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)

#!/usr/bin/ruby
# -*- coding: utf-8 -*-
=begin
ALDS1_5-B

Recursion / Divide and Conquer - Merge Sort
Merge Sort

=end

class Merge
  def merge(a, left, mid, right)
    sentinel = 1000000001
    n1 = mid - left;
    n2 = right - mid;
    l = Array.new(n1+1);
    r = Array.new(n2+1);

    0.upto(n1-1) {|i|
      l[i] = a[left + i]
    }
    0.upto(n2-1) {|i|
      r[i] = a[mid + i]
    }
    l[n1] = sentinel;
    r[n2] = sentinel;
    i = 0;
    j = 0;
    q = 0;
    left.upto(right-1) {|k|
      q = q + 1;
      if (l[i] <= r[j]) then
        a[k] = l[i];
        i = i + 1;
      else
        a[k] = r[j];
        j = j + 1;
      end
    }
    return q;
  end

  def mergeSort(a, left, right)
    if left + 1 < right then
      mid = (left + right)/2
      n1 = mergeSort(a, left, mid)
      n2 = mergeSort(a, mid, right)
      n3 = merge(a, left, mid, right)
      return n1+n2+n3
    else
      return 0
    end
  end

end

class Main

  def initialize()
    #fh = open("/home/muz/Downloads/ALDS1_5_B_in1.txt")
    fh = STDIN
    n = fh.gets.to_i
    a = fh.gets.chomp.split.map{|x| x.to_i}
    abort("size does not match") if n != a.length 
    ms = Merge.new

    q1 = ms.mergeSort(a, 0, n)

    puts a.map{|x| x.to_s}.join(" ")
    puts q1
  end

end

if $0 == __FILE__ then
  Main.new
end