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>
using namespace std;

int cnt;
int L[500000/2+2], R[500000/2+2];

void merge( int A[], int left, int mid, int right ){
  int n1 = mid-left;
  int n2 = right-mid;

  for( int i=0; i<n1; i++ ){
    L[i] = A[left+i];
  }
  for( int i=0; i<n2; i++ ){
    R[i] = A[mid+i];
  }
  L[n1] = 1000000000;
  R[n2] = 1000000000;

  int a=0, b=0;
  for( int j=left; j<right; j++ ){
    cnt++;
    if( L[a] <= R[b] ){
      A[j] = L[a++];
    }else{
      A[j] = R[b++];
    }
  }
}

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

int main(){
  int n;
  cin >> n;

  int S[500000];
  for( int i=0; i<n; i++ ){
    cin >> S[i];
  }

  mergeSort( S, 0, n );

  for( int i=0; i<n; i++ ){
     if( i!=n-1 ){
       cout << S[i] << " ";
     }else{
       cout << S[i] << endl;
    }
  }

  cout << cnt << endl;

  return 0;
}