// Preliminary Part about the 3n+1 conjecture+
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//============================================+
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object CW6a {+
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//(1) Complete the collatz function below. It should+
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//    recursively calculate the number of steps needed +
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//    until the collatz series reaches the number 1.+
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//    If needed, you can use an auxiliary function that+
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//    performs the recursion. The function should expect+
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//    arguments in the range of 1 to 1 Million.+
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def collatz(n: Long) : Long = ???+
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//(2) Complete the collatz_max function below. It should+
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//    calculate how many steps are needed for each number +
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//    from 1 up to a bound and then calculate the maximum number of+
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//    steps and the corresponding number that needs that many +
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//    steps. Again, you should expect bounds in the range of 1+
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//    up to 1 Million. The first component of the pair is+
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//    the maximum number of steps and the second is the +
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//    corresponding number.+
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def collatz_max(bnd: Long) : (Long, Long) = ???+
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//(3) Implement a function that calculates the last_odd+
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//    number in a collatz series.  For this implement an+
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//    is_pow_of_two function which tests whether a number +
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//    is a power of two. The function is_hard calculates +
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//    whether 3n + 1 is a power of two. Again you can+
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//    assume the input ranges between 1 and 1 Million,+
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//    and also assume that the input of last_odd will not +
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//    be a power of 2.+
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def is_pow_of_two(n: Long) : Boolean = ???+
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def is_hard(n: Long) : Boolean = ???+
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def last_odd(n: Long) : Long = ???+
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}+
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