diff -r c40f364d87eb -r b4def82f3f9f progs/collatz_sol.scala --- a/progs/collatz_sol.scala Sun Nov 05 12:56:55 2017 +0000 +++ b/progs/collatz_sol.scala Tue Nov 07 13:08:18 2017 +0000 @@ -1,53 +1,31 @@ -// Part 1 about the 3n+1 conceture -//================================= +// Part 1 about the 3n+1 conjecture +//================================== - +object CW6a { -//(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 1 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)) +def collatz(n: Long): Long = + if (n == 1) 1 else + if (n % 2 == 0) 1 + collatz(n / 2) else + 1 + 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 and the corresponding number that needs that many -// steps. You should expect bounds in the range of 1 -// upto 1 million. - -def collatz_max(bnd: Int): (Int, Int) = { - val all = for (i <- (1 to bnd).toList) yield collatz(i).length +def collatz_max(bnd: Long): (Long, Long) = { + val all = for (i <- (1 to bnd.toInt).toList) yield collatz(i) val max = all.max - (all.indexOf(max) + 1, max) + (max, all.indexOf(max) + 1) } -// some testing harness -val bnds = List(2, 10, 100, 1000, 10000, 100000, 77000, 90000, 1000000, 5000000) +// some testing harness...5 Mio pushes the envelope + +val bnds = List(2, 10, 100, 1000, 10000, 100000, + 77000, 90000, 1000000, 5000000) for (bnd <- bnds) { - val (max, steps) = collatz_max(bnd) + val (steps, max) = collatz_max(bnd) println(s"In the range of 1 - ${bnd} the number ${max} needs the maximum steps of ${steps}") } -//val all = for (i <- (1 to 100000).toList) yield collatz1(i) -//println(all.sorted.reverse.take(10)) +} - -