Happy Number

easyPROHash Maps & SetsApple DSA

A happy number is defined by repeatedly replacing it with the sum of squares of its digits until it either reaches 1 (happy) or loops endlessly (not happy).

Return True if n is a happy number.

Example

Input

Output

True

Reasoning

The input n is a positive integer, here $19$ . Each step replaces the number with the sum of the squares of its decimal digits.
Starting at $19$ : $1^2 + 9^2 = 1 + 81 = 82$ .
From $82$ : $8^2 + 2^2 = 64 + 4 = 68$ . From $68$ : $6^2 + 8^2 = 36 + 64 = 100$ .
From $100$ : $1^2 + 0^2 + 0^2 = 1$ . The sequence $19 \to 82 \to 68 \to 100 \to 1$ reached $1$ , so $19$ is happy and the output is True.
Notice what the other ending looks like: for $n = 2$ the sequence runs $2 \to 4 \to 16 \to 37 \to 58 \to 89 \to 145 \to 42 \to 20 \to 4$ , landing back on a value it already produced, so it repeats forever without touching $1$ and the answer is False.
The input $1$ is already $1$ , so it counts as happy with zero steps.

Constraints

1 <= n <= 2^31 - 1

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solution.py

Python 3.13

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Happy Number

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