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 {
	int count = 0;

	public static void main(String[] args) {
		new Main().run();
	}

	private void run() {
		Scanner scanner = new Scanner(System.in);
		int n = scanner.nextInt();
		int[] num = new int[n];
		for (int i = 0; i < n; i++) {
			num[i] = scanner.nextInt();
		}
		mergeSort(num, 0, n);
		System.out.print(num[0]);
		for (int i = 1; i < n; i++) {
			System.out.print(" " +num[i]);
		}
		System.out.println();
		System.out.println(count);
	}

	private void mergeSort(int[] num, int left, int right) {
		if (left + 1 < right) {
			int mid = (left + right) / 2;
			mergeSort(num, left, mid);
			mergeSort(num, mid, right);
			merge(num, left, mid, right);
		}
	}

	private void merge(int[] num, int left, int mid, int right) {
		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] = num[left + i];
		}
		for (int i = 0; i < n2; i++) {
			r[i] = num[mid + i];
		}
		l[n1] = Integer.MAX_VALUE;
		r[n2] = Integer.MAX_VALUE;

		int L = 0;
		int R = 0;
		for (int k = left; k < right; k++) {
			if (l[L] <= r[R]) {
				num[k] = l[L++];
			} else {
				num[k] = r[R++];
			}
			count++;
		}
	}

}