#15The Digital Alchemy Experiment
An alchemist is experimenting with a mysterious number n.
During each experiment, the alchemist: Breaks the current number into its individual digits. Squares each digit. Adds all the squared values together. Uses the resulting sum as the number for the next experiment.
The experiment is considered a success if the number eventually transforms into the legendary number 1. However, if the transformation starts repeating numbers in a cycle and never reaches 1, the experiment fails.
Determine whether the alchemist's experiment will succeed. Return true if the number eventually reaches 1; otherwise, return false.
Examples
Example 1
Input: n = 19
Output: true
Explanation: 19 → 1² + 9² = 82 82 → 8² + 2² = 68 68 → 6² + 8² = 100 100 → 1² + 0² + 0² = 1
Example 2
Input: n = 2
Output: false
Explanation: 2 → 4 → 16 → 37 → 58 → 89 → 145 → 42 → 20 → 4 ... The transformation enters a repeating cycle and never reaches 1.
Example 3
Input: n = 1
Output: true
Explanation: The number is already the legendary number 1.
Constraints
- 1 <= n <= 2³¹ - 1