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 C (judge verdict: Accepted)

#include<stdio.h>
#include<stdlib.h>

struct node{
	struct node *right;
	struct node *left;
	struct node *parent;
	int key;
};

typedef struct node * Node;
#define NIL NULL

Node root;

Node treeMinimum (Node x ){

}

Node treeSearch (Node u, int k ){
	if (u == NIL || u->key == k ) return u;
	else
	if (u->key < k ){
		return treeSearch (u->right, k );
	}else{
		return treeSearch (u->left, k );
	} // end if 
}

Node treeSuccessor (Node x ){

}

void treeDelete (Node z ){
	Node y;	// node to be deleted
	Node x;	// child of y
}

void insert (int k ){
	Node y = NIL;
	Node x = root;
	Node z;

	z = malloc (sizeof (struct node ) );
	z->key = k;
	z->left = NIL;
	z->right = NIL;

	if (x == NIL ){
		root = z;
	}else{
		do{
			if (x->key < k ){
				y = x->right;
			}else{
				y = x->left;
			} // end if

			if (y != NIL ){
				y->parent = x;
			}else{
				if (x->key < k )
					x->right = z;
				else
					x->left = z;
			} // end if
			x = y;
		}while (x != NIL ); // end while
	} // end if
}

void inorder (Node u ){
	if (u == NIL ) return;
	inorder (u->left );
	printf (" %d", u->key );
	inorder (u->right );
}

void preorder (Node u ){
	if (u == NIL ) return;
	printf (" %d", u->key );
	preorder (u->left );
	preorder (u->right );
}

int main()
{
	int n, i, x;
	char com[20];

	root = NIL;
	scanf ("%d", &n );
	for (i = 0; i < n; i++ ){
		scanf ("%s", com );
		if (com[0] == 'i' ){	// case insert 
			scanf ("%d", &x );
			insert (x );
		}else
		if (com[0] == 'p' ){ // case print
			inorder (root );
			printf ("\n" );
			preorder (root );
			printf ("\n" );
		}else
		if (com[0] == 'f' ){	// case find
			scanf ("%d", &x );
			Node t = treeSearch (root, x );
			if ( t != NIL ) printf ("yes\n" );
			else printf ("no\n" );
		} // end if
	} // end for

	return 0;
}