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: Memory 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 IOException {
		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
		
		int n = Integer.parseInt(reader.readLine());
		String[] strArray = reader.readLine().split(" ");
		int[] arr = new int[n];
		for (int i = 0; i < n; i++) {
			arr[i] = Integer.parseInt(strArray[i]);
		}
		
		mergeSort(arr);
		for (int i = 0; i < n; i++) {
			System.out.print(arr[i]);
			if (i != n - 1) {
				System.out.print(" ");
			}
		}
		System.out.println("");
		System.out.println(count);
	}

	private static void mergeSort(int[] arr) {		
		mergeSort(0, arr.length - 1, arr);
	}

	private static void mergeSort(int floor, int ceiling, int[] arr) {		
		if (floor < ceiling) {
			int mid = floor + (ceiling - floor) / 2;
			mergeSort(floor, mid, arr);
			mergeSort(mid + 1, ceiling, arr);
			merge(floor, mid, ceiling, arr);
		}		
	}

	private static void merge(int floor, int mid, int ceiling, int[] arr) {
		
		int[] tempArray = new int[arr.length];
		for (int i = floor; i <= ceiling; i++) {
			tempArray[i] = arr[i];
		}

		int i = floor;
		int j = mid + 1;
		int k = floor;
		while (k <= ceiling) {
			count++;
			if (j > ceiling || (i <= mid && tempArray[i] < tempArray[j])) {
				arr[k] = tempArray[i];
				i++;
			} else {
				arr[k] = tempArray[j];
				j++;
			}
			k++;
		}
	}
}