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 JAVA (judge verdict: Accepted)

import java.util.Scanner;
  
class Node {
    static Node root;
  
    int key;
    Node left;
    Node right;
  
    Node(int key) {
        this.key = key;
    }
  
    void insert() {
        Node y = null;
        Node x = root;
        while(x != null) {
            y = x;
            if(key < x.key) x = x.left;
            else x = x.right;
        }
  
        if(y == null) root = this;
        else if(key < y.key) y.left = this;
        else y.right = this;
    }
  
    static boolean find(int key) {
        Node x = root;
        while(x != null) {
            if(key < x.key) x = x.left;
            else if(x.key < key) x = x.right;
            else return true;
        }
        return false;
    }
  
    static String inorder(Node x) {
        String str = "";
        if(x == null) return str;
  
        if(x.left != null) str += inorder(x.left);
        str += " " + x.key;
        if(x.right != null)str += inorder(x.right);
  
        return str;
    }
  
    static String preorder(Node x) {
        String str = "";
        if(x == null) return str;
  
        str += " " + x.key;
        if(x.left != null) str += preorder(x.left);
        if(x.right != null) str += preorder(x.right);
  
        return str;
    }
}
  
public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
   
        Node.root = null;
        int m = sc.nextInt();
        for(int i = 0; i < m; i++) {
            String cmd = sc.next();
            if(cmd.equals("insert")) {
                new Node(sc.nextInt()).insert();
            }else if(cmd.equals("find")) {
                System.out.println(Node.find(sc.nextInt())? "yes" : "no");
            }else {
                System.out.println(Node.inorder(Node.root));
                System.out.println(Node.preorder(Node.root));
            }
        }
  
        sc.close();
    }
}