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}

object Main {
  def merge(a: Array[Int], left: Int, mid: Int, right: Int) = {
    val l = new Array[Int](mid-left+1)
    val r = new Array[Int](right-mid+1)
    Array.copy(a,left,l,0,l.length-1)
    Array.copy(a,mid,r,0,r.length-1)
    l(mid-left) = Int.MaxValue
    r(right-mid) = Int.MaxValue

    def loop(a: Array[Int], i: Int, j: Int, k: Int, cnt: Int):Int = {
      if(k==right) cnt
      else if( l(i) <= r(j) ) {
        a(k) = l(i)
        loop(a, i+1, j, k+1, cnt+1)
      } else {
        a(k) = r(j)
        loop(a, i, j+1, k+1, cnt+1)
      }
    }
    loop(a, 0, 0, left, 0)
  }

  def mergeSort(a: Array[Int], left: Int, right: Int):Int = {
    if(left+1<right) {
      val mid = (left + right) / 2
      val x = mergeSort(a, left, mid)
      val y = mergeSort(a, mid, right)
      x + y + merge(a,left,mid,right)
    } else 0
  }

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