15. Pascal's Triangle

easyAsked at TripAdvisor

Generate the first numRows of Pascal's triangle.

By Alex Chen, Founder, InterviewChamp.AI · Last verified 2026-05-20

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. Closed-form binomial

Compute row i with nCk via factorial.

Time: O(n^2)
Space: O(n^2)

// computing factorials each time wastes work
// and accumulates rounding error for larger n

Tradeoff:

2. Build row from previous

Row[i] = sum of adjacent entries in row[i-1]. Edges always 1.

Time: O(n^2)
Space: O(n^2)

function generate(numRows) {
  const rows = [];
  for (let i = 0; i < numRows; i++) {
    const row = new Array(i + 1).fill(1);
    for (let j = 1; j < i; j++) {
      row[j] = rows[i-1][j-1] + rows[i-1][j];
    }
    rows.push(row);
  }
  return rows;
}

Tradeoff:

TripAdvisor-specific tips

TripAdvisor uses combinatorial table problems to gauge if you precompute aggregates instead of recomputing per request.

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Output

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