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 C++ (judge verdict: Time Limit Exceeded)

#include<iostream>
#include<limits>
using namespace std;
int conpareCount = 0;
void merge(int* A, int left, int mid, int right){
	int n1 = mid - left;
	int n2 = right - mid;
	//int L[n1 + 1], R[n2 + 1];
	int *L = new int[50000000], *R = new int[50000000];
	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] = numeric_limits<int>::infinity();
	R[n2] = numeric_limits<int>::infinity();*/
	L[n1] = 100000;
	R[n2] = 100000;
	int i = 0; 
	int j = 0;
	for(int k = left; k < right; k++){
		conpareCount++;
		if(L[i] <= R[j]){
			A[k] = L[i];
			i++;
		}else{
			A[k] = R[j];
			j++;
		}
	}
delete[]L;
delete[]R;
}

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);
	}
}

int main(){
	int n = 0;
	cin >> n;
	//int A[n];
	int A[n];
	for(int i = 0; i < n; i++){
		cin >> A[i];
	}
	mergeSort(A, 0, n);
	cout << A[0];
	for(int i = 1; i < n; i++){
		cout << ' ' << A[i];
	}
	cout << '\n';
	cout << conpareCount << '\n';
	cin >> n;
	return 0;
}