What is the optimal time complexity of solving Perfect 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 Perfect 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 Perfect 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 Perfect 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

Perfect number

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

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Problem Statement

Easy

Write a function is_perfect(n) that takes a positive integer n and returns True if it is a perfect number, or False otherwise. A perfect number is a number that equals the sum of its proper divisors (all divisors excluding the number itself). For example, 6 = 1 + 2 + 3.

Constraints

•1 <= n <= 10^6

Examples

Example 1

Input

n = 6

Output

True

Explanation

The proper divisors of 6 are 1, 2, 3. Their sum is 1 + 2 + 3 = 6.

Example 2

Input

n = 28

Output

True

Explanation

The proper divisors of 28 are 1, 2, 4, 7, 14. Their sum is 1 + 2 + 4 + 7 + 14 = 28.

Example 3

Input

n = 12

Output

False

Explanation

The proper divisors of 12 are 1, 2, 3, 4, 6. Their sum is 16, which is not 12.

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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