readme.md

202. 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 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 <= 2^31 - 1

Solution

class Solution:
    def isHappy(self, n: int) -> bool:
        def get_next(number):
            total_sum = 0
            while number > 0:
                number, digit = divmod(number, 10)
                total_sum += digit ** 2
            return total_sum

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

        return fast == 1

Thoughts

Use the Floyd's Cycle Detection algorithm (Tortoise and Hare approach) to detect cycles in the sequence of numbers generated by the above function.

Time Complexity

• Each digit extraction and squaring operation is constant time, but the number of digits can be at most O(log n).
• The detection of cycles using Floyd's Cycle Detection algorithm typically runs in linear time with respect to the number of elements in the cycle and the length of the non-cyclic head of the list (or sequence in our case).

Space Complexity

The space complexity is O(1) since we use only a few variables and no additional data structures that grow with the input size.