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 Kotlin (judge verdict: Accepted)

import java.io.PrintWriter
import java.util.*

val pw = PrintWriter(System.out)
val sc = Scanner(System.`in`)

class Node(var key:Int, var par:Node?, var lef: Node?,var rig:Node?) {
    fun find(value :Int) : Node? = when {
        this.key > value -> lef?.find(value)
        this.key < value -> rig?.find(value)
        this.key == value -> this
        else -> null
    }

    fun insert(value :Int) {
        if(this.key > value){
            if(this.lef == null){
                this.lef = Node(value, this, null, null)
            }else{
                this.lef!!.insert(value)
            }
        }else{
            if(this.rig == null){
                this.rig = Node(value, this, null, null)
            }else{
                this.rig!!.insert(value)
            }
        }
    }
}

val root = Node(-1, null, null, null)

fun main(args: Array<String>) {
    val n = nextInt()
    for(i in 0 until n) {
        val command = next()
        if (command == "print") {
            printTree()
        } else {
            val (com, value) = command.split(" ")
            val key = value.toInt()
            if (com == "insert") {
                if (root.key == -1) {
                    root.key = key
                    continue
                }
                root.insert(key)
            }
            else if (com == "find") {
                if(root.find(key) != null) println("yes") else println("no")
            }
        }
    }

}

fun preOrder(d :Node?) {
    if (d == null) return
    print(" ${d.key}")
    preOrder(d.lef)
    preOrder(d.rig)
}

fun inOrder(d :Node?) {
    if(d == null) return
    inOrder(d.lef)
    print(" ${d.key}")
    inOrder(d.rig)
}

fun printTree(){
    inOrder(root)
    print("\n")
    preOrder(root)
    print("\n")
}


fun abc000a() {
}

fun next() = readLine()!!
fun nextInt() = next().toInt()
fun nextLong() = next().toLong()
fun nextDouble() = next().toDouble()
fun nextListOfString() = next().split(" ")
fun nextListOfInt() = nextListOfString().map { it.toInt() }
fun nextListOfLong() = nextListOfString().map { it.toLong() }
fun nextListOfDouble() = nextListOfString().map { it.toDouble() }