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: Memory Limit Exceeded)

import scala.io.StdIn.{readLine,readInt}
import scala.collection.mutable.ListBuffer

object Main {
  var cnt = 0

  def merge(a:Array[Int],left:Int,mid:Int,right:Int) = {
    val n1 = mid-left
    val n2 = right-mid
    val l = a.slice(left,left+n1) :+ Int.MaxValue
    val r = a.slice(mid,mid+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 sort(n:Int,l:List[(Int,Int)]):List[(Int,Int)] = {
    var l2 = l.to[ListBuffer]
    var n2 = n
    while(n2>1) {
      val newl = new ListBuffer[(Int,Int)]
      for(i<-l2) {
        val mid = (i._2+i._1)/2
        newl ++= List((i._1,mid),(mid,i._2))
      }
      l2 = newl.to[ListBuffer]
      n2 = n2/2
    }
    l2.toList
  }

  def mergeSort(l:List[(Int,Int)],a:Array[Int]):Unit = {
    if(l.length==1) return
    else {
      var i = 0
      var left = 0
      var right = 0
      val b = new ListBuffer[(Int,Int)]
      for(e<-l) {
          val mid = (e._2+e._1)/2
          if(e._2-e._1>1)
            merge(a,e._1,mid,e._2)
          if(i==1) {
            right = e._2
            b += ((left,right))
            i = 0
          } else {
            left = e._1
            i+=1
          }
      }
      mergeSort(b.toList,a)
    }
  }

  def main(args:Array[String]) = {
    val n = readInt
    val a = readLine.split(" ").map(_.toInt)
    val r = sort(n/2,List((0,n/2),(n/2,n)))
    mergeSort(r,a)
    merge(a,0,n/2,n)
    println(a.mkString(" "))
    println(cnt)
  }
}