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.{readInt, readLine}

object Main extends App {

  val n  = readInt()
  val xs = readLine().split(" ").map { _.toInt }

  val cnt = MergeSort.sort(xs)

  println(xs.mkString(" "))
  println(cnt)
}

object MergeSort {
  val Max: Int      = 500000
  val Sentinel: Int = 2000000000

  def sort(xs: Array[Int]): Int = {

    val ls = new Array[Int](Max / 2 + 2)
    val rs = new Array[Int](Max / 2 + 2)

    def mergeSort(left: Int, right: Int): Int = {
      val m = right - left
      if (m <= 1) 0
      else {
        val mid  = (left + right) / 2
        val cnt1 = mergeSort(left, mid)
        val cnt2 = mergeSort(mid, right)
        merge(left, mid, right)
        cnt1 + cnt2 + m
      }
    }

    def merge(left: Int, mid: Int, right: Int): Unit = {
      val n1 = mid - left
      val n2 = right - mid
      Array.copy(xs, left, ls, 0, n1)
      Array.copy(xs, mid, rs, 0, n2)
      ls(n1) = Sentinel
      rs(n2) = Sentinel
      var i  = 0
      var j  = 0
      var k  = left
      while (k < right) {
        if (ls(i) <= rs(j)) {
          xs(k) = ls(i)
          i += 1
        } else {
          xs(k) = rs(j)
          j += 1
        }
        k += 1
      }
    }

    mergeSort(0, xs.length)
  }
}