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Problem 2: Cycle Detection (Happy Number)

Problem Statement

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.

Input Format

  • An integer n.

Example

Input: n = 19
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