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: Wrong Answer)

import java.util.Scanner;

class Main {
	static Node node;
	static Node root;
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		String ins;
		for (int i = 0; i < n; i++) {
			ins = sc.next();
			if (ins.equals("print")) {
				inorder(root);
				System.out.println();
				preorder(root);
				System.out.println();
			} else if (ins.equals("insert")) {
				Node z = new Node();
				z.key = sc.nextInt();
				insert(z);
			} else if (ins.equals("find")){
				int k = sc.nextInt();
				find(k);
			}

		}
	}
	static void inorder(Node node) {
		if (node == null) return;
		inorder(node.l);
		System.out.print(" " + node.key);
		inorder(node.r);
	}

	static void preorder(Node node) {
		if (node == null) return;
		System.out.print(" " + node.key);
		preorder(node.l);
		preorder(node.r);
	}

	static void insert(Node z) {
		if (root == null) {
			root = z;
			return;
		}
		Node y = null;
		Node x = root;
		while (x != null) {
			y = x;
			if (z.key < x.key) x = x.l;
			else x = x.r;
		}

		if (z.key < y.key) y.l = z;
		else y.r = z;
	}

	static void find(int k){
		node = root;
		while(node.l != null && node.r != null){
			if(node.key > k){
				node = node.l;
			}else if(node.key < k){
				node = node.r;
			}else if(node.key == k){
				System.out.println("yes");
				return;
			}else{
				System.out.println("no");
				return;
			}
		}
		System.out.println("no");
		return;
	}
}

class Node {
	int key;
	Node l;
	Node r;
	Node() {
		key = -1;
		l = null;
		r = null;
	}
}