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 <iostream>
#include <iomanip>
#include <algorithm>
#include <cfloat>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <functional>
#include <sstream>
#include <string>
#include <utility>
#include <map>
#include <memory>
#include <set>
#include <vector>
#include <deque>
#include <list>
#include <stack>
#include <queue>

using namespace std;

class MergeSort
{
public:
  MergeSort() : cnt(0) {}
  int solve();
  int merge(int left, int mid, int right);
  int mergeSort(int left, int right);
  int showCnt();
  int n, cnt;
  int s[500000];
};

int MergeSort::merge(int left, int mid, int right)
{
  const int infty = 2000000000;
  int n1 = mid - left;
  int n2 = right - mid;

  int *l = new int [n1 + 1];
  int *r = new int [n2 + 1];

  for ( int i = 0; i < n1; i++ )
    l[i] = s[left + i];
  
  for ( int i = 0; i < n2; i++ )
    r[i] = s[mid + i];

  l[n1] = infty;
  r[n2] = infty;

  int i = 0;
  int j = 0;

  for ( int k = left; k < right; k++ )
    {
      cnt++;
      if ( l[i] <= r[j] )
        s[k] = l[i++];
      else
        s[k] = r[j++];
    }

  delete[] l;
  delete[] r;
  
  return 0;
}

int MergeSort::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 );
    }
  
  return 0;
}

int MergeSort::showCnt()
{
  cout << cnt << endl;
  return 0;
}

int MergeSort::solve()
{
  cin >> n;
  for ( int i = 0; i < n; i++ )
    {
      cin >> s[i];
    }

  mergeSort( 0, n );
  
  for ( int i = 0; i < n; i++ )
    {
      if ( i ) cout << " ";
      cout << s[i];
    }
  cout << endl;

  showCnt();
  
  return 0;
}

int main()
{
  MergeSort ms;

  ms.solve();

  return 0;
}