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: Time Limit Exceeded)

#include<stdio.h>
#include<stdlib.h>
#include<string.h>
#define cmdMax 10

typedef struct node *link;
struct node{
	int key;
	link left,right;
};

link insert(link head,link z){
	link y=NULL;
	link x=head;
	
	while(x!=NULL){
		y=x;
		if(z->key < x->key)x=x->left;
		else x=x->right;
	}
	
	if(y==NULL)head=z;
	else if(z->key < y->key)y->left=z;
	else y->right=z;
	return head;
}

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

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

int find(link u,int key){
	if(u==NULL)return 0;
	if(u->key==key)return 1;
	return find(u->left,key)+find(u->right,key);
}

int main(void){
	int m,i,key;
	char cmd[cmdMax];
	link head=NULL,z;
	scanf("%d",&m);
	for(i=0;i<m;i++){
		scanf("%s",cmd);
		if(!strcmp(cmd,"insert")){
			scanf("%d",&key);
			z = malloc(sizeof(*z));
			z->key=key;z->left=NULL;z->right=NULL;
			head=insert(head,z);
		}else if(!strcmp(cmd,"print")){
			inorder(head);
			printf("\n");
			preorder(head);
			printf("\n");
		}else if(!strcmp(cmd,"find")){
			scanf("%d",&key);
			if(find(head,key)!=0)printf("yes\n");
			else  printf("no\n");
		}
	}
	return 0;
}