Known happy
Input
n = 19
Output
True
19 -> 82 -> 68 -> 100 -> 1, so 19 is happy.
Full lesson preview
Detect a happy number
Determine whether a number is happy using hashing or cycle detection.
Python practice14 minHashing & SetsIntermediateLast updated March 26, 2026
Problem statement
A happy number is defined by the following process: Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number equals 1 (happy) or it loops endlessly in a cycle that does not include 1 (unhappy). Given n, return True if n is happy, otherwise False.
Task
Implement the sequence transformation (sum of squares of digits) and detect cycles using a set or Floyd's algorithm.
Examples
Input format
A positive integer n.
Output format
Boolean True if n is a happy number, otherwise False.
Constraints
1 <= n <= 2^31 - 1. Aim for O(log n) work per transformation and detect cycles efficiently.
Samples
Sample 1
Input
n = 7
Output
True
7 is a known happy number sequence leading to 1.