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
 
int count = 0;
 
void Merge(int a[],int left,int mid,int right);
void MergeSort(int a[],int left,int right);
 
int main(){
  int a[MAX],n,i;
 
  scanf("%d",&n);
 
  for(i = 0; i < n; i++){
    scanf("%d",&a[i]);
  }
 
  MergeSort(a,0,n);
 
  for(i = 0; i < n; i++){
 
    if(i == n-1){
      printf("%d\n",a[i]);
      printf("%d\n",count);
      break;
    }
    printf("%d ",a[i]);
  }
 
  return 0;
}
 
 
 
void Merge(int a[],int left,int mid,int right){
 
  int n1 = mid-left, n2 = right-mid, l[n1],r[n2],i,j,k;
 
 
  for(i = 0; i < n1; i++){
    l[i] = a[left+i];
  }
 
  for(i = 0; i < n2; i++){
    r[i] = a[mid+i];
  }
 
  l[n1] = 1000000000;
  r[n2] = 1000000000;
 
  i = 0;
  j = 0;
 
  for(k = left; k < right ;k++){
    if(l[i] <= r[j]){
      a[k] = l[i];
      i++;
      count++;
    }
 
    else{
      a[k] = r[j];
      j++;
      count++;
    }
 
  }
}
 
 
 
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);
  }
 
}