import scala.annotation.tailrec+
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// Core Part 1 about the 3n+1 conjecture+
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//============================================+
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+
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object C1 {+
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+
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@tailrec+
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private def collatz(n: Long, steps: Long = 0): Long = {+
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  if (n == 1) steps+
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  else if (n % 2 == 0) collatz(n / 2, steps + 1)+
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  else collatz(n * 3 + 1, steps + 1)+
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}+
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+
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def collatz_max(upper: Long): (Long, Long) = {+
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  (1L to upper).map(n => (collatz(n), n)).maxBy(_._1)+
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}+
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+
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+
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private def is_pow_of_two(n: Long) : Boolean = {+
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  (n & (n - 1)) == 0+
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}+
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+
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private def is_hard(n: Long) : Boolean = {+
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  is_pow_of_two(3 * n + 1)+
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}+
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+
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+
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private def last_odd(n: Long): Long = {+
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  (1L to n).filter(is_hard).max+
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}+
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+
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}+
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// This template code is subject to copyright +
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// by King's College London, 2022. Do not +
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// make the template code public in any shape +
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// or form, and do not exchange it with other +
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// students under any circumstance.+
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