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 MAX 500000
#define INFTY 2000000000

void merge(int[],int,int,int);
void mergeSort(int[],int,int);

int L[(MAX/2)+2],R[(MAX/2)+2];
int cnt;


int main(){

  int i,n,A[MAX];
  cnt = 0;

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

  mergeSort(A,0,n);

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

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

  return 0;
}


void merge(int A[],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] = A[left+i];
  for(i=0;i<=n2;i++)R[i] = A[mid+i];

   L[n1] = INFTY;
   R[n2] = INFTY;

    i = 0;
    j = 0;
    for(k=left;k<right;k++){
      cnt++;
      if(L[i] <= R[j]){
	A[k] = L[i];
	i = i + 1;
      }
      else{
	A[k] = R[j];
	j = j + 1;
      }
    }

}

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

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