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++14 (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
#define MAX 500000
#define SENTINEL 2000000000

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

void Merge(int A[], int n, int left, int mid, int right){
  int n1 = mid - left;
  int n2 = right - mid;
  int L[n1+1], R[n2+1];
  for(int i = 0; i < n1; i++) L[i] = A[left + i];
  for(int i = 0; i < n2; i++) R[i] = A[mid + i];

  L[n1] = SENTINEL;
  R[n2] = SENTINEL;
  int i = 0;
  int j = 0;
  for(int k = left; k < right; k++){
    if(L[i] <= R[j]){ // L < R 小さい方を左から挿入していく
      A[k] = L[i++];
    } else { // R < L
      A[k] = R[j++];
    }
    cnt++;
  }
}

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 n, A[MAX], i;
  cnt = 0;

  scanf("%d", &n);
  for(int i = 0; i < n; i++) scanf("%d", &A[i]);

  MergeSort(A, n, 0, n);

  for(int i = 0; i < n; i++){
    if ( i < n - 1 ) printf("%d ", A[i]);
    else printf("%d\n", A[i]);
  }

  printf("%d\n", cnt);

  return 0;
}