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 INFTY 1000000001

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

int count;

int main()
{
  int i, n, S[500000];

  scanf("%d", &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+1 < n) printf(" ");
    }
  printf("\n");
  printf("%d\n", count);
  
  return 0;
}
void merge(int *A, int left, int mid, int right)
{
  int i, j, k;
  int n1 = mid-left;
  int n2 = right-mid;
  int L[n1+1], R[n2+1];

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

  L[n1] = R[n2] = INFTY;
  i = j = 0;

  for(k=left; k<right; k++)
    {
      count++;
      if(L[i] <= R[j])
	{
	  A[k] = L[i];
	  i = i+1;
	}
      else
	{
	  A[k] = R[j];
	  j = j+1;
	}
    }
}
void mergeSort(int *A, int left, int right)
{
  int mid;
  
  if(left+1 < right)
    {
      mid = (left + right)/2;
      mergeSort(A, left, mid);
      mergeSort(A, mid, right);
      merge(A, left, mid, right);
    }
}