ORIGINAL CODING QUESTION
Digit-square convergence
Repeatedly replace a positive integer with the sum of squares of its decimal digits. Print 1 if this reaches 1, otherwise 0 when a cycle repeats.
Original exercise · easy. Editorial role relevance does not imply a company has asked this question.
Input and output
One positive integer x.
Constraints
1 ≤ x ≤ 1000000000.
Example 1
Input
19
Output
1
19→82→68→100→1.
Example 2
Input
2
Output
0
The sequence enters a cycle that excludes 1.
Explain your approach
Explain your time and auxiliary space complexity. Which input makes your algorithm work hardest?
Private grading inputs, expected outputs and canonical reference implementations are withheld. Authored expected outputs were cross-checked with independent reference oracles; compiler/runtime behavior still needs a verified execution provider.
Hint 1
The sequence eventually reaches a previously visited state or one.
Hint 2
A set detects repeats.
Hint 3
Fast/slow state transitions can detect a cycle without a set.
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