Happy Number

Problem

Write an algorithm to determine if a number n is happy. Replace the number by the sum of the squares of its digits, and repeat the process until the number equals 1 (happy) or loops endlessly in a cycle that does not include 1. Return true if n is a happy number, and false if not.

Examples

The brute-force approach

Just run the process for a fixed large number of steps. If you reach 1, return true. If you haven't hit 1 after, say, 1000 iterations, assume it's stuck in a cycle and return false.

def sum_of_squares(n):
    total = 0
    while n > 0:
        digit = n % 10
        total += digit * digit
        n //= 10
    return total

for _ in range(1000):    # arbitrary limit
    n = sum_of_squares(n)
    if n == 1:
        return True

return False

The magic number 1000 is arbitrary, you're guessing at a limit instead of detecting the cycle. If the limit is too low you get wrong answers; too high and you waste work. There's a precise way to know exactly when you've seen a number before.

Spotting the pattern

This is a Set problem. The key question to ask yourself:

How would I know if this process is stuck in a loop?

Answering that is where it clicks, and it's exactly what the guided walkthrough below builds with you: the pattern reasoning, a progressive hint ladder that never spoils the answer, a row-by-row dry run, the optimized solution, and an in-browser editor to run your code against real test cases.