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>

#define INFTY 1000000001
#define MAX 500000

void merge(int *, int, int, int);
void mergeSort(int *, int, int);

int cnt=0;

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

void merge(int *A, int left, int mid, int right)
{
	int i, j, n1, n2, k;
	int L[MAX/2 +2], R[MAX/2 +2];
	
	n1 = mid - left;
	n2 = right - mid;
	for (i=0; i<n1; i++) {
		L[i] = A[left + i];
	}
	for (i=0; i<n2; i++) {
		R[i] = A[mid + i];
	}
	L[n1] = INFTY;
	R[n2] = INFTY;
	
	i = 0;
	j = 0;
	for (k=left; k<right; k++) {
		if( L[i] <= R[j] ) {
			A[k] = L[i];
			i++;
			cnt++;
		} else {
			A[k] = R[j];
			j++;
			cnt++;
		}
	}
}

void mergeSort(int *A, int left, int right)
{
	int mid;
	if( left + 1 < right ) {
		mid = ( left + right ) / 2;
		mergeSort(A, left, mid);
		mergeSort(A, mid, right);
		merge(A, left, mid, right);
	}
}