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<cstdio>
#include<iostream>
#include<list>
#include<cstring>
#include<stack>
#include<string>
#include<vector>
#include<set>
#include<algorithm>
using namespace std;
const int maxn = 510000;
int cnt = 0, id[maxn], lson[maxn], rson[maxn];
long long val[maxn];

int insert(int root,long long in)
{
	if (root == -1)
	{
		root = cnt++;
		val[root] = in;
		return root;
	}
	if (in > val[root])
		rson[root] = insert(rson[root], in);
	else
		lson[root] = insert(lson[root], in);
	return root;
}
vector<long long> preorder, inorder;
void ps(int root)
{
	if (root == -1)
		return;
	preorder.push_back(val[root]);
	ps(lson[root]);
	ps(rson[root]);
}
void ino(int root)
{
	if (root == -1)
		return;
	ino(lson[root]);
	inorder.push_back(val[root]);
	ino(rson[root]);
}
int main()
{
	char inp[100];
	//freopen("out.txt", "w", stdout);
	memset(lson, -1, sizeof lson);
	memset(rson, -1, sizeof rson);
	int n, root=-1;
	long long pp;
	scanf("%d", &n);
	set<long long> si;
	for (int i = 1; i <= n; i++)
	{
		scanf("%s",inp);
		if (inp[0] == 'i')
		{
			scanf("%lld", &pp);
			root = insert(root, pp);

			si.insert(pp);
		}
		else if (inp[0] == 'p')
		{
			preorder.clear();
			inorder.clear();
			ps(root);
			ino(root);
			printf(" ");
			for (int i = 0; i < inorder.size(); i++)
				printf(i == inorder.size() - 1 ? "%lld\n" : "%lld ", inorder[i]);
			printf(" ");
			for (int i = 0; i < preorder.size(); i++)
				printf(i == preorder.size() - 1 ? "%lld\n" : "%lld ", preorder[i]);
			
			
		}
		else if (inp[0] == 'f')
		{
			scanf("%lld", &pp);
			if (si.find(pp) != si.end())
				puts("yes");
			else
				puts("no");
		}
		
	}
	return 0;
}