What is the optimal time complexity of solving Happy 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 Happy Number?

The space complexity is O(n) 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 Happy 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 Happy 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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Happy Number

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

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Problem Statement

Easy

Write an algorithm to determine if a number n is happy.

A happy number is a number defined by the following process:

- Starting with any positive integer, replace the number by the sum of the squares of its digits.

- Repeat the process until the number equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1.

- Those numbers for which this process ends in 1 are happy.

Return true if n is a happy number, and false if not.

Implement a function isHappy(n: int) -> bool.

Constraints

•1 <= n <= 2^31 - 1

Examples

Example 1

Input

Output

True

Explanation

1^2 + 9^2 = 82. 8^2 + 2^2 = 68. 6^2 + 8^2 = 100. 1^2 + 0^2 + 0^2 = 1. Since we reached 1, 19 is a happy number.

Example 2

Input

Output

False

Explanation

2 -> 4 -> 16 -> 37 -> 58 -> 89 -> 145 -> 42 -> 20 -> 4 -> ... This loops forever without reaching 1.

Need a Hint?

Analyze the input constraints. Try sorting first (O(n log n)) or using a hash map/set to track seen elements in O(n) time.

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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