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>
#include <limits.h>
 
long c = 0;
 
void merge(long *a, long left, long mid, long right){
  long n1, n2, i, j, k;
  n1 = mid - left;
  n2 = right - mid;
  long l[n1 + 1], r[n2 + 1];
  for(i = 0; i < n1; ++i) l[i] = a[left + i];
  for(i = 0; i < n2; ++i) r[i] = a[mid + i];
  l[n1] = LONG_MAX;
  r[n2] = LONG_MAX;
  i = 0;
  j = 0;
  for(k = left; k < right; ++k){
    if(l[i] <= r[j]) a[k] = l[i++];
    else a[k] = r[j++];
    c++;
  }
}
 
void merge_sort(long *a, long left, long right){
  if(left + 1 < right){
    long mid = (left + right) / 2;
    merge_sort(a, left, mid);
    merge_sort(a, mid, right);
    merge(a, left, mid, right);
  }
}
 
int main(){
  long n, s[500000], i, j;
  scanf("%ld", &n);
  for(i = 0; i < n; ++i) scanf("%ld", s + i);
 
  merge_sort(s, 0, n);
 
  for(i = 0; i < n; ++i) printf(i != 0 ? " %ld" : "%ld", s[i]);
  printf("\n%ld\n", c);
  return 0;
}