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 Ruby (judge verdict: Accepted)

# merge_sort
# 1. divide
# 2. solve
# 3. conquer

n = gets.to_i
@arr = gets.split.map(&:to_i)
@count = 0
@L = []
@R = []
SENTINEL = 20000000000.freeze

def merge(n, left, mid, right)
  n1 = mid - left
  n2 = right - mid
  n1.times do |i|
    @L[i] = @arr[left + i]
  end
  
  n2.times do |i|
    @R[i] = @arr[mid + i]
  end
  
  @L[n1] = SENTINEL
  @R[n2] = SENTINEL
  
  i = 0
  j = 0
  (left...right).each do |k|
    @count += 1
    
    if @L[i] <= @R[j]
      @arr[k] = @L[i]
      i += 1
    else
      @arr[k] = @R[j]
      j += 1
    end
  end
end

def merge_sort(n, left, right)
  if left+1 < right
    mid = (left + right) / 2
    merge_sort(n, left, mid)
    merge_sort(n, mid, right)
    merge(n, left, mid, right)
  end
end

merge_sort(n, 0, n)

@arr.each_with_index do |v, idx|
  print " " if idx > 0
  print v
end

print "\n"
puts @count