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

int count;

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

int main(){
  int n,i;
  int A[MAX];

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

  return 0;
}


void merge(int A[],int left,int mid,int right){
  int L[MAX / 2 + 2],R[MAX / 2 + 2];
  int n1,n2,i,j,k;
  
  n1 = mid - left;
  n2 = right - mid;
  /*L[0...n1],R[0...n2]を生成*/
  for(i = 0;i <= n1-1;i++){
    L[i] = A[left + i];
  }
  for(i = 0;i <= n2-1;i++){
    R[i] = A[mid + i];
  }
  L[n1] = INFTY;
  R[n2] = INFTY;
  i = 0;
  j= 0;
  for(k = left;k <= right-1;k++){
    count++;
    if (L[i] <= R[j]){
      A[k] = L[i++];
    }
    else{
      A[k] = R[j++];
    }
  }
}

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