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.*;

public class Main{

	static int merge(int[] A, int left, int mid, int right){
		int cnt = 0;
		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++){
			cnt++;
			if(L[i] < R[j]){
				A[k] = L[i];
				i++;
			}else{
				A[k] = R[j];
				j++;
			}
		}
		return cnt;
	}

	static int mergeSort(int[] A, int left, int right){
		int cnt = 0;
		if(left+1 < right){
			int mid = (left + right) / 2;
			cnt += mergeSort(A, left, mid);
			cnt += mergeSort(A, mid, right);
			cnt += merge(A, left, mid, right);
		}
		return cnt;
	}

	public static void main(String[] args){

		Scanner scan = new Scanner(System.in).useDelimiter("[\\s]+");
		int cnt = 0;
		int n = scan.nextInt();
		int[] S = new int[n];
		for(int i = 0; i < n; i++){
			S[i] = scan.nextInt();
		}
		cnt = mergeSort(S, 0, n);
		for(int i = 0; i < n; i++)
			System.out.printf(i != n-1? "%d " : "%d\n", S[i]);
		System.out.printf("%d\n", cnt);
	}
}