What is the optimal time complexity of solving Last non-zero digit in factorial?

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 Last non-zero digit in factorial?

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 Last non-zero digit in factorial?

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 Last non-zero digit in factorial?

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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Last non-zero digit in factorial

Learn how to solve the 'Last non-zero digit in factorial' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function last_non_zero_digit(n) that returns the last non-zero digit of n! (n factorial). For example, 5! = 120, and the last non-zero digit is 2. The function takes a non-negative integer n and returns a single digit (1-9).

Constraints

•0 <= n <= 1000

Examples

Example 1

Input

n = 5

Output

Explanation

5! = 120. Ignoring trailing zeros, the last non-zero digit is 2.

Example 2

Input

n = 10

Output

Explanation

10! = 3628800. The last non-zero digit is 8.

Example 3

Input

n = 1

Output

Explanation

1! = 1. The last non-zero digit is 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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