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16. Pascal's Triangle

easyAsked at Workday

Generate the first numRows of Pascal's triangle. Workday uses this to test 2D-array construction and row-from-previous-row dependency — analogous to month-over-month payroll deltas.

By Alex Chen, Founder, InterviewChamp.AI · Last verified

Source citations

Public interview reports confirming this problem appears in Workday loops.

  • Glassdoor (2025)— Workday SDE1 phone screen.

Problem

Given an integer numRows, return the first numRows of Pascal's triangle. In Pascal's triangle, each number is the sum of the two numbers directly above it.

Constraints

  • 1 <= numRows <= 30

Examples

Example 1

Input
numRows = 5
Output
[[1],[1,1],[1,2,1],[1,3,3,1],[1,4,6,4,1]]

Example 2

Input
numRows = 1
Output
[[1]]

Approaches

1. Binomial coefficient formula

Compute C(n, k) directly for each cell.

Time
O(numRows^2)
Space
O(numRows^2) output)
// row[i][j] = factorial(i) / (factorial(j) * factorial(i-j))
// integer overflow for n=30 with naive factorial

Tradeoff: Correct but factorials overflow quickly without BigInt and you compute the same things repeatedly.

2. Iterative row build

Start each row with [1]. For inner positions, sum the two values above. End with [1].

Time
O(numRows^2)
Space
O(numRows^2) output)
function generate(numRows) {
  const out = [];
  for (let i = 0; i < numRows; i++) {
    const row = new Array(i + 1).fill(1);
    for (let j = 1; j < i; j++) {
      row[j] = out[i - 1][j - 1] + out[i - 1][j];
    }
    out.push(row);
  }
  return out;
}

Tradeoff: No factorial overhead. Each cell read from the previous row directly.

Workday-specific tips

Workday grades for index discipline — the inner loop runs from j=1 to j<i, NOT j<=i. Pre-filling with 1 lets you skip writing the boundary cells. Articulate the invariant.

Common mistakes

  • Off-by-one in the inner loop (j <= i causes overwrite of the trailing 1).
  • Forgetting that row[0] and row[i] are both 1 — over-engineered initialization.
  • Reading from out[i] instead of out[i - 1] for the parent row.

Follow-up questions

An interviewer at Workday may pivot to one of these next:

  • Pascal's Triangle II (LC 119) — only return the kth row, O(k) space.
  • Bell triangle.
  • Combinations via Pascal (LC 77).

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Output

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FAQ

Why fill with 1 first?

Boundaries of every row are 1. Pre-filling saves you from special-casing the first and last column inside the loop.

Can I do this with the binomial formula?

Yes — row[i][j] = C(i, j). But factorials grow fast and modular arithmetic gets fussy. The iterative version is cleaner.

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