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.{readLine,readInt}
import scala.language.postfixOps

object Main {
  var cnt = 0
  val l = new Array[Int](250001)
  val r = new Array[Int](250001)

  def merge(a:Array[Int],left:Int,mid:Int,right:Int) = {
    val n1 = mid-left
    val n2 = right-mid
    Array.copy(a,left,l,0,n1)
    l(n1) = Int.MaxValue
    Array.copy(a,mid,r,0,n2)
    r(n2) = Int.MaxValue
    var i=0
    var j=0
    for(k<-left until right) {
      if(l(i)<=r(j)){
        a(k) = l(i)
        i += 1
      } else  {
        a(k)=r(j)
        j += 1
      }
      cnt += 1
    }
  }

  def scan(h:Int,l:List[IndexedSeq[(Int,Int)]]):List[IndexedSeq[(Int,Int)]] =
    if(h==0) l
    else scan(h-1,(for(i<-l.head;j<-List((i._1,(i._2+i._1)/2),((i._2+i._1)/2,i._2))) yield j)::l)

  def getSortIndex(n:Int):Iterator[IndexedSeq[(Int,Int)]] = {
    var w = n
    var h = 0
    while(w>1) {
      h += 1
      w /= 2
    }
    scan(h-1,List(IndexedSeq((0,n/2),(n/2,n)))).to[Iterator]
  }

  def main(args:Array[String]) = {
    val n = readInt
    val a = readLine.split(" ").map(_.toInt)
    val l = getSortIndex(n)
    for(e2<-l) {
      for(e<-e2) {
        val mid = (e._2+e._1)/2
        if(e._2-e._1>1)
          merge(a,e._1,mid,e._2)
      }
    }
    merge(a,0,n/2,n)
    println(a.mkString(" "))
    println(cnt)
  }
}