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 <stdlib.h>


void merge(int[],int,int,int);
void Sort(int[],int,int);


int count = 0;

int main()
{
  int i,n,S[500000];
  scanf("%d",&n);
  for(i = 0;i < n;i++)
    {
      scanf("%d",&S[i]);
    }
  Sort(S,0,n);
  for(i = 0;i < n;i++)
    {
      if(i >0) printf(" ");
      printf("%d",S[i]);
    }
  printf("\n");
  printf("%d\n",count);
  return 0;
}
void merge(int S[],int left,int mid,int right)
{
  int i,j,k,n1,n2;
  int *L,*R;
  n1 = mid - left;
  n2 = right - mid;
  L = (int *)malloc(sizeof(int)*(n1 + 1));
  R = (int *)malloc(sizeof(int)*(n2 + 1));
  for(i = 0;i <= n1 - 1;i++)
    {
      L[i] = S[left + i];
    }
  for(i = 0;i <= n2 - 1;i++)
    {
      R[i] = S[mid + i];
    }
  L[n1] = R[n2] = 2000000000;
  i = 0;
  j = 0;
  for(k = left;k <= right - 1;k++)
    {
      count++;
      if(L[i] <= R[j])
	{
	  S[k] = L[i];
	  i++;
	} else
	{
	  S[k] = R[j];
	  j++;
	}
    }
  free(L);
  free(R);
}
void Sort(int S[],int left,int right)
{
  int i,mid;
  if(left + 1 < right)
    {
      mid = (left + right) / 2;
      Sort(S,left,mid);
      Sort(S,mid,right);
      merge(S,left,mid,right);
    }
    
}