How do you approach Happy Number?

Use a Set to keep track of numbers you've already seen to detect cycles.

What is the time complexity of Happy Number?

Time complexity: O(log n) - the number of digits decreases quickly. Space complexity: O(log n) - for the set of visited numbers.

What are common mistakes on Happy Number?

Overflowing at an intermediate step even though the final answer fits. Assuming a modulo is non-negative. In most languages -1 % n is negative, which breaks cyclic indexing. Testing floating-point values for exact equality where integer arithmetic would have been exact.

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Happy Number

EasyAlgorithms

Description

Write an algorithm to determine if a number `n` is a happy number. 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. - A number for which this process ends in 1 is a happy number. Return `true` if `n` is a happy number, and `false` if not.

Example 1

Input: n = 19

Output: true

Explanation: 1^2 + 9^2 = 82 -> 8^2 + 2^2 = 68 -> 6^2 + 8^2 = 100 -> 1^2 + 0^2 + 0^2 = 1

Example 2

Input: n = 2

Output: false

Constraints

- 1 <= n <= 2^31 - 1

Happy Number: approach, complexity and pitfalls

An easy math problem, graded against 7 test cases (4 of them hidden).

The pattern: Math

Number theory, digit manipulation, and closed-form reasoning.

Reach for it when you see: Primes, digits, base conversion, or a problem with a formula hiding behind it.

More Mathproblems →

If you are stuck

Show the 3-step hint ladder

Use a Set to keep track of numbers you've already seen to detect cycles.
Alternatively, use Floyd's cycle detection (fast and slow pointers).
To get digits, use modulo 10 and integer division by 10.

The optimal approach

Show the approach: HashSet Cycle Detection

Use a Set to track numbers we've already seen. For each number, compute the sum of squares of its digits. If we reach 1, it's happy. If we see a number we've already visited, there's a cycle and it's not happy.

Time: O(log n) - the number of digits decreases quickly
Space: O(log n) - for the set of visited numbers

The full reference solution in every supported language stays in the editor above - reveal it there once you have had a real attempt.

Common Math mistakes

These apply to the pattern as a whole, not just this problem.

Overflowing at an intermediate step even though the final answer fits.
Assuming a modulo is non-negative. In most languages `-1 % n` is negative, which breaks cyclic indexing.
Testing floating-point values for exact equality where integer arithmetic would have been exact.