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 MAX 500000
#define INFTY 2000000000

int Left[MAX/2+2],Right[MAX/2+2];
int cnt,A[MAX];

void merge(int A[],int l,int m , int r)
{
  int i,j,n1,n2,k;
   n1 = m - l;
   n2 = r - m;
   for(i=0;i < n1;i++)
     {
       Left[i]=A[l+i];
     }
 
   for(i=0;i < n2;i++)
     {
       Right[i]=A[m+i];
     }
   Left[n1]=INFTY;
   Right[n2]=INFTY;
   i=0;
   j=0;
   for(k=l;k < r;k++)
     {
       cnt++;
       if(Left[i]<=Right[j])
	 {
	   A[k] = Left[i];
	   i++;
	 }
       else 
	 {
	 A[k] = Right[j];
	 j++;
	 }
     }
}

void mergeSort(int A[],int l, int r)
{
  int mid=0;
  if(l+1 < r)
    {
      mid = (l+r)/2;
      mergeSort(A,l,mid);
      mergeSort(A,mid,r);
      merge(A,l,mid,r);
    }
}

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

  mergeSort(A,0,n);

  for(i = 0; i < n-1;i++)
    {
      printf("%d ",A[i]);
    }
  printf("%d\n",A[i]);
  printf("%d\n",cnt);
  return 0;
}