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;

public class Main {
    static int comparisons;

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = in.nextInt();
        }
        comparisons = 0;
        mergeSort(a, 0, a.length);
        System.out.println(printArray(a));
        System.out.println(comparisons);
    }

    private 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);
        }
    }

    private static void merge(int[] a, int left, int mid, int right) {
        int n1 = mid - left;
        int n2 = right - mid;
        int[] l = new int[n1];
        int[] r = new int[n2];
        for (int i = 0; i < n1; i++) {
            l[i] = a[left + i];
        }
        for (int i = 0; i < n2; i++) {
            r[i] = a[mid + i];
        }
        int i = 0;
        int j = 0;
        for (int k = left; k < right; k++) {
            if (i < n1 && (j == n2 || l[i] <= r[j])) {
                a[k] = l[i];
                i++;
                comparisons++;
            } else {
                a[k] = r[j];
                j++;
                comparisons++;
            }
        }
    }

    static String printArray(int[] a) {
        StringBuilder sb = new StringBuilder();
        sb.append(a[0]);
        for (int i = 1; i < a.length; i++) {
            sb.append(" ").append(a[i]);
        }
        return sb.toString();
    }
}