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 cnt = 0;

    public static void main(String[] args) {
        
    	//Input
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        
        int[] S = new int[n];
        
        for(int i = 0; i < n; i++){
        	S[i] = sc.nextInt();
        }
        
        //Calculation
        int[] result = new int[S.length];
        result = margeSort(S);
        
        //Output
        print(result);
    }

    private static void print(int[] ar){
    	for(int i = 0; i < ar.length; i++){
        	System.out.print(ar[i]);
        	if(i < ar.length - 1){
        		System.out.print(" ");
        	}
        }
    	System.out.println();
    	System.out.println(cnt);
    }

    private static int[] margeSort(int[] ar){
    	
    	if(ar.length == 1){
    		return ar;
    	}

        int mid = ar.length / 2;
        int[] s_01 = new int[mid],
              s_02 = new int[ar.length - mid];

        for (int i = 0; i < mid; i++) s_01[i] = ar[i];
        for (int i = 0; i < ar.length - mid; i++) s_02[i] = ar[mid + i];
        
        int[] r_01 = margeSort(s_01);
        int[] r_02 = margeSort(s_02);
        return marge(r_01,r_02);
    }

    private static int[] marge(int[] a,int[] b){

    	int j = 0,k = 0;
    	int[] r = new int[a.length + b.length];

    	for (int i = 0; i < r.length; i++,cnt++) {
    		//guard
			if (j == a.length) {
				r[i] = b[k];
				k++;
				continue;
			}
			if (k == b.length) {
				r[i] = a[j];
				j++;
				continue;
			}
			//comparison
			if (a[j] < b[k]) {
				r[i] = a[j];
				j++;
			} else {
				r[i] = b[k];
				k++;
			}
		}
    	return r;
    }
}