Pascal's Triangle.md

LeetCode – 118. Pascal's Triangle

Problem Statement

Given an integer numRows, generate the first numRows rows of Pascal’s Triangle.
Each number is the sum of the two numbers directly above it.

Description

• Row starts and ends with 1.

• Inner numbers follow:
  row[j] = prev_row[j - 1] + prev_row[j]

• Return as a list of lists.

Input

One integer:

numRows

Output

A 2D list representing Pascal’s Triangle.

Examples

Example 1

Input:

numRows = 5

Output:

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

Explanation:
Each row is created using the previous row.

Example 2

Input:

numRows = 1

Output:

[
[1]
]

Constraints

• 1 ≤ numRows ≤ 30

Hints

• First and last elements of every row are 1.

• Each middle element is the sum of two numbers above it.

• Build one row at a time.

Approach / Explanation

1. Create an empty result list.

2. For each row index:

   • Start with all 1s.

   • Update inner elements using previous row.

3. Append row to the triangle.

Complexity

• Time: O(numRows²)

• Space: O(numRows²)