Problem:
Binary Search Tree III Write a program which performs the following operations to a binary search tree $T$ by adding delete operation to B: Binary Search Tree II.  insert $k$: Insert a node containing $k$ as key into $T$.  find $k$: Report whether $T$ has a node containing $k$.  delete $k$: Delete a node containing $k$.  print : Print the keys of the binary search tree by inorder tree walk and  preorder tree walk respectively.  The operation delete $k$ for deleting a given node $z$ containing key $k$ from $T$ can be implemented by an algorithm which considers the following cases:  If $z$ has no children, we modify its parent $z.p$ to replace $z$ with NIL as its child (delete $z$).  If $z$ has only a single child, we "splice out" $z$ by making a new link between its child and its parent.  If $z$ has two children, we splice out $z$'s successor $y$ and replace $z$'s key with $y$'s key.  Input In the first line, the number of operations $m$ is given. In the following $m$ lines, operations represented by insert $k$, find $k$, delete $k$ 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  18
insert 8
insert 2
insert 3
insert 7
insert 22
insert 1
find 1
find 2
find 3
find 4
find 5
find 6
find 7
find 8
print
delete 3
delete 7
print  Sample Output 1  yes
yes
yes
no
no
no
yes
yes
 1 2 3 7 8 22
 8 2 1 3 7 22
 1 2 8 22
 8 2 1 22  Reference  Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.

Solution (Python):
from sys import stdin

class TreeNode:
    def __init__(self,key,val,left=None,right=None,parent=None):
        self.key = key
        self.payload = val
        self.leftChild = left
        self.rightChild = right
        self.parent = parent

    def hasLeftChild(self):
        return self.leftChild

    def hasRightChild(self):
        return self.rightChild

    def isLeftChild(self):
        return self.parent and self.parent.leftChild == self

    def isRightChild(self):
        return self.parent and self.parent.rightChild == self

    def isRoot(self):
        return not self.parent

    def isLeaf(self):
        return not (self.rightChild or self.leftChild)

    def hasAnyChildren(self):
        return self.rightChild or self.leftChild

    def hasBothChildren(self):
        return self.rightChild and self.leftChild

    def spliceOut(self):
        if self.isLeaf():
            if self.isLeftChild():
                self.parent.leftChild = None
            else:
                self.parent.rightChild = None
        elif self.hasAnyChildren():
            if self.hasLeftChild():
                if self.isLeftChild():
                    self.parent.leftChild = self.leftChild
                else:
                    self.parent.rightChild = self.leftChild
                self.leftChild.parent = self.parent
            else:
                if self.isLeftChild():
                    self.parent.leftChild = self.rightChild
                else:
                    self.parent.rightChild = self.rightChild
                    self.rightChild.parent = self.parent

    def findSuccessor(self):
        succ = None
        if self.hasRightChild():
            succ = self.rightChild.findMin()
        else:
            if self.parent:
                    if self.isLeftChild():
                        succ = self.parent
                    else:
                        self.parent.rightChild = None
                        succ = self.parent.findSuccessor()
                        self.parent.rightChild = self
        return succ

    def findMin(self):
        current = self
        while current.hasLeftChild():
            current = current.leftChild
        return current

    def replaceNodeData(self,key,value,lc,rc):
        self.key = key
        self.payload = value
        self.leftChild = lc
        self.rightChild = rc
        if self.hasLeftChild():
            self.leftChild.parent = self
        if self.hasRightChild():
            self.rightChild.parent = self

class BinarySearchTree:
    def __init__(self):
        self.root = None
        self.size = 0

    def length(self):
        return self.size

    def __len__(self):
        return self.size

    def put(self,key,val):
        if self.root:
            self._put(key,val,self.root)
        else:
            self.root = TreeNode(key,val)
        self.size = self.size + 1

    def _put(self,key,val,currentNode):
        if key < currentNode.key:
            if currentNode.hasLeftChild():
                   self._put(key,val,currentNode.leftChild)
            else:
                   currentNode.leftChild = TreeNode(key,val,parent=currentNode)
        else:
            if currentNode.hasRightChild():
                   self._put(key,val,currentNode.rightChild)
            else:
                   currentNode.rightChild = TreeNode(key,val,parent=currentNode)

