Happy Number

Question

Write an algorithm to determine if a number 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, and 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 numbers.

Example: 19 is a happy number

1^2 + 9^2 = 82 8^2 + 2^2 = 68 6^2 + 8^2 = 100 1^2 + 0^2 + 0^2 = 1

Tags

• Mathematics
• Hash

Thought

Use a set to store the visited numbers and run the loop until found 1 or an element in the visited set.

Code

class Solution(object):
    def isHappy(self, n):
        """
        :type n: int
        :rtype: bool
        """
        visited = set()
        number = n
        while number not in visited:
            number = sum([int(num)**2 for num in list(str(number))])
            if number == 1:
                return True
            else:
                visited.add(number)
        return False