// Part 1 about the 3n+1 conceture

//=================================

//(1) Complete the collatz function below. It should

//    recursively calculate the number of steps needed 

//    until the collatz series reaches the number 1.

//    If needed you can use an auxilary function that

//    performs the recursion. The function should expect

//    arguments in the range of 1 to 10 Million.

def collatz(n: Long): List[Long] =

  if (n == 1) List(1) else

    if (n % 2 == 0) (n::collatz(n / 2)) else 

      (n::collatz(3 * n + 1))

// an alternative that calculates the steps directly

def collatz1(n: Long): Int =

  if (n == 1) 1 else

    if (n % 2 == 0) (1 + collatz1(n / 2)) else 

      (1 + collatz1(3 * n + 1))

//(2)  Complete the collatz bound function below. It should

//     calculuate how many steps are needed for each number 

//     from 1 upto a bound and return the maximum number of

//     steps. You should expect bounds in the range of 1

}

// some testing harness

for (bnd <- bnds) {

}