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<string.h>
#include<stdlib.h>
#include<math.h>
#include <stdint.h>
#include <inttypes.h>

#define M 500000
#define INFTY 1000000001

int count;

void merge(int *, int ,int ,int );
void mergeSort(int *, int , int );
  
int main(){
  int S[M];

  int i,j,n;
  int l, mid , r;

  scanf("%d",&n);
  for(i=0;i<n;i++)
    scanf("%d",&S[i]);
  l=0;
  r=n;
  
  mergeSort(S,l,r);

  
  printf("%d",S[0]);
  for(i=1;i<n;i++)
    printf(" %d",S[i]);
  printf("\n");
  printf("%d\n",count);
  
  return 0;

}


void merge(int *A, int left, int mid,int right)
{
  int i,j,k,n1,n2;
  int L[M],R[M];

  
  n1 = mid - left;
  n2 = right - mid;


  
  /* L[0...n1], R[0...n2] を生成*/
  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++){
      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 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);
     }
   }