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: Accepted)

import java.util.Scanner;

class Main {
	public static int sum = 0;
	
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		
		int n = scan.nextInt();
		
		int[] S = new int[n];
		
		for(int i = 0; i < n; i++) {
			S[i] = scan.nextInt();
		}
		
		margeSort(S, 0, n);

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

		System.out.println();
		System.out.println(sum);
		
		scan.close();
	}
	
	static void marge(int[] A, 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;
		int j = 0;
		
		for(int k = left; k < right; k++) {
			sum++;
			if(L[i] <= R[j]) {
				A[k] = L[i];
				i++;
				
			} else {
				A[k] = R[j];
				j++;
			}
		}
	}
	
	 static void margeSort(int[] A, int left, int right) {
		if(left + 1 < right) {
			int mid = (left + right) / 2;
			
			margeSort(A, left, mid);
			margeSort(A, mid, right);
			marge(A, left, mid, right);
		}
	}
}