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 N 500000
#define AEN 1000000000
 
int merge(int *,int,int,int);
void mergeSort(int *,int,int);
 
int n,s[N],count=0,tmp[N],x[N];
 
int main()
{
 
  int i,x;
 
  scanf("%d",&n);
 
  for(i=0;i<n;i++){
 
    scanf("%d",&s[i]);
 
  }
 
  mergeSort(s,0,n-1);
 
  for(i=0;i<n-1;i++){
 
    printf("%d ",s[i]);
 
  }
  printf("%d\n",s[n-1]);
 
  printf("%d\n",count);
 
  return 0;
 
}
 
 
 
void mergeSort(int A[],int left,int right){
 
  int mid,i,j,k;
 
  if(left>=right) return;
 
  mid=(left+right)/2;
 
  mergeSort(A,left,mid);
  mergeSort(A,mid+1,right);
 
  for(i=left;i<=mid;i++){
    tmp[i]=A[i];}
 
  for(i=mid+1,j=right;i<=right;i++,j--){
    tmp[i]=A[j];
  }
 
  i=left;
  j=right;
 
  for(k=left;k<=right;k++){
 
    if(tmp[i]<=tmp[j]) A[k]=tmp[i++];
    else A[k]=tmp[j--];  
 
    count++;
  }
}