Happy Number

Happy Number

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 otherwise.

Examples

Example 1:

Input: n = 19
Output: true
Explanation:
1² + 9² = 82
8² + 2² = 68
6² + 8² = 100
1² + 0² + 0² = 1

Example 2:

Input: n = 2
Output: false
Explanation: The sequence 2 → 4 → 16 → 37 → 58 → 89 → 145 → 42 → 20 → 4 → ... enters a cycle and never reaches 1.

Example 3:

Input: n = 1
Output: true
Explanation: 1 is already 1.

Constraints

• 1 <= n <= 2^31 - 1

Expected Complexity

• Time: O(log n) per step, total steps bounded by cycle length
• Space: O(1) using Floyd's algorithm, or O(log n) using HashSet