Capital One·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Jul 2026

Summary

Capital One software engineer interview with two meaty coding problems back to back. The matrix manipulation part was fine but the street lights problem took a while to click and I'm not sure I nailed the complexity analysis on the spot.

Questions Asked (2)

Given an m×n integer matrix, implement several in-place operations: swapping two rows, swapping two columns, reversing row order, reversing column order, and rotating the matrix 90 degrees in either direction. For the rotation, handle both square and rectangular matrices and explain your time and space complexity for each operation.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

The swap and reverse stuff was pretty mechanical.

Create a free account to read the full note

AI HintsAI Generated

Suggested Approach

Start by clarifying that in-place operations mean modifying the original matrix without allocating a new one, then implement each operation using index manipulation and swaps. For rotation, handle square matrices with a transpose-and-reverse approach, and rectangular matrices by reversing rows/columns or using a cycle-based method, while clearly stating time and space complexity for each.

Pro tip: Emphasize that in-place rotation of a rectangular matrix is non-trivial because the dimensions change; you can either allocate a new matrix (O(mn) space) or perform the rotation in-place using a cycle-based algorithm that works for any m×n matrix, but the latter is complex and rarely expected in interviews. Showing awareness of this trade-off demonstrates depth.

1. Clarify requirements and constraints

Confirm that operations must be in-place (O(1) extra space) and that the matrix is mutable. Ask about edge cases like 1×1, empty matrix, or non-square matrices.

2. Implement simple operations

For swapping rows or columns, use a loop to swap elements pairwise. For reversing row or column order, swap symmetric rows/columns from the outside in.

3. Handle square matrix rotation

For 90° clockwise: transpose the matrix (swap matrix[i][j] with matrix[j][i]) then reverse each row. For counter-clockwise: transpose then reverse each column (or reverse rows then transpose).

4. Address rectangular matrix rotation

Explain that in-place rotation changes dimensions, so you either allocate a new matrix of size n×m (O(mn) space) or use a cycle-based in-place algorithm (O(1) space) that is more complex. Choose based on constraints.

5. Analyze complexity

State time and space complexity for each operation: swaps and reversals are O(m) or O(n) time and O(1) space; rotation is O(mn) time and O(1) space for square, O(mn) space for rectangular if using new matrix.

Key Points to Mention

In-place means O(1) auxiliary space, but rotation of rectangular matrices may require O(mn) space if not using advanced techniques.
Swapping rows/columns and reversing order are O(m) or O(n) time and O(1) space.
Square matrix rotation can be done in O(mn) time and O(1) space via transpose and reverse.
Rectangular matrix rotation changes dimensions; in-place is possible but complex, often requiring a cycle-based algorithm.
Time complexity for all operations is at least O(mn) for rotation, O(m) or O(n) for row/column operations.
Edge cases: empty matrix, 1×1, 1×n, m×1, and non-square matrices.

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

You have a list of street lights, each defined by a position and a radius, illuminating a segment on a 1D line. Find the point covered by the most lights. If there's a tie, return the smallest such coordinate. Implement an optimal solution and analyze time and space complexity.

Algorithms & Data Structures

Author's notes

This one took me a minute to frame correctly.

Create a free account to read the full note

AI HintsAI Generated

Suggested Approach

Use a sweep line algorithm: create events for each light's start and end, sort them, and sweep to track the maximum coverage. For ties, handle end events before start events at the same coordinate to correctly identify the smallest coordinate with maximum coverage.

Pro tip: Clarify whether the light segments are inclusive or exclusive at endpoints, as this affects tie-breaking and event ordering. Also, mention that if the input is already sorted, the sweep can be done in O(n) time without sorting.

1. Clarify problem details

Ask about input format, whether endpoints are inclusive, and if the list is sorted. Confirm that ties should return the smallest coordinate.

2. Design sweep line algorithm

Create events for each light: (start, +1) and (end, -1). Sort events by coordinate, with end events before start events at the same coordinate to handle ties correctly.

3. Sweep and track maximum

Initialize current coverage and max coverage. Iterate through sorted events, updating current coverage. When current coverage exceeds max, update max and record the coordinate. If equal, keep the smaller coordinate.

4. Analyze complexity

Time complexity: O(n log n) due to sorting, where n is the number of lights. Space complexity: O(n) for storing events.

5. Test with edge cases

Consider cases like overlapping lights, no overlap, all lights identical, and ties at multiple coordinates. Verify the algorithm returns the correct smallest coordinate.

Key Points to Mention

Sweep line algorithm with events for start and end of each light's coverage.
Sorting events by coordinate, with end events processed before start events at the same coordinate to handle ties.
Tracking current coverage and updating maximum coverage and the coordinate when a new maximum is found.
Time complexity: O(n log n) due to sorting; space complexity: O(n) for events.
Edge cases: inclusive/exclusive endpoints, ties, and unsorted input.
Potential optimization: if input is sorted, use two pointers or a difference array for O(n) time.

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