. Analyze complexity and edge cases

State that each union/find operation is nearly O(1) with path compression and union by rank, giving O(n α(n)) total time. Handle edge cases like deleting the first or last element, and ensure the initial segment count is correct.

Key Points to Mention

Use of Disjoint Set Union (Union-Find) for efficient merging of adjacent segments.
Reverse processing: adding elements back instead of deleting simplifies segment count updates.
Segment count update rule: +1 if isolated, 0 if adjacent to one segment, -1 if bridging two segments.
Time complexity: O(n α(n)) with DSU, which is nearly linear.
Space complexity: O(n) for the DSU parent array and active flags.
Handling edge cases: deletions at boundaries, all elements deleted, no deletions.

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