Easy — Two Pointers | Math | Hash Table | Floyd’s Algorithm

The Problem

Determine if a number is happy by repeatedly replacing it with the sum of the square of its digits until it equals 1 (happy) or loops endlessly in a cycle (not happy).

Approach

Uses Floyd’s cycle detection algorithm (tortoise and hare) with two pointers moving at different speeds to detect if the sequence enters a cycle or reaches 1. The helper function calculates the sum of squares of digits efficiently using divmod.

Time: O(log n) · Space: O(1)

Code

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

        slow, fast = n, get_next(n)

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

        return fast == 1

Watch It Run

Try it yourself: Open TraceLit and step through every line.

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Built with TraceLit — the visual algorithm tracer for LeetCode practice.

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