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: Accepted)

#include<stdio.h>
#include<limits.h>

int compTimes = 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 i, j, k;
	for( i = 0; i < n1; i++ ){ L[i] = A[left+i]; }
	for( i = 0; i < n2; i++ ){ R[i] = A[mid+i]; }
	L[n1] = INT_MAX;
	R[n2] = INT_MAX;
	i = 0;
	j = 0;
	for( k = left; k < right; k++ ){
		compTimes++;
		if( L[i] <= R[j] ){
			A[k] = L[i++];
		}else{
			A[k] = R[j++];
		}
	}
	return;
}

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);
	}
	return;
}

int main(){
	int n, S[500000], i;
	scanf("%d", &n);
	for( i = 0; i < n; i++ ){ scanf("%d", &S[i]); }
	mergeSort(S, 0, n);
	printf("%d", S[0]);
	for( i = 1; i < n; i++ ){ printf(" %d", S[i]); }
	printf("\n");
	printf("%d\n", compTimes);
	return 0;
}