Happy Number

Easy · happy-number cycle. Real solution for this problem — same player as the hand-authored deep-dives.

Problem

Read the prompt, flip through the examples, then steal the idea.

LeetCode 202. Happy Number. The copyrighted prompt is on LeetCode. This page is a working happy-number cycle for this problem: editable input, Python, Go, and a step-by-step animation.

Constraints

—Player inputs are capped so the animation stays readable.
—Match LeetCode's own constraints when you submit there.

Examples

Input

n =: 19

Output

true

Solution

Python and Go. The walkthrough below runs this same code.

Approach 1Optimal▶ Animated

Sum of squared digits, detect a cycle

Replace n with the sum of the squares of its digits. If you hit 1, it is happy. If you see a number twice, you are in a loop — not happy.

The map of n → digit-square-sum is finite, so you either reach 1 or a cycle (the famous 4-loop).

Algorithm

While n ≠ 1 and n is new, record it and replace it with the digit-square sum.
Return whether you landed on 1.

Time: O(log n)
Space: O(log n)

Solution.py

1class Solution:2    def isHappy(self, n: int) -> bool:3        seen: set[int] = set()4        while n != 1 and n not in seen:5            seen.add(n)6            n = sum(int(d) ** 2 for d in str(n))7        return n == 1

Watch this run

Interactive walkthrough

Playing “Sum of squared digits, detect a cycle”. Edit the input, hit Run, then scrub.

Approach: Sum of squared digits, detect a cycle

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