    def __setitem__(self,k,v):
        self.put(k,v)

    def get(self,key):
        if self.root:
            res = self._get(key,self.root)
            if res:
                   return res.payload
            else:
                   return None
        else:
            return None

    def _get(self,key,currentNode):
        if not currentNode:
            return None
        elif currentNode.key == key:
            return currentNode
        elif key < currentNode.key:
            return self._get(key,currentNode.leftChild)
        else:
            return self._get(key,currentNode.rightChild)

    def __getitem__(self,key):
        return self.get(key)

    def __contains__(self,key):
        if self._get(key,self.root):
            return True
        else:
            return False

    def print_nodes(self):
        A = [] 
        B = [] 
        def walk_tree(u):
            if u == None:
                return
            r = u.rightChild
            l = u.leftChild
            A.append(u.key)
            walk_tree(l)
            B.append(u.key)
            walk_tree(r)

        walk_tree(self.root)
        print(" ", end="")
        print(*B, sep=" ")
        print(" ", end="")
        print(*A, sep=" ")

    def delete(self,key):
        if self.size > 1:
            nodeToRemove = self._get(key,self.root)
            if nodeToRemove:
                self.remove(nodeToRemove)
                self.size = self.size-1
            else:
                raise KeyError('Error, key not in tree')
        elif self.size == 1 and self.root.key == key:
            self.root = None
            self.size = self.size - 1
        else:
            raise KeyError('Error, key not in tree')

    def __delitem__(self,key):
        self.delete(key)

    def remove(self,currentNode):
        if currentNode.isLeaf(): 
            if currentNode == currentNode.parent.leftChild:
                currentNode.parent.leftChild = None
            else:
                currentNode.parent.rightChild = None
        elif currentNode.hasBothChildren(): 
            succ = currentNode.findSuccessor()
            succ.spliceOut()
            currentNode.key = succ.key
            currentNode.payload = succ.payload

        else: 
            if currentNode.hasLeftChild():
                if currentNode.isLeftChild():
                    currentNode.leftChild.parent = currentNode.parent
                    currentNode.parent.leftChild = currentNode.leftChild
                elif currentNode.isRightChild():
                    currentNode.leftChild.parent = currentNode.parent
                    currentNode.parent.rightChild = currentNode.leftChild
                else:
                    currentNode.replaceNodeData(currentNode.leftChild.key,
                                    currentNode.leftChild.payload,
                                    currentNode.leftChild.leftChild,
                                    currentNode.leftChild.rightChild)
            else:
                if currentNode.isLeftChild():
                    currentNode.rightChild.parent = currentNode.parent
                    currentNode.parent.leftChild = currentNode.rightChild
                elif currentNode.isRightChild():
                    currentNode.rightChild.parent = currentNode.parent
                    currentNode.parent.rightChild = currentNode.rightChild
                else:
                    currentNode.replaceNodeData(currentNode.rightChild.key,
                                    currentNode.rightChild.payload,
                                    currentNode.rightChild.leftChild,
                                    currentNode.rightChild.rightChild)

def read_and_print_BSTree(bst, n):
    for _ in range(n):
        cmd = stdin.readline().strip().split()
        if cmd[0] == 'insert':
            bst.put(int(cmd[1]), int(cmd[1]))
        elif cmd[0] == 'print':
            bst.print_nodes()
        elif cmd[0] == 'find':
            if bst.get(int(cmd[1])):
                print('yes')
            else:
                print('no')
        elif cmd[0] == 'delete':
            bst.delete(int(cmd[1]))

def __main():
    n = int(input())
    bst = BinarySearchTree()
    read_and_print_BSTree(bst, n)

if __name__ == '__main__':
    __main()

