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)

/*マージソート*/
#include <stdio.h>
#define N 1000000

void merge(int *, int, int, int);
void mergeSort(int *, int, int);
int count=0;

int main(){
  int n, s[N], i, j;
  
  /*値の入力*/
  scanf("%d", &n);
  for (i=0; i<n; i++){
    scanf("%d", &s[i]);
  }
  
  mergeSort(s, 0, n);
  
  for (i=0; i<n-1; i++){
    printf("%d ", s[i]);
  }
  
  printf("%d\n", s[n-1]);
  
  printf("%d\n", count);
  
  return 0;
}

void merge(int *s, int left, int mid, int right){
  int n1, n2, i, j, k;
  int l[N], r[N];
  n1 = mid - left;
  n2 = right - mid;
  
  for(i=0; i<n1; i++){
    l[i] = s[left+i];
  }
  for(i=0; i<n2; i++){
    r[i] = s[mid+i];
  }
  
  l[n1] = 1000000000;
  r[n2] = 1000000000;
  
  i=0;
  j=0;
  
  for(k=left; k<right; k++){
    if (l[i] <= r[j]){
      s[k] = l[i];
      i++;
      count++;
    }
    else{
      s[k] = r[j];
      j++;
      count++;
    }
  }
}

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