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: Time Limit Exceeded)

#include <stdio.h>

#define N 524288 // 2^19
#define HALFN 262144 // 2^18
#define INFTY 1000000001 // 10^9 + 1

int count = 0;

void merge(int *A, int left, int mid, int right) {
  int i, j, k, n1, n2, L[HALFN] = {0}, R[HALFN] = {0};
  
  n1 = mid - left;
  n2 = right - mid;

  // L[0...n1], R[0...n2] を生成
  for (i = 0; i < n1; i++)
    L[i] = A[left + i];
  for (i = 0; i < n2; i++)
    R[i] = A[mid + i];
  L[n1] = INFTY;
  R[n2] = INFTY;

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

int main(void){
  int i, n, S[N] = {0};
  
  scanf("%d", &n);
  for (i = 0; i < n; i++)
    scanf("%d", &S[i]);

  mergeSort(S, 0, n);
  for (i = 0; i < n; i++) {
    if(i)
      printf(" ");
    printf("%d", S[i]);
  }
  puts("");
  printf("%d\n", count);

  return 0;
}