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: Runtime Error)

#include <stdio.h>
#define MAX 500000
#define SENTINEL 200000000
// sentinel 10^2 分少ない

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

void merge(int A[],int n,int left,int mid,int right){
  int i,j,k;
  int n1 = mid - left;
  int 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] = R[n2] = SENTINEL;

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

void mergeSort(int A[],int n,int left,int right){
   if( left+1 < right){
       int 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;
     cnt =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)printf(" ");
     printf("%d",A[i]);
    
     }

     printf("\n");
     printf("%d\n",cnt);
  
 return 0;
}