What is the optimal time complexity of solving Nth row of Pascal Triangle?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Nth row of Pascal Triangle?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Nth row of Pascal Triangle?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Nth row of Pascal Triangle?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Python BasicsEasy

Nth row of Pascal Triangle

Learn how to solve the 'Nth row of Pascal Triangle' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function pascal_row(n) that returns the nth row of Pascal's Triangle as a list of integers using recursion. Rows are 0-indexed: row 0 is [1], row 1 is [1, 1], row 2 is [1, 2, 1], etc. Each element is the sum of the two elements directly above it in the previous row.

Constraints

•0 <= n <= 30

Examples

Example 1

Input

n = 0

Output

[1]

Explanation

The 0th row of Pascal's Triangle is just [1].

Example 2

Input

n = 4

Output

[1, 4, 6, 4, 1]

Explanation

Row 3 is [1,3,3,1]. Row 4: 1, (1+3)=4, (3+3)=6, (3+1)=4, 1.

Example 3

Input

n = 2

Output

[1, 2, 1]

Explanation

Row 1 is [1,1]. Row 2: 1, (1+1)=2, 1.

Need a Hint?

Use simple arithmetic operators (like modulo `%`, division `//`), conditional checks, or loops to inspect number properties.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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