Problem:
A : 指折り数えて / Finger Counting

問題文

肉西くんは指の数を増やしたり減らしたりできる．

肉西くんの前には n 個のまんじゅうがある．

肉西くんは指を折ってまんじゅうの個数を数えようとしている．

肉西くんの指が取れる形は折れているか折れていないかの 2 つしか無い．

肉西くんは 2 進数を理解している．

肉西くんは各指に 2 進数の桁を対応させて数を数えることが出来る．

肉西くんは対数を理解していない．

肉西くんのかわりにまんじゅうを数え上げるのに必要な指の本数の最小値を求めよ．

入力

n

制約

整数である

0 ≤ n ≤ 1018

出力

答えを 1 行に出力し，最後に改行を出力せよ．

サンプル

サンプル入力1

0

サンプル出力1

0

サンプル入力2

4

サンプル出力2

3

サンプル入力3

31

サンプル出力3

5

サンプル入力4

36028797018963968

サンプル出力4

56

Solution in Scala (judge verdict: Accepted)

import java.util.Scanner

import scala.collection.Searching._
import scala.annotation.tailrec
import scala.collection.mutable
import scala.collection.immutable._
import scala.io.StdIn.readLine

class IUnionFind(val size: Int) {

  private case class Node(var parent: Option[Int], var treeSize: Int)

  private val nodes = Array.fill[Node](size)(new Node(None, 1))

  def union(t1: Int, t2: Int): IUnionFind = {
    if (t1 == t2) return this

    val root1 = root(t1)
    val root2 = root(t2)
    if (root1 == root2) return this

    val node1 = nodes(root1)
    val node2 = nodes(root2)

    if (node1.treeSize < node2.treeSize) {
      node1.parent = Some(t2)
      node2.treeSize += node1.treeSize
    } else {
      node2.parent = Some(t1)
      node1.treeSize += node2.treeSize
    }
    this
  }

  def connected(t1: Int, t2: Int): Boolean = t1 == t2 || root(t1) == root(t2)

  def root(t: Int): Int = nodes(t).parent match {
    case None => t
    case Some(p) => {
      nodes(t).parent = Some(root(p))
      nodes(t).parent.get
    }
  }
}

class Sushi() {

  private case class Order(val order: Array[String])

  private var orders = Array.empty[(Long, Order)];

  def come(n: Long, a: Array[String]): Unit = {
    orders = (orders.takeWhile(_ match { case (x: Long, _) => x < n }) :+ (n, Order(a))) ++ orders.dropWhile(_ match { case (x: Long, _) => x <= n })
  }

  def takeout(s: String): Long = {
    orders.filter(_ match { case (_, order) => order.order.contains(s) }).headOption match {
      case Some((id, order)) => {
        come(id, order.order.takeWhile(_ != s) ++ order.order.dropWhile(_ != s).tail)
        id
      }
      case None => -1
    }
  }

  def leave(id: Long) = {
    orders = orders.filter(_._1 != id)
  }
}

object Main {
  def solve(sc: => Scanner): Unit = {
    println(recursive(sc.nextLong))
  }

  def recursive(N: Long): Long = {
    if (N == 0) (0) else (1 + recursive(N >> 1))
  }

  def recursive2(N: Long): String = {
    if (N == 0) ("") else (('a'.toInt + (N % 26)).toChar + recursive2(N / 26))
  }

  def check(A: Array[List[Int]]): Boolean = {
    A.map(_.size == 0).fold(true)((a, b) => a & b)
  }

  def shift(n: Long): Long = {
    if (n == 0) (0) else if (n == 1) (1) else (shift(n - 1) << 1)
  }

  def unShift(n: Long): Long = {
    if (n == 0) (0) else (unShift(n >> 1) + 1)
  }

  def gcd(i: Long, j: Long): Long = {
    if (i < j) (gcd(j, i)) else (if (j == 0) (i) else (gcd(j, i % j)))
  }

  def main(args: Array[String]): Unit = {
    val sc: Scanner = new Scanner(System.in)
    solve(sc)
  }
}

object Util {
  def getPermutation(begin: Long = 0): Stream[Long] =
    Stream.cons(begin, getPermutation(begin + 1))

  def getPrimeList(): Stream[Long] =
    getPrimeListRecursive(getPermutation(begin = 2))

  private def getPrimeListRecursive(A: Stream[Long]): Stream[Long] =
    Stream.cons(A.head, getPrimeListRecursive(A.tail.filter(_ % A.head != 0)))

  def fib(a: Long = 0, b: Long = 1, mod: Long = Long.MaxValue): Stream[Long] = a #:: fib(b % mod, (a + b) % mod, mod)
}

object ArabicRoman {

  type =?>[A, B] = PartialFunction[A, B]

  val codeTable = List(
    (1000, "M"), (900, "CM"), (500, "D"), (400, "CD"), (100, "C"),
    (90, "XC"), (50, "L"), (40, "XL"), (10, "X"), (9, "IX"), (5, "V"), (4, "IV"), (1, "I"))

  val arabicToRoman: (Int) =?> String = {
    case src if (src >= 1 && src <= 3999) => {

      def convert(left: Int, cont: String = "", code: List[(Int, String)] = codeTable): String = {
        val (unitVal, unitChar) = code.head
        left - unitVal match {
          case n if (n == 0) => cont + unitChar
          case n if (n > 0) => convert(n, cont + unitChar, code)
          case _ => convert(left, cont, code.tail)
        }
      }

      convert(src)
    }
  }

  val romanToArabic: (String) =?> Int = {
    case src if (Option(src).exists { s => {
      s.nonEmpty && ("""[^MDCLXVI]""".r.findFirstMatchIn(s.toUpperCase) == None)
    }
    }) => {

      def convert(left: String, cont: Int = 0, code: List[(Int, String)] = codeTable): Int = {
        val (unitVal, unitChar) = code.head
        left.splitAt(unitChar.length) match {
          case ("", _) => cont
          case (`unitChar`, tail) => convert(tail, cont + unitVal, code)
          case _ => convert(left, cont, code.tail)
        }
      }

      convert(src.toUpperCase())
    }
  }
}