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 java.util.Scanner

object Main {
  var cnt = 0

  def merge(a:Array[Int],left:Int,mid:Int,right:Int) = {
    var i=0
    var j=0
    val n1 = mid-left
    val n2 = right-mid
    val l = a.slice(left,left+n1) ++ Array(Int.MaxValue)
    val r = a.slice(mid,mid+n2) ++ Array(Int.MaxValue)
    i=0;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 mergeSort(a:Array[Int],left:Int,right:Int):Unit = {
    if(left+1>=right) return
    else {
      val mid = (left+right)/2
      mergeSort(a,left,mid)
      mergeSort(a,mid,right)
      merge(a,left,mid,right)
    }
  }

  def main(args:Array[String]) = {
    val sc = new Scanner(System.in)
    val n = sc.nextInt()
    val a = new Array[Int](n)
    for(i<-0 until n) {
      a(i) = sc.nextInt()
    }
    mergeSort(a,0,n)
   println(a.mkString(" "))
    println(cnt)
  }
}