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16. Pascal's Triangle

easyAsked at Expedia

Generate the first numRows of Pascal's triangle.

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

Problem

Given an integer numRows, return the first numRows of 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. Combinatoric formula

Compute each entry as C(n,k).

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 r;}

Tradeoff:

2. Build row from previous

Each row[i] = prev[i-1] + prev[i]. Expedia uses similar row-by-row buildups for cumulative price tables.

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

Tradeoff:

Expedia-specific tips

Expedia values the build-from-previous-row approach; mention it's the same pattern as building cumulative night-by-night price tables for stays.

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Output

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