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>
#define INFTY 1000000000

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

int *S,count=0;
int main(){
  int n,i;
  scanf("%d",&n);
  S=(int *)malloc(sizeof(int)*n);
  for(i=0;i<n;i++) scanf("%d",&S[i]);

  mergeSort(S,0,n);

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

void merge(int *S, int left, int mid, int right){
  int i,j,k;
  int n1 = mid - left;
  int n2 = right - mid;
  int L[n1],R[n2];
  /*L[0...n1], R[0...n2] を生成*/
  for(i=0;i<n1;i++) L[i]=S[left+i];
  for(i=0;i<n2;i++) R[i]=S[mid + i];
 
  L[n1]=INFTY;
  R[n2]=INFTY;
  i=0;
  j=0;
  for(k=left;k<right;k++){
    if(L[i]<=R[j]){
      S[k]=L[i];
      i=i+1;
      count++;
    }else{ 
      S[k]=R[j];
      j=j+1;
      count++;
    }
  }
}

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