faire·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

May 2026

Summary

Faire SWE interview had me implementing Pascal's Triangle with a specific symmetric formatting requirement. The logic itself wasn't too bad but the display math took longer than I expected.

Questions Asked (1)

Implement Pascal's Triangle for a given height, printing each row so the overall triangle appears visually centered and symmetric. The formatting requires right-padding every number to the width of the largest number in the triangle, using that same width as the gap between adjacent numbers, and indenting each row to center it.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

The actual value generation was fine, standard row-by-row accumulation.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the exact formatting requirements and edge cases, then outline a two-phase solution: first generate the triangle values, then compute the maximum width and format each row with proper padding and centering. Emphasize modularity and testability, and discuss trade-offs between precomputing all rows versus generating row-by-row.

Pro tip: Mention that the centering indent for each row can be computed as (maxWidth + gap) * (height - rowIndex - 1) / 2, and that using string formatting with dynamic width simplifies the implementation. Also, proactively discuss how you would handle large heights and potential integer overflow.

1. Clarify requirements and edge cases

Ask about input constraints (e.g., height range), expected output format (spaces vs tabs), and how to handle height 0 or negative. Confirm that numbers should be right-padded to the max width and that the gap equals that width.

2. Generate Pascal's Triangle values

Use a simple iterative approach: start with [1], then each new row is built from the previous by summing adjacent elements with 1s at the ends. Store all rows in a list for later formatting.

3. Compute maximum number width

Find the largest number in the triangle (the middle element of the last row) and determine its string length. This width will be used for padding each number and as the gap between numbers.

4. Format each row with centering

For each row, convert numbers to strings padded to max width, join with a gap of max width spaces. Then prepend an indent of ((maxWidth + gap) * (height - rowIndex - 1)) // 2 spaces to center the row.

5. Test and discuss trade-offs

Test with small heights (1, 2, 3) and a larger one (e.g., 5) to verify symmetry. Discuss time/space complexity (O(n^2) time and space) and possible optimizations like generating row-by-row without storing all rows if only printing is needed.

Key Points to Mention

Time and space complexity: O(n^2) for generating n rows, and O(n^2) space if storing all rows; can be O(n) space if generating row-by-row.
Edge cases: height 0 (print nothing), height 1 (just '1'), and large heights causing integer overflow (use arbitrary-precision integers if needed).
Formatting details: right-padding each number to max width, using max width as gap, and computing indent as (maxWidth + gap) * (height - rowIndex - 1) / 2.
Modularity: separate triangle generation from formatting for testability and reusability.
Trade-offs: precomputing all rows simplifies centering but uses more memory; streaming rows saves memory but requires knowing max width in advance (can compute from last row's middle element).
Testing strategy: verify output for small heights, check symmetry, and ensure numbers align correctly.

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