# LeetCode 202: Happy Number — Step-by-Step Visual Trace

**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

```python
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

> **[Open interactive visualization](https://tracelit.dev/app?trace=0202_happy-number)**

> **Try it yourself:** Open [TraceLit](https://tracelit.dev/app?trace=0202_happy-number) and step through every line.

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