What is the optimal time complexity of solving Factorial using recursion?

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 Factorial using recursion?

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 Factorial using recursion?

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 Factorial using recursion?

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 BasicsMedium

Factorial using recursion

Learn how to solve the 'Factorial using recursion' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Medium

Write a function factorial(n) that computes the factorial of a non-negative integer n using recursion. The factorial of n (written as n!) is the product of all positive integers from 1 to n. By definition, 0! = 1. The function should return the factorial as an integer.

Constraints

•0 <= n <= 20

Examples

Example 1

Input

n = 5

Output

Explanation

5! = 5 * 4 * 3 * 2 * 1 = 120.

Example 2

Input

n = 0

Output

Explanation

0! is defined as 1.

Example 3

Input

n = 7

Output

Explanation

7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040.

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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