Problem:
Merge Sort

Write a program of a Merge Sort algorithm implemented by the following pseudocode. You should also report the number of comparisons in the Merge function.

Merge(A, left, mid, right)
n1 = mid - left;
n2 = right - mid;
create array L[0...n1], R[0...n2]
for i = 0 to n1-1
do L[i] = A[left + i]
for i = 0 to n2-1
do R[i] = A[mid + i]
L[n1] = SENTINEL
R[n2] = SENTINEL
i = 0;
j = 0;
for k = left to right-1
if L[i] <= R[j]
then A[k] = L[i]
i = i + 1
else A[k] = R[j]
j = j + 1

Merge-Sort(A, left, right){
if left+1 < right
then mid = (left + right)/2;
call Merge-Sort(A, left, mid)
call Merge-Sort(A, mid, right)
call Merge(A, left, mid, right)

Input

In the first line n is given. In the second line, n integers are given.

Output

In the first line, print the sequence S. Two consequtive elements should be separated by a space character.

In the second line, print the number of comparisons.

Constraints

n ≤ 500000

0 ≤ an element in S ≤ 109

Sample Input 1

10
8 5 9 2 6 3 7 1 10 4

Sample Output 1

1 2 3 4 5 6 7 8 9 10
34

Notes

Solution in Scala (judge verdict: Accepted)


import scala.io.StdIn

object Main extends App {

  final val infity = Int.MaxValue
  var compareCount = 0
  
  def merge(left: Int, mid: Int, right: Int): Unit ={
    var al = a.slice(left, mid) ++ Array(infity)
    var ar = a.slice(mid, right) ++ Array(infity)
    var i = 0
    var j = 0
    //println("left:" + al.toList)
    //println("right:" + ar.toList)
    (left until right).foreach{ k =>
      compareCount += 1
      if(al(i) <= ar(j)){
        a(k) = al(i)
        i += 1
      } else {
        a(k) = ar(j)
        j += 1
      } 
    }
    //println("all:" + a.toList.mkString(" "))
  }
  
  val n = StdIn.readLine().trim.toInt
  val a = StdIn.readLine().trim.split(' ').map(_.toInt)

  def mergeSort(left: Int, right: Int): Unit ={
    if(left+1 < right){
      val mid = (left + right) / 2
      mergeSort(left, mid)
      mergeSort(mid, right)
      merge(left, mid, right)
    }
  }
  
  mergeSort(0, a.size)
  println(a.toList.mkString(" "))
  println(compareCount)

}