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 INF 999999999
#define N 500000


int a[N],b[N],c=0;

void merge(int s[],int left,int mid,int right){
  int i,j,k;
  int n1,n2;
  
  n1=mid-left;
  n2=right-mid;
  
  for(i=0;i<n1;i++)a[i]=s[left+i];
  for(i=0;i<n2;i++)b[i]=s[mid+i];
  a[n1]=INF;
  b[n2]=INF;

  i=0;
  j=0;
  for(k=left;k<right;k++){
    c++;
    if(a[i]<=b[j]){
      s[k]=a[i];
      i++;
    }
    else {
      s[k]=b[j];
      j++;
    }
  }
}

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);
  }
}

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

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

  mergeSort(s,0,n);

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