Problem:
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Reconstruction of a Tree

Write a program which reads two sequences of nodes obtained by the preorder tree walk and the inorder tree walk on a binary tree respectively, and prints a sequence of the nodes obtained by the postorder tree walk on the binary tree.

Input

In the first line, an integer $n$, which is the number of nodes in the binary tree, is given.

In the second line, the sequence of node IDs obtained by the preorder tree walk is given separated by space characters.

In the second line, the sequence of node IDs obtained by the inorder tree walk is given separated by space characters.

Every node has a unique ID from $1$ to $n$. Note that the root does not always correspond to $1$.

Output

Print the sequence of node IDs obtained by the postorder tree walk in a line. Put a single space character between adjacent IDs.

Constraints

$1 \leq n \leq 40$

Sample Input 1

5
1 2 3 4 5
3 2 4 1 5

Sample Output 1

3 4 2 5 1

Sample Input 2

4
1 2 3 4
1 2 3 4

Sample Output 2

4 3 2 1

Solution in Ruby (judge verdict: Accepted)

class NilClass
  def postorder
    nil
  end
end

class Node
  attr_accessor :id, :left_child, :right_child

  def initialize(id)
    @id = id
    @left_child = nil
    @right_child = nil
  end

  def postorder
    [@left_child.postorder, @right_child.postorder, @id].flatten.compact
  end

  def print_postorder
    puts postorder.join(" ")
  end
end

class TreeConstructor
  attr_accessor :root

  def initialize(preorder, inorder)
    if !preorder[0]
      return
    end

    @root = Node.new(preorder[0])

    inorder_right = inorder[(inorder.index(@root.id) + 1)..-1]
    inorder_left = inorder - [@root.id] - inorder_right
    preorder_right = preorder.reject { |item| [@root.id, *inorder_left].include? item }
    preorder_left = preorder - [@root.id] - preorder_right

    @root.left_child = TreeConstructor.new(preorder_left, inorder_left).root
    @root.right_child = TreeConstructor.new(preorder_right, inorder_right).root
  end
end

n = gets.to_i
preorder = gets.split(" ").map(&:to_i)
inorder = gets.split(" ").map(&:to_i)

tree_constructor = TreeConstructor.new(preorder, inorder)
root = tree_constructor.root
root.print_postorder