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)


CMD=0
VAL=1

class Node
  attr_accessor :value,:left,:right
  def initialize (value)
    @value = value
    @left = nil
    @right = nil
  end

  def insert (value)
    if value < @value
      if @left.nil?
        @left = Node.new(value)
      else
        @left.insert(value)
      end
    else
      if @right.nil?
        @right = Node.new(value)
      else
        @right.insert(value)
      end
    end
  end

  def find(value)
    #p "@value:#{@value}"
    if value==@value
      print "yes\n"
    elsif value < @value
      #p "left:#{@left}"
      if @left.nil?
        print "no\n"
      else
        @left.find(value)
      end
    else
      #p "right:#{@right}"
      if @right.nil?
        print "no\n"
      else
        @right.find(value)
      end
    end
  end
  
  def print_inorder
    @left.print_inorder unless @left.nil?
    print " #{value}"
    @right.print_inorder unless @right.nil?
  end
  
  def print_preorder
    print " #{value}"
    @left.print_preorder unless @left.nil?
    @right.print_preorder unless @right.nil?
  end
end

num_of_cmd = STDIN.gets()
inputs = STDIN.read().split("\n").map{ |input| input.split(' ') }

root=nil
inputs.each do |input|
  if input[CMD] == 'insert'
    if root.nil?
      root = Node.new(input[VAL].to_i)
    else
      root.insert(input[VAL].to_i)
    end
  elsif input[CMD] == 'find'
    root.find(input[VAL].to_i)
  else
    root.print_inorder unless root.nil?
    print "\n"
    root.print_preorder unless root.nil?
    print "\n"
  end
end