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 JAVA (judge verdict: Time Limit Exceeded)

import java.util.Scanner;



public class Main {
static int n;
static int S[]=new int[500001];
static int count=0;

  public static void merge(int left,int mid,int right){
	  int i,j;
	  mid=(left+right)/2;

	 
	  ;
	  int infty=Integer.MAX_VALUE;

	  int R[]=new int[mid-left+2];
	  int L[]=new int[right-mid+2];

	  for(i=0;i<mid-left+2;i++){
		  L[i]=S[left+i];
	  }
	  for(i=0;i<right-mid;i++){
		  R[i]=S[mid+i];
	  }

	  L[mid-left]=infty;
	  R[right-mid]=infty;
	i=0;
	j=0;

	for(int k=left;k<right;k++){
		count++;
		if(L[i]<=R[j]){
			S[k]=L[i];
			i++;
		}
		else{
			S[k]=R[j];
			j++;
		}
	}
  }
  
  public static void mergesort(int left,int right){
	  if(left+1<right){
		  int mid=(left+right)/2;
		  
		  mergesort(left,mid);
		  mergesort(mid,right);
		  merge(left,mid,right);
		 
	  }
  }
  
  
	public static void main(String[] args) {
		int i;
	    int left1,right1;

		 Scanner sc=new Scanner(System.in);
		 n=Integer.parseInt(sc.next());

		  for(i=0;i<n;i++){
		  	  S[i]=Integer.parseInt(sc.next());
		  }
		  left1=0;
		  right1=n;
		 
		  mergesort(left1,right1);
		 

			  for(i=0;i<n;i++){
					System.out.print(S[i]);
					if(i==n-1){System.out.println("");
					}
			  else{
				  System.out.print(" ");
			  }
			  }
			  System.out.println(count);
  }
}