Solution (Python):
import sys
class Tree():
    def __init__(self):
        self.root = None
    def insert(self, key):
        z = Node(key)
        y = None
        x = self.root
        while x:
            y = x
            if z.key < x.key:
                x = x.left
            else:
                x = x.right
        z.parent = y
        if y == None:
            self.root = z
        elif z.key < y.key:
            y.left = z
        else:
            y.right = z
    def find(self, key):
        x = self.root
        while x and x.key != key:
            if x.key < key:
                x = x.right
            else:
                x = x.left
        return x
    def delete(self, key):
        z = self.find(key)
        y = self.successor(z) if z.left and z.right else z
        x = y.left if y.left else y.right

        if x:
            x.parent = y.parent
        if y.parent == None:
            self.root = x 
        elif y == y.parent.left:
            y.parent.left = x
        else:
            y.parent.right = x
        if y != z:
            z.key = y.key
    def successor(self, x):
        if x.right:
            return self.minimum(x.right)
        y = x.parent
        while y and x == y.right:
            x = y
            y = y.parent
        return y

    def minimum(self, x):
        while x.left:
            x = x.left
        return x
    
    def print(self):
        print('',' '.join(map(str, self.root.inwalk())))
        print('',' '.join(map(str, self.root.prewalk())))
    
class Node():
    def __init__(self, key):
        self.key = key
        self.parent = self.left = self.right = None
    def prewalk(self):
        ret = [self.key]
        if self.left:
            ret += self.left.prewalk()
        if self.right:
            ret += self.right.prewalk()
        return ret
    def inwalk(self):
        ret = []
        if self.left:
            ret += self.left.inwalk()
        ret += [self.key]
        if self.right:
            ret += self.right.inwalk()
        return ret
tree = Tree()
n = sys.stdin.readline()
for line in sys.stdin:
    if line[0] == 'i':
        tree.insert(int(line.split()[1]))
    elif line[0] == 'f':
        print('yes' if tree.find(int(line.split()[1])) else 'no')
    elif line[0] == 'd':
        tree.delete(int(line.split()[1]))            
    else:
        tree.print()

Solution (Python):
import sys
 
class TreeNode:
    def __init__(self, val):
        self.val = val
        self.left = self.right = None
    
    def __eq__(self, other):
        return self.val == other.val
 
class BST:
    def __init__(self):
        self.root = None
     
    def insert(self, node):
        def helper(root):
            y, x = None, root
            while isinstance(x, TreeNode):
                y = x
                if node.val < x.val:
                    x = x.left
                else:
                    x = x.right
            if y is None:
                root = node
            elif node.val < y.val:
                y.left = node
            else:
                y.right = node
            return root
             
        self.root = helper(self.root)
 
    def find(self, val):
        def helper(root):
            if root is None:
                return None
            elif root.val == val:
                return root
            elif val < root.val:
                return helper(root.left)
            else:
                return helper(root.right)
        return helper(self.root)
        
    def delete(self, val):
        node = TreeNode(val)
        def findMin(root):
            while root.left is not None:
                root = root.left
            return root
        
        def helper(root, node):
            if root is None:
                return None
            elif root == node:
                if root.left is None:
                    root = root.right
                elif root.right is None:
                    root = root.left
                else:
                    tmp = findMin(root.right)
                    root.val = tmp.val
                    rr = helper(root.right, TreeNode(tmp.val))
                    root.right = rr
                return root
            else:
                if node.val < root.val:
                    root.left = helper(root.left, node)
                else:
                    root.right = helper(root.right, node)
                return root

        helper(self.root, node)

    def inorder(self):
        def helper(root):
            return [] if root is None else helper(root.left) + [root.val] + helper(root.right)
        return helper(self.root)
 
    def preorder(self):
        def helper(root):
            return [] if root is None else [root.val] + helper(root.left) + helper(root.right)
        return helper(self.root)
 
if __name__ == '__main__':
    q = sys.stdin.readline()
    q = int(q)
    bst = BST()
    for _ in range(q):
        tmp = sys.stdin.readline()
        if tmp.startswith('print'):
            print ' ' + ' '.join(map(lambda x: str(x), bst.inorder()))
            print ' ' + ' '.join(map(lambda x: str(x), bst.preorder()))
        elif tmp.startswith('insert'):
            _, val = tmp.split()
            node = TreeNode(int(val))
            bst.insert(node)
        elif tmp.startswith('find'):
            _, val = tmp.split()
            print ('yes' if bst.find(int(val)) is not None else 'no')
        else:
            _, val = tmp.split()
            bst.delete(int(val))

