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15. Pascal's Triangle

easyAsked at Box

Generate the first numRows of Pascal's triangle — Box uses this row-building pattern as a warm-up for index-array manipulation in metadata layouts.

By Sam K., Founder, InterviewChamp.AI · Last verified

Problem

Given an integer numRows, return the first numRows of Pascal's triangle.

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. Combinatorial

Compute each cell with C(n,k) factorial formula.

Time
O(n^2)
Space
O(n^2)
function C(n,k){ let r=1; for(let i=0;i<k;i++) r = r*(n-i)/(i+1); return Math.round(r); }
// fill triangle via C

Tradeoff:

2. Row-by-row sum

Each row built from the prior by adding adjacent values, with 1s at the ends.

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

Tradeoff:

Box-specific tips

Box wants the row-by-row construction with bounded allocations — they map it to building per-folder index-row tables for the file-listing API.

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Output

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