Problem:
Binary Search Tree II

Write a program which performs the following operations to a binary search tree $T$ by adding the find operation to A: Binary Search Tree I.

insert $k$: Insert a node containing $k$ as key into $T$.

find $k$: Report whether $T$ has a node containing $k$.

print: Print the keys of the binary search tree by inorder tree walk and preorder tree walk respectively.

Input

In the first line, the number of operations $m$ is given. In the following $m$ lines, operations represented by insert $k$, find $k$ or print are given.

Output

For each find $k$ operation, print "yes" if $T$ has a node containing $k$, "no" if not.

In addition, for each print operation, print a list of keys obtained by inorder tree walk and preorder tree walk in a line respectively. Put a space character before each key.

Constraints

The number of operations $\leq 500,000$

The number of print operations $\leq 10$.

$-2,000,000,000 \leq key \leq 2,000,000,000$

The height of the binary tree does not exceed 100 if you employ the above pseudo code.

The keys in the binary search tree are all different.

Sample Input 1

10
insert 30
insert 88
insert 12
insert 1
insert 20
find 12
insert 17
insert 25
find 16
print

Sample Output 1

yes
no
1 12 17 20 25 30 88
30 12 1 20 17 25 88

Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.

Solution in Ruby (judge verdict: Accepted)

class Tree

  def initialize(key)
    @key = key
    @left = nil
    @right = nil
  end

  def insert(k)
    if @key > k
      if !@left
        @left = Tree.new(k)
      else
        @left.insert(k)
      end

    else

      if !@right
        @right = Tree.new(k)
      else
        @right.insert(k)
      end
    end
  end

  def inorder(list)
    if @left
      list = @left.inorder(list)
    end

    list.push(@key)

    if @right
      list = @right.inorder(list)
    end
    return list
  end

  def preorder(list)

    list.push(@key)

    if @left
      list = @left.preorder(list)
    end

    if @right
      list = @right.preorder(list)
    end
    return list
  end

  def find(key, bool)
    if @key == key
      bool = "yes"
    else
      if @left && @key > key
        bool = @left.find(key, bool)
      end

      if @right && @key < key
        bool = @right.find(key, bool)
      end
    end
    return bool
  end
end

n = gets.chomp.to_i
head = nil
n.times do
  num = gets.to_s.chomp!
  if num == "print"
    puts " #{head.inorder([]).join(" ")}"
    puts " #{head.preorder([]).join(" ")}"
  else
    num = num.split
    if num[0].to_s == "insert"
      if head
        head.insert(num[1].to_i)
      else
        head = Tree.new(num[1].to_i)
      end
    else
      puts head.find(num[1].to_i, "no")
    end
  end
end