LeetCode 202: Happy Number — Python Solution

Solve LeetCode 202: Happy Number in Python with a cycle detection approach. The key is to make the state invariant explicit, so the implementation and complexity follow naturally.

This guide paraphrases the task and does not reproduce LeetCode’s prompt. Use the official page for the complete statement, examples, constraints, and submission runner.

What the problem is testing

Repeatedly replace the number with the sum of squared digits. Stop at one or when a previously seen value proves a cycle.

Algorithm

1. Repeatedly replace the number with the sum of squared digits. Stop at one or when a previously seen value proves a cycle.
2. Maintain this invariant: Every generated value is recorded once, so a repeat identifies a non-one cycle.
3. Continue until every input item or reachable state has been resolved, then return the accumulated result.

Python solution

from collections import Counter, defaultdict, deque, OrderedDict
import random

class Solution:
    def isHappy(self, n):
        seen = set()
        while n != 1 and n not in seen:
            seen.add(n)
            n = sum(int(digit) ** 2 for digit in str(n))
        return n == 1

Why this is correct

The proof follows the maintained state: Every generated value is recorded once, so a repeat identifies a non-one cycle. Each iteration preserves that claim while permanently resolving at least one position, node, interval, or search state. When the loop or recursion ends, every candidate required by the problem has therefore been included or ruled out, so the returned value is correct.

Complexity

O(log n) space per generated state and bounded practical time. The stated auxiliary space excludes the returned output unless the output is the data structure being built.

Edge cases

Single-digit values other than one may still enter a longer cycle.

Tested reference code

This implementation is included in the site’s downloadable 100-solution Python library. The complete suite compiles every solution and runs a behavioral assertion for every problem before publication.

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