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>
#include<stdlib.h>
#include<limits.h>

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

int n, c=0;
int S[500000];

int main(){
  int i;

  scanf("%d",&n);
  if( n<1 || 500000<n ) exit(1);

  for( i=0 ; i<n ; i++ ){
    scanf("%d",&S[i]);
    if( S[i]<0 || 1000000000<S[i] ) exit(2);
  }

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


  return 0;
}

void 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);
  }
}

void merge(int left, int mid, int right){
  int i,j, k;
  int n1 = mid - left;
  int n2 = right - mid;
  int L[n1+1];
  int R[n2+1];

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

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

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