What is the optimal time complexity of solving Automorphic number?

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 Automorphic number?

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 Automorphic number?

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 Automorphic number?

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

Automorphic number

Learn how to solve the 'Automorphic number' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function is_automorphic(n) that takes a non-negative integer n and returns True if n is an automorphic number, or False otherwise. An automorphic number is a number whose square ends with the number itself. For example, 25 is automorphic because 25^2 = 625, which ends with 25.

Constraints

•0 <= n <= 10^6

Examples

Example 1

Input

n = 25

Output

True

Explanation

25^2 = 625. The last two digits of 625 are 25, which matches n.

Example 2

Input

n = 76

Output

True

Explanation

76^2 = 5776. The last two digits of 5776 are 76, which matches n.

Example 3

Input

n = 13

Output

False

Explanation

13^2 = 169. The last two digits of 169 are 69, which does not match 13.

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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