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 Scala (judge verdict: Accepted)

import scala.collection.mutable.ListBuffer
import scala.io.StdIn

object Main extends App {

  val n = StdIn.readLine().trim.toInt
  var root: Node = _
  val buff = ListBuffer.empty[String]
  case class Node(key: Int, var parent: Node, var left: Node, var right: Node){
    private def getDefaultKey(p: Node) = if(p == null) -1 else p.key
    override def toString: String = s"Node($key, ${getDefaultKey(parent)} ${getDefaultKey(left)} ${getDefaultKey(right)})"
  }
  
  (0 until n).foreach { _ =>
    val command = StdIn.readLine()
    command.split(' ') match {
      case Array("insert", key) => insert(Node(key.toInt, null, null, null))
      case Array("find"  , key) => 
        buff += (if(find(root, key.toInt) == null) f"no%n" else f"yes%n")
      case _ => 
        // print
        inorder(root)
        buff += f"%n"
        preorder(root)
        buff += f"%n"
    }
  }
  
  
  def insert(z: Node): Unit = {
    var y:Node = null
    var x:Node = root
    while(x != null){
      y = x
      if(z.key < x.key){
        x = x.left
      } else {
        x = x.right
      }
    }
    z.parent = y
    
    if(y == null){
      root = z
    } else if(z.key < y.key){
      y.left = z
    } else {
      y.right = z
    }
  }
  
  def preorder(n: Node): Unit = {
    buff += " " + n.key
    if(n.left != null) preorder(n.left)
    if(n.right != null) preorder(n.right)
  }

  def inorder(n: Node): Unit = {
    if(n.left != null) inorder(n.left)
    buff += " " + n.key
    if(n.right != null) inorder(n.right)
  }
  
  def find(x: Node, key: Int) = {
    var temp = x
    while(temp != null && key != temp.key){
      if(key < temp.key){
        temp = temp.left
      } else {
        temp = temp.right
      }
    }
    temp
  }
  
  print(buff.mkString(""))
}