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: Wrong Answer)

#include <stdio.h>
#define N 500000
#define INFTY 2000000000

int S[N];
int L[N/2],R[N/2];
int count=0;

int merge(int S[],int n, int left, int mid, int right){
  int n1,n2,i,j,k;
  n1 = mid - left;
  n2 = right - mid;

  j=0;
  k=0;

  for(i=0; i<n1; i++) L[i] = S[left+i];
  for(i=0; i<n2; i++) R[i] = S[mid+i];

  L[n1] = R[n2] = INFTY;

  for(i=left; i<right; i++){
    count++;
    if(L[j]<=R[k]) S[i] = L[j++];
    else {
      S[i] = R[k++];
    }

  }
 //printf("%d\n",count);
}

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

int main(){
  int S[N],i,n;

  scanf("%d",&n);
  for(i=0; i<n; i++){
    scanf("%d",&S[i]);
  }

  mergeSort(S,n,0,n);

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

  printf("%d\n",count);

  return 0;

}