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>

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

Node *tree_insert(Node *top, Node *z) {
	Node *y, *x;

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

int tree_find(Node *node, int key) {
	if (node == NULL)
		return 0;
	if (node->key == key)
		return 1;
	if (key < node->key)
		return tree_find(node->left, key);
	return tree_find(node->right, key);
}

void inorder_walk(Node *node) {
	if (node->left != NULL) {
		inorder_walk(node->left);
	}
	printf(" %d", node->key);
	if (node->right != NULL) {
		inorder_walk(node->right);
	}
}

void preorder_walk(Node *node) {
	printf(" %d", node->key);
	if (node->left != NULL) {
		preorder_walk(node->left);
	}
	if (node->right != NULL) {
		preorder_walk(node->right);
	}
}

int main(void) {
	int n, i, key;
	char cmd[20];
	Node *top = NULL, *p;

	scanf("%d ", &n);
	for (i = 0; i < n; i++) {
		scanf("%s %d ", cmd, &key);
		if (cmd[0] == 'i') {
			p = malloc(sizeof(Node));
			p->key = key;
			p->parent = p->left = p->right = NULL;
			top = tree_insert(top, p);
		} else if (cmd[0] == 'f') {
			puts(tree_find(top, key) ? "yes" : "no");
		} else {
			inorder_walk(top);
			putchar('\n');
			preorder_walk(top);
			putchar('\n');
		}
	}
	return 0;
}