12. Pascal's Triangle

easyAsked at SoFi

Generate the first numRows of Pascal's triangle — SoFi uses this to test whether candidates can derive each row from the previous, a pattern that mirrors compounding interest schedules.

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

Problem

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

Constraints

1 <= numRows <= 30

Examples

Example 1

Input

Output

[[1],[1,1],[1,2,1],[1,3,3,1],[1,4,6,4,1]]

Example 2

Input

Output

[[1]]

Approaches

1. Brute force combinatorial

Compute each entry as C(r, c) using factorials.

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

function generate(numRows) {
  const fact = n => n <= 1 ? 1 : n * fact(n-1);
  const c = (r,k) => fact(r)/(fact(k)*fact(r-k));
  return Array.from({length: numRows}, (_, r) =>
    Array.from({length: r+1}, (_, k) => c(r,k))
  );
}

Tradeoff:

2. Iterative row-from-previous

Each row starts and ends with 1; middle entries are sums of adjacent pairs from the previous row.

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

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

Tradeoff:

SoFi-specific tips

SoFi appreciates iterative-from-previous solutions — it's exactly how interest accrual works (each day's balance is yesterday's balance plus daily interest), so candidates who think in recurrences score higher.

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