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: Runtime Error)

#include<stdio.h>
#define MAX 500000
#define INFTY 100000000
int L[MAX/2 + 2], R[MAX/2 + 2];
int count;
int i,k;
void merge( int A[] , int n , int left , int mid ,int right ){
  int n1 = mid - left;
  int 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] = INFTY;
  R[n2] = INFTY;
  int i = 0 , 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 ){
  if( left + 1 < right ){
    int mid = ( right + left )/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 == n-1){
      printf("%d",A[i]);
    }
    else{
      printf("%d ",A[i]);
      }
  }
  printf("\n");
  printf("%d\n",count);
  return 0;
}