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>
#include <string.h>
#define NIL NULL
struct Node {
	int key;
	struct Node* right, * left, * parent;
};
typedef struct Node* Node;

Node root;

void inorder(Node);
void preordee(Node);
void insert(int);
Node find(Node, int);

Node find(Node u, int k) {
	while (u != NIL && k != u->key) {
		if (k < u->key)u = u->left;
		else u = u->right;
	}
	return u;
}

void insert(int k) {
	Node x, y, z;
	y = NIL;
	x = root;
	z = malloc(sizeof(struct Node));
	z->key = k;
	z->left = NIL;
	z->right = NIL;
	while (x != NIL) {
		y = x;
		if (z->key < x->key) {
			x = x->left;
		}
		else {
			x = x->right;
		}
	}
	z->parent = y;
	if (y == NIL) {
		root = z;
	}
	else {
		if (z->key < y->key) {
			y->left = z;
		}
		else {
			y->right = z;
		}
	}
}

void inorder(Node u) {
	if (u->left != NIL && u->right != NIL) {
		inorder(u->left);
		printf(" %d", u->key);
		inorder(u->right);
	}
	if (u->left != NIL && u->right == NIL) {
		inorder(u->left);
		printf(" %d", u->key);
	}
	if (u->right != NIL && u->left == NIL) {
		printf(" %d", u->key);
		inorder(u->right);
	}
	if (u->left == NIL && u->right == NIL)printf(" %d", u->key);
}

void preorder(struct Node* u) {
	printf(" %d", u->key);
	if (u->left != NIL) {
		preorder(u->left);
	}
	if (u->right != NIL) {
		preorder(u->right);
	}
}

int main(void) {
	int n, i, x;
	char com[7];
	scanf("%d", &n);
	for (i = 0; i < n; i++) {
		scanf("%s", com);
		if (com[0] == 'f') {
			scanf("%d", &x);
			Node t = find(root, x);
			if (t != NIL)printf("yes\n");
			else printf("no\n");
		}
		else if (strcmp(com, "print") == 0) {
			inorder(root);
			printf("\n");
			preorder(root);
			printf("\n");
		}
		else if (strcmp(com, "insert") == 0) {
			scanf("%d", &x);
			insert(x);
		}
	}
	return 0;
}