Solution (Python):



import sys

class BinarySearchTree(object):
    def __init__(self):
        super(BinarySearchTree, self).__init__()
        self.root = None
        self.count = 0

    def insert(self, val):
        node = Node(val)
        y = None
        x = self.root
        while x != None:
            y = x
            if node.id_ < x.id_:
                x = x.left
            else:
                x = x.right
        node.parent = y

        if y == None:
            self.root = node
        elif node.id_ < y.id_:
            y.left = node
        else:
            y.right = node

    def find(self, val):
        x = self.root
        while x != None:
            if val == x.id_:
                break
            elif val < x.id_:
                x = x.left
            else: 
                x = x.right
        if x != None:
            return True
        else:
            return False

    def delete(self, val):
        p = None
        x = self.root
        while x != None:
            if val == x.id_:
                break
            p = x
            if val < x.id_:
                x = x.left
            else: 
                x = x.right
        if x != None:
            if x.left != None and x.right != None:
                next_ = self._next_node_in_inorder(x)
                x.id_ = next_.id_
                x = next_
                p = next_.parent
            if x.left == None and x.right == None:
                if x == self.root:
                    self.root = None
                else:
                    if p.left == x:
                        p.left = None
                    else: 
                        p.right = None
            elif x.left == None: 
                x.right.parent = p
                if p != None:
                    if p.left == x:
                        p.left = x.right
                    else:
                        p.right = x.right
                else: 
                    self.root = x.right
            elif x.right == None: 
                x.left.parent = p
                if p != None:
                    if p.left == x:
                        p.left = x.left
                    else:
                        p.right = x.left
                else: 
                    self.root = x.left
            else:
                assert True

    def _next_node_in_inorder(self, node):
        x = node.right
        while x.left != None:
            x = x.left
        return x

    def __str__(self):
        return 'Call to_inorder_walk() or to_preorder_walk()'

    def to_inorder_walk(self):
        return self._to_inorder_walk(self.root)

    def to_preorder_walk(self):
        return self._to_preorder_walk(self.root)

    def _to_inorder_walk(self, node):
        if node == None: return ''
        str_ = self._to_inorder_walk(node.left)
        str_ += ' %d' % (node.id_)
        str_ += self._to_inorder_walk(node.right)
        return str_

    def _to_preorder_walk(self, node):
        if node == None: return ''
        str_ = ' %d' % (node.id_)
        str_ += self._to_preorder_walk(node.left)
        str_ += self._to_preorder_walk(node.right)
        return str_

class Node(object):
    def __init__(self, id_):
        super(Node, self).__init__()
        self.id_ = id_
        self.parent = None
        self.left = None
        self.right = None

    def __str__(self):
        str_ = '%d' % (self.id_)
        return str_


bst = BinarySearchTree()

_nops = int(sys.stdin.readline())
for _ in range(0, _nops):
    op = sys.stdin.readline().rstrip().split(' ')
    if op[0] == 'insert':
        bst.insert(int(op[1]))
    elif op[0] == 'print':
        print bst.to_inorder_walk()
        print bst.to_preorder_walk()
    elif op[0] == 'find':
        if bst.find(int(op[1])):
            print 'yes'
        else:
            print 'no'
    elif op[0] == 'delete':
        bst.delete(int(op[1]))
    else:
        pass

Solution (Python):






import sys


class Node(object):
    def __init__(self, key=None, parent=None):
        self.key = key
        self.parent = parent
        self.left = None
        self.right = None


def insert(key, node):
    """
    ??????????????????????????????, ???????????°???????????? node.left ????????? node.right ?????????????????????
    """
    if key < node.key:
        if node.left is None:
            left_node = Node(key, node)
            node.left = left_node
        else:
            insert(key, node.left)
    else:
        if node.right is None:
            right_node = Node(key, node)
            node.right = right_node
        else:
            insert(key, node.right)


def find(key, node):
    """
    ??????????????????????????????, ?????????????????¨????????°?????????????????????????????´?????????
    ????????????????????§??????????????????????????????????????¨??????????????° None ????????????
    """
    if key == node.key:
        return node
    elif key < node.key:
        if node.left is None:
            return None
        else:
            return find(key, node.left)
    else:
        if node.right is None:
            return None
        else:
            return find(key, node.right)


def print_preorder(node):
    print(" %d" % node.key, end="")
    if node.left is not None:
        print_preorder(node.left)
    if node.right is not None:
        print_preorder(node.right)


