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 {
	struct node *right;
	struct node *left;
	struct node *parent;
	int key;
};

typedef struct node * Node;

Node root;

Node treeMinimum(Node x) {
	while (x->left != NULL) x = x->left;
	return x;
}

Node treeMaximum(Node x) {
	while (x->right != NULL) x = x->right;
	return x;
}

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

Node treeSuccessor(Node x) {
	if (x->right != NULL) return treeMinimum(x->right);
	Node y = x->parent;
	while (y != NULL && x == y->right) {
		x = y;
		y = y->parent;
	}
	return y;
}

void treeDelete(Node z) {
	Node y; // node to be deleted
	Node x; // child of y

	if (z->left == NULL || z->right == NULL) y = z;
	else y = treeSuccessor(z);

	if (y->left != NULL) x = y->left;
	else x = y->right;

	if (x != NULL) x->parent = y->parent;

	if (y->parent == NULL) root = x;
	else {
		if (y == y->parent->left) y->parent->left = x;
		else y->parent->right = x;
	}

	if (y != z) z->key = y->key;

	free(y);
}

void insert(int k) {
	Node y = NULL;
	Node x = root;
	Node z;

	z = malloc(sizeof(struct node));
	z->key = k;
	z->left = NULL;
	z->right = NULL;

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

	z->parent = y;
	if (y == NULL) root = z;
	else {
		if (z->key < y->key) y->left = z;
		else y->right = z;
	}
}

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

void preorder(Node u) {
	if (u == NULL) return;
	printf(" %d", u->key);
	preorder(u->left);
	preorder(u->right);
}


int main() {
	int n, i, x;
	char com[20];
	scanf("%d", &n);

	for (i = 0; i < n; i++) {
		scanf("%s", com);
		if (com[0] == 'f') {
			scanf("%d", &x);
			Node t = treeSearch(root, x);
			if (t != NULL) printf("yes\n");
			else printf("no\n");
		}
		else if (com[0] == 'i') {
			scanf("%d", &x);
			insert(x);
		}
		else if (com[0] == 'p') {
			inorder(root);
			printf("\n");
			preorder(root);
			printf("\n");
		}
		else if (com[0] == 'd') {
			scanf("%d", &x);
			treeDelete(treeSearch(root, x));
		}
	}

	return 0;
}