← Goldman Sachs Interview Insights

Goldman Sachs·Software Engineer·Technical Phone Screen·Junior

Junior
May 2026

Summary

Goldman Sachs SWE interview with a Pascal's triangle problem. Pretty standard coding round, nothing too wild.

Questions Asked (1)

Q1

Given a row and column index, return the value at that position in Pascal's triangle.

Algorithms & Data Structures
Author's notes

Classic problem but I second-guessed myself on the indexing.

Create a free account to read the full note

AI HintsAI Generated

Suggested Approach

Clarify the indexing convention (0-based or 1-based) and then present the optimal combinatorial solution using the formula C(row, col) = row! / (col! * (row - col)!). Discuss trade-offs with the naive dynamic programming approach, emphasizing time and space complexity.

Pro tip: Mention that you can compute the binomial coefficient iteratively to avoid overflow and reduce multiplications, and that this approach runs in O(col) time and O(1) space. This shows you consider efficiency and numerical stability, which is valued in high-frequency trading environments.

1. Clarify the problem

Ask whether the row and column indices are 0-based or 1-based, and confirm the definition of Pascal's triangle (e.g., row 0 is [1]).

2. Identify the mathematical relationship

Recognize that the value at row r, column c is the binomial coefficient C(r, c). Explain that this can be computed directly without generating the entire triangle.

3. Present the optimal solution

Write the formula C(r, c) = r! / (c! * (r-c)!) and optimize it by computing the product iteratively: result = result * (r - i) / (i + 1) for i from 0 to c-1.

4. Analyze complexity and edge cases

State that time complexity is O(c) and space is O(1). Handle edge cases: c > r (return 0), c == 0 or c == r (return 1), and potential integer overflow.

5. Discuss alternatives and trade-offs

Mention the dynamic programming approach (O(r*c) time, O(c) space) and explain why the combinatorial method is superior for a single query.

Key Points to Mention

  • Binomial coefficient formula: C(row, col) = row! / (col! * (row - col)!)
  • Iterative computation to avoid factorial overflow and reduce multiplications
  • Time complexity O(col) and space complexity O(1)
  • Edge cases: col > row, col == 0, col == row
  • Comparison with dynamic programming approach (O(row*col) time, O(col) space)
  • Potential integer overflow and use of modulo if required

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