← Goldman Sachs Interview Insights
Classic problem but I second-guessed myself on the indexing.
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.
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]).
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.
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.
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.
Mention the dynamic programming approach (O(r*c) time, O(c) space) and explain why the combinatorial method is superior for a single query.
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