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 S 2000000000

int L[MAX/2+2],R[MAX/2+2];
int c;

void merge(int *A, int n, int left, int mid, int right){
  int n1 = mid - left;
  int n2 = right -mid;
  int i;
  for(i=0;i<n1;i++)L[i]=A[left+i];
  for(i=0;i<n2;i++)R[i]=A[mid+i];
  L[n1]=S;
  R[n2]=S;
  i=0;
    int j=0, k=0;
  for(j=left;j<right;j++){
    c++;
    if(L[i]<=R[k]){
      A[j]=L[i];
      i++;
    }else{
      A[j]=R[k];
      k++;
    }
  }
}

void mergeSort(int *A,int n, int left,int right){
  int mid;
  if(left+1<right){
    mid=(left+right)/2;
    mergeSort(A,n,left,mid);
    mergeSort(A,n,mid,right);
    merge(A,n,left,mid,right);
  }
}
int main(){
  int A[MAX],n,i;
  c=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\n",A[i]);
    else  printf("%d ",A[i]);
  }
  printf("%d\n",c);
  return 0;
}