Pascal's Triangle · Interview Problem

Leetcode

Medium

Arrays

Combinatorics

Math

Pascal's Triangle

Generate the first $numRows$ rows of Pascal's triangle, where each number is the sum of the two numbers directly above it.

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Pascal Triangle

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Problem Statement

Problem

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

Pascal's Triangle is built row by row:

The first row is [1].
Each subsequent row starts and ends with 1.
Every inner value is the sum of the two values directly above it from the previous row.

Your task is to construct and return the triangle up to the requested number of rows.

Notes

Row indexing is 1-based in the natural description of the triangle.
You only need to return the rows that exist; do not pad shorter rows.

Input Format

A single integer numRows.
numRows is the number of rows to generate.

Output Format

Return a list of lists of integers representing the first numRows rows of Pascal's Triangle.

Constraints

$1 \le numRows \le 30$
All generated values fit in a 32-bit signed integer.

Examples

Sample cases returned by the problem API.

Example 1

Input

numRows = 5

Output

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

Explanation

Start with [1]. Each new row is formed by adding adjacent pairs from the previous row, with 1 at both ends.

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