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<cstdio>
#include<vector>
#include<algorithm>
#include<utility>
#include<numeric>
#include<iostream>
#include<array>
#include<string>
#include<sstream>
#include<stack>
#include<queue>
#include<list>
#define _USE_MATH_DEFINES

#include<math.h>
#include<map>

#define SENTINEL 1000000001

#define min(a,b) (a)>(b)?(b):(a)
#define max(a,b) (a)>(b)?(a):(b)

using namespace std;

struct OwnNode
{
	int key;
	OwnNode* parent;
	OwnNode* left;
	OwnNode* right;

	OwnNode(int key):key(key),parent(nullptr),left(nullptr),right(nullptr){}
};

void Insert(OwnNode* &top, OwnNode* &z)
{
	OwnNode* y = nullptr;
	OwnNode* x = top;

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

	z->parent = y;

	if (y == nullptr)
	{
		top = z;
	}
	else if (z->key < y->key)
	{
		y->left = z;
	}
	else
	{
		y->right = z;
	}
}

bool Find(OwnNode* top, int key)
{
	if (top == nullptr)
	{
		return false;
	}
	if (top->key == key)
	{
		return true;
	}
	else
	{
		if (top->key < key)
		{
			if (top->right == nullptr)
			{
				return false;
			}
			else
			{
				return Find(top->right, key);
			}
		}
		else
		{
			if (top->left == nullptr)
			{
				return false;
			}
			else
			{
				return Find(top->left, key);
			}
		}
	}
}

void PrintPre(OwnNode* top)
{
	printf(" %d", top->key);
	if (top->left != nullptr)
	{
		PrintPre(top->left);
	}
	if (top->right != nullptr)
	{
		PrintPre(top->right);
	}
}

void PrintIn(OwnNode* top)
{
	if (top->left != nullptr)
	{
		PrintIn(top->left);
	}
	printf(" %d", top->key);
	if (top->right != nullptr)
	{
		PrintIn(top->right);
	}
}

void Print(OwnNode* top)
{
	if (top == nullptr)
	{
		return;
	}
	PrintIn(top);
	printf("\n");
	PrintPre(top);
	printf("\n");
}

int main()
{
	OwnNode* T;
	OwnNode* z;
	T = nullptr;

	int m;
	cin >> m;

	for (int i = 0; i < m; i++)
	{
		char command[10];
		//int key;

		scanf("%s", command);

		//string command;

		//cin >> command;

		if (command[0] == 'i')
		{
			int key;
			scanf("%d", &key);
			z = new OwnNode(key);
			Insert(T, z);
		}
		else if (command[0] == 'f')
		{
			int key;
			cin >> key;
			printf(Find(T, key) ? "yes\n" : "no\n");
		}
		else
		{
			Print(T);
		}
	}

	return 0;
}