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 sentinel 2000000000

int L[max/2 + 2];
int R[max/2 + 2];
int count;



int merge(int A[], int n, int left, int mid, int right)  {
  int i, j, k, n1, n2;
  n1 = mid - left;
  n2 = right - mid;
  
  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] = sentinel;
  
  i = j = 0;
  for ( k = left; k < right; k++)  {
    count++;
    if ( L[i] <= R[j])  
      A[k] = L[i++];
    else 
      A[k] = R[j++];
  }
}

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

int main(void)  {
  int A[max], n, i;
  count = 0;
  
  scanf("%d", &n);
  for (i = 0; i < n; i++) 
    scanf("%d", &A[i]);
  
  mergeSort(A, n, 0, n);

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