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 1000000000
 
int S[MAX], count=0;
 
void merge(int *, int, int, int);
void mergeSort(int *, int, int);
 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);
    }
}
void merge(int *A, int left, int mid, int right)
{
  int n1 = mid - left;
  int n2 = right - mid;
  int L[n1+1], R[n2+1], i, j, k;
 
  for(i=0; i<n1; i++)
    {
      L[i] = A[left+i];
    }
  for(i=0; i<n2; i++)
    {
      R[i] = A[mid+i];
    }
  L[n1] = SENTINEL;
  R[n2] = SENTINEL;
 
  i=0;
  j=0;
 
  for(k=left; k<right; k++)
    {
      if(L[i] <= R[j])
        {
          A[k] = L[i];
          i = i + 1;
        }
      else
        {
          A[k] = R[j];
          j = j + 1;
        }
      count++;
    }
}
 

int main()
{
  int n, i, left, right;
 
  scanf("%d", &n);
  for(i=0; i<n; i++)
    {
      scanf("%d", &S[i]);
    }
 
  left = 0;
  right = n;
 
  mergeSort(S, left, right);
 
  for(i=0; i<n; i++)
    {

      if(i < n-1)printf("%d ", S[i]);
      else printf("%d\n%d\n", S[i], count);
    }
 
  return 0;
}