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 L 500000

int s[L];
int workspace[L];
int cnt = 0;

void mergeSort(int *a, int low, int high) {
  int mid, i, j, k;

  if(low >= high)
    return;

  mid = (high + low) / 2;
  mergeSort(a, low, mid);
  mergeSort(a, mid + 1, high);

  for(i = low;i <= mid;i++) {
    workspace[i] = a[i];
  }

  for(i = 0;i <= high - mid - 1;i++) {
    workspace[mid + i + 1] = a[high - i];
  }

  j = low;
  k = high;
  int l;
  for(i = low;i <= high;i++) {
    cnt++;
    if(workspace[j] <= workspace[k])
      a[i] = workspace[j++];
    else
      a[i] = workspace[k--];
  }
}

int main() {
  int n, i;

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

  mergeSort(s, 0, n - 1);

  for(i = 0;i < n - 1;i++)
    printf("%d ", s[i]);
  printf("%d\n", s[i]);
  printf("%d\n", cnt);

  return 0;
}