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15. Pascal's Triangle

easyAsked at Slack

Return 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 entry 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. Combinatorics formula

Compute each cell via nCr.

Time
O(n^2)
Space
O(n^2)
function comb(n,k){ let r=1; for(let i=0;i<k;i++) r=r*(n-i)/(i+1); return r; }
return Array.from({length:numRows},(_,i)=>Array.from({length:i+1},(_,j)=>comb(i,j)));

Tradeoff:

2. Iterative row-from-prev

Build each row by summing adjacent entries of the previous row. Both ends are 1.

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

Slack-specific tips

Slack engineers like the iterative approach because it mirrors how they pre-compute UI-grid layouts row-by-row.

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Output

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