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 2000000000
#define MAX 500000

int n,count=0;

void merge(int A[],int n,int left, int mid,int right)
{
	int n1=mid-left;
	int n2=right-mid;
	int L[MAX/2+2],R[MAX/2+2];
	int i,j;
	
	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(int k=left;k<right;k++)
	{
		count++;
		if(L[i]<=R[j])
		{
			A[k]=L[i];
			i=i+1;
		}
		else
		{
			A[k]=R[j];
			j=j+1;
		}
	}
}

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

int main(void)
{
	int i;
	
	scanf("%d",&n);
	
	int S[n];
	
	for(i=0;i<n;i++)
	{
		scanf("%d",&S[i]);
	}
	
	int left=0,right=n;
	
	mergeSort(S,n,left,right);
	
	for(i=0;i<n;i++)
	{
		printf("%d",S[i]);
		if(i!=n-1)
		{
			printf(" ");
		}
	}
	
	printf("\n");
	printf("%d\n",count);
}