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>

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

Node *root,*NIL;

void insert(int k);
void find(int k);
void inOrder(Node *x);
void preOrder(Node *x);

int main(){
	int i,n,x;	scanf("%d",&n);
	char com[10];

	for(i=0;i<n;i++){
		scanf("%s",com);
		if(com[0]=='i'){
			scanf("%d",&x);
			insert(x);

		}else if(com[0]=='p'){
			inOrder(root);
			printf("\n");
			preOrder(root);
			printf("\n");
		}else{
			scanf("%d",&x);
			find(x);
		}
	}

	return 0;
}

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

	z=(Node*)malloc(sizeof(Node));

	z->key=k;	z->left=NIL;	z->right=NIL;

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

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

void find(int k){
	Node* p=root;

	while(p!=NIL){
		if(p->key==k){
			printf("yes\n");
			return;
		}

		if(k < p->key)p=p->left;
		else p=p->right;
	}



	printf("no\n");
	return;
}

void inOrder(Node* x){
	if(x==NIL)return;
	inOrder(x->left);
	printf(" %d",x->key);
	inOrder(x->right);
}
void preOrder(Node* x){
	if(x==NIL)return;
	printf(" %d",x->key);
	preOrder(x->left);
	preOrder(x->right);
}