0202-happy-number

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Description

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.

 

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

 

Constraints:

  • 1 <= n <= 231 - 1

Solution(Python)

class Solution:
    def isHappy(self, n: int) -> bool:
        # base 10 converges to 1
        #
        # case 1 converge to 1
        # case 2 cycle
        # case 3 infinity
        #

        def get_next(num):
            total_sum = 0
            while num > 0:
                num,digit = divmod(num, 10)
                total_sum += digit **2
            return total_sum

        slow = n
        fast = get_next(n)
        while slow!= 1 and slow != fast:
            slow = get_next(slow)
            fast = get_next(get_next(fast))
        return fast == 1

Dry Run