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>

int merge(int, int, int);
int mergeSort(int, int);

int S[500000], L[250001], R[250001];
int count=0;

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

  mergeSort(0,i);

  for( i=0 ; i<n-1 ; i++ )
    printf("%d ",S[i]);
  printf("%d\n",S[i]);
  printf("%d\n",count);

  return 0;
}

int merge(int left, int mid, int right)
{
  int n1, n2, i, j, k;
  n1 = mid-left;
  n2 = right - mid;
  for( i=0 ; i<n1 ; i++ )
    L[i] = S[left+i];
  for( i=0 ; i<n2 ; i++ )
    R[i] = S[mid+i];
  L[n1]=1000000100;
  R[n2]=1000000100;
  i=0;
  j=0;
  for( k=left ; k<right ; k++ ){
    if(L[i]<=R[j]){
      S[k]=L[i];
      i++;
    }
    else{
      S[k]=R[j];
      j++;
    }
    count++;
  }
}
int mergeSort(int left, int right)
{
  int mid;
  if((left+1)<right){
    mid=(left+right)/2;
    mergeSort(left,mid);
    mergeSort(mid,right);
    merge(left,mid,right);
  }
}