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 {
	
	int n;
	int[] A;
	int cnt =0;
	
	public static void main(String[] args) {
		new Main().solve();
		
	}
	
	public void solve(){
		Scanner scanner = new Scanner(System.in);
		n = scanner.nextInt();
		A = new int[n];
		
		for(int i=0;i<n;i++){
			A[i]= scanner.nextInt();
		}
		mergeSort(0, n);
		solvePrint();
	}
	
	public void merge(int left,int mid,int right){
		int n1 = mid -left;
		int n2 = right -mid;
		
		int[] L = new int[n1+1];
		int[] R = new int[n2+1];
		
		for(int i=0;i<n1;i++){
			L[i]=A[left +i];
		}
		for(int i=0;i<n2;i++){
			R[i]=A[mid+i];
		}
		L[n1]=Integer.MAX_VALUE;
		R[n2]=Integer.MAX_VALUE;
		int i=0,j=0;
		for(int k=left;k<right;k++){
			if(L[i]<=R[j]){
				A[k]=L[i];
				i++;
			}
			else{
				A[k]=R[j];
				j++;
			}
			cnt++;
		}
	}
	
	public 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 void solvePrint(){
		for(int i=0;i<A.length;i++){
			if(i>0){
				System.out.print(" ");
			}
			System.out.print(A[i]);
		}
		System.out.println("");
		System.out.println(cnt);
	}
}