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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main {

	static int count = 0;
	
	public static void main(String[] args) throws NumberFormatException, IOException{
		
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		int[] S = new int[n];
		
		String[] str = br.readLine().split(" ");
		for(int i = 0; i < n; i++) S[i] = Integer.parseInt(str[i]);
		
		mergeSort(S, 0, n);
		
		for(int i = 0; i < n; i++){
			System.out.print(S[i]);
			if(i + 1 == n) System.out.print("\n");
			else System.out.print(" ");
		}
		System.out.println(count);
	}
	
	public static void merge(int[] A, int left, int mid, int right){
		int n1 = mid - left, n2 = right - mid;
		int[] L = new int[n1 + 1], 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] = R[n2] = Integer.MAX_VALUE;
		
		for(int i = 0, j = 0, k = left; k < right; k++){
			count++;
			if(L[i] <= R[j]) A[k] = L[i++];
			else A[k] = R[j++];
		}
	}
	
	public static void mergeSort(int[] A, int left, int right){
		if(left + 1 < right){
			int mid = (left + right)/2;
			mergeSort(A, left, mid);
			mergeSort(A, mid, right);
			merge(A, left, mid, right);
		}
	}
}