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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
public class Main {
	static NODE node;
	static NODE root;
	public static void main(String[] args) throws IOException{
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));	
		int n=Integer.parseInt(br.readLine());
		
		for(int i=0;i<n;i++){
			String[] str=br.readLine().split(" ");
		
			if("print".equals(str[0])) {
				inorder(root);
				System.out.println("");	
				preorder(root);
				System.out.println("");	
			}
			else if("insert".equals(str[0])){
				int key=Integer.parseInt(str[1]);
				NODE newnode=new NODE();
				newnode.key=key;
				insert(newnode);
			}
			
			else if("find".equals(str[0])){
				int key=Integer.parseInt(str[1]);
				findnum(root,key);
			}

		}
	}
	
	static void findnum(NODE node,int key){
		boolean flag=false;
		while(node!=null){
			if(node.key==key){
				flag=true;
				break;
			}
			else{
				if(key<node.key) node=node.left;
				else node=node.right;
			}
		}
		if (flag) System.out.println("yes");
		else System.out.println("no");
	}

	static void inorder(NODE node){
		if(node==null) return;
		inorder(node.left);
		System.out.print(" " + node.key);
		inorder(node.right);
	}
	
	static void preorder(NODE node){		
		if(node==null) return;
		System.out.print(" " + node.key);
		preorder(node.left);
		preorder(node.right);	
	}
	
	static void insert(NODE node){
        if(root==null){
            root = node;
            return;
        }
        NODE tnode = root;
        NODE parent = null;
        while(tnode != null) {
            parent = tnode;
            if(tnode.key > node.key)
                tnode = tnode.left;
            else
                tnode = tnode.right;
        }
        if(parent.key > node.key)
            parent.left = node;
        else
            parent.right = node;
		
	}
}

class NODE{
	int key;
	NODE left;
	NODE right;;
	NODE(){
		key=-1;
		left=null;
		right=null;
	}
}