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++11 (judge verdict: Accepted)

#include<iostream>
#include<string>
#include<cstdio>
using namespace std;
struct Node
{
	int key;
	Node* parent;
	Node* left;
	Node* right;
};
Node* root;
void insert(int val)
{
	Node* x = new Node();
	x->key = val;
	x->left = nullptr;
	x->right = nullptr;
	Node *q = nullptr;
	Node *p = root;
	while (p != nullptr)
	{
		q = p;
		if (x->key < p->key)
			p = p->left;
		else
			p = p->right;
	}
	x->parent = q;
	if (q == nullptr)
		root = x;
	else if (x->key < q->key)
		q->left = x;
	else
		q->right = x;
}
Node* find(Node* root,int x)
{
	while (root != nullptr&&root->key != x)
	{
		if (x < root->key)
			root = root->left;
		else
			root = root->right;
	}
	return root;
}
void inorder(Node* root)
{
	if (root == nullptr)
		return;
	inorder(root->left);
	printf(" %d", root->key);
	inorder(root->right);
}
void preorder(Node* root)
{
	if (root == nullptr)
		return;
	printf(" %d", root->key);
	preorder(root->left);
	preorder(root->right);
}
int main()
{
	int n;
	cin >> n;
	for (int i = 0; i < n; i++)
	{
		string s;
		int t;
		cin >> s;
		if (s[0] == 'i')
		{
			cin >> t;
			insert(t);
		}
		else if (s[0] == 'p')
		{
			inorder(root);
			cout << endl;
			preorder(root);
			cout << endl;
		}
		else if (s[0] == 'f')
		{
			cin >> t;
			cout << (find(root,t) ? "yes" : "no") << endl;
		}
	}
}