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 INFTY 2000000000;
#define MAX 500000

int count=0;
int S[MAX], L[MAX], R[MAX];

void merge(int *, int, int, int, int);
void mergeSort(int *, int, int, int);

int main()
{
  int i, n;

  scanf("%d", &n);

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

  mergeSort(S, n, 0, n);

  for( i = 0 ; i < n ; i++ ){
    if( i >= 1 ) printf(" ");
    printf("%d", S[i]);
  }
  printf("\n");

  printf("%d\n", count);

  return 0;
}

void merge(int S[], int n, 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] = R[n2] = INFTY;

  i = j = 0;
  
  for( k = left ; k < right ; k++ ){
    count++;
    if( L[i] <= R[j] ){
      S[k] = L[i];
      i++;
    }
    else {
      S[k] = R[j];
      j++;
    }
  }
}

void mergeSort(int S[], int n, int left, int right)
{
  int mid;

  if( left+1 < right ){
    mid = (left + right)/2;
    mergeSort(S, n, left, mid);
    mergeSort(S, n, mid, right);
    merge(S, n, left, mid, right);
  }
}