def print_inorder(node):
    if node.left is not None:
        print_inorder(node.left)
    print(" %d" % node.key, end="")
    if node.right is not None:
        print_inorder(node.right)


def search_minimum_node(node):
    """
    node ???????????¨??????(??¨???)??¨??????????°????????????????????????????????????????
    ?????? node ??????????????±????????´??? leaf ?????¢?´¢??????????????§?????????
    """
    if node.left is not None:
        return search_minimum_node(node.left)
    else:
        return node


def delete(node):
    if node.left is None and node.right is None:
        
        if node.parent.left is node:
            node.parent.left = None
        else:
            node.parent.right = None
    elif node.left is None and node.right is not None:
        
        
        if node is node.parent.left:
            
            node.parent.left = node.right
        else:
            
            node.parent.right = node.right
        node.right.parent = node.parent
    elif node.left is not None and node.right is None:
        
        
        if node is node.parent.left:
            
            node.parent.left = node.left
        else:
            
            node.parent.right = node.left
        node.left.parent = node.parent
    else:
        
        
        successor = search_minimum_node(node.right)
        if successor.right is not None:
            
            successor.right.parent = successor.parent
            successor.parent.left = successor.right
        else:
            
            if successor.parent.left is successor:
                successor.parent.left = None
            else:
                successor.parent.right = None
        
        node.key = successor.key


def main():
    lines = sys.stdin.readlines()
    root = Node()

    for order in lines[1:]:
        if order.startswith("insert"):
            _, key = order.strip().split(" ")
            key = int(key)
            if root.key is None:
                root.key = key
            else:
                insert(key, root)
        elif order.startswith("find"):
            _, key = order.strip().split(" ")
            fild_result = "no" if find(int(key), root) is None else "yes"
            print(fild_result)
        elif order.startswith("print"):
            print_inorder(root)
            print("")
            print_preorder(root)
            print("")
        elif order.startswith("delete"):
            _, key = order.strip().split(" ")
            node = find(int(key), root)  
            delete(node)


if __name__ == "__main__":
    main()

Solution (Python):
from __future__ import print_function
from sys import stdin
class Node:
    def __init__(self, id):
        self.id = id
        self.left = None
        self.right = None
        self.parent = None

def preorder_tree_walk(root):
    print('', root.id, end='')
    if root.left != None:
        preorder_tree_walk(root.left)
    if root.right != None:
        preorder_tree_walk(root.right)

def inorder_tree_walk(root):
    if root.left != None:
        inorder_tree_walk(root.left)
    print('', root.id, end='')
    if root.right != None:
        inorder_tree_walk(root.right)

def insert(root, z):
    y = None
    x = root
    while isinstance(x, Node):
        y = x
        if z.id < x.id:
            x = x.left
        else:
            x = x.right
    z.parent = y

    if y == None:
        root = z
    elif z.id < y.id:
        y.left = z
    else:
        y.right = z
    return root

def find(root, x):
    while root != None and x != root.id:
        if x < root.id:
            root = root.left
        else:
            root = root.right
    return root

def delete(root, z):
    
    if  z.left == None or z.right == None:
        y = z
    else:
        y = get_successor(z)

    
    if y.left != None:
        x = y.left
    else:
        x = y.right

    if x != None:
        x.parent = y.parent

    if y.parent == None:
        root = x
    elif y == y.parent.left:
        y.parent.left = x
    else:
        y.parent.right = x

    if y != z:
        z.id = y.id


def get_successor(x):
    if x.right != None:
        return get_minimum(x.right)

    y = x.parent
    while y != None and x == y.right:
        x = y
        y = y.parent
    return y

def get_minimum(x):
    while x.left != None:
        x = x.left
    return x


n = int(raw_input())
root = None
for i in xrange(n):
    cmd = stdin.readline()
    if cmd.startswith('i'):
        num = int(cmd[7:])
        root = insert(root, Node(num))
    elif cmd.startswith('p'):
        inorder_tree_walk(root)
        print()
        preorder_tree_walk(root)
        print()
    elif cmd.startswith('d'):
        num = int(cmd[7:])
        node = find(root, num)
        if node != None:
            delete(root, node)
    else:
        
        num = int(cmd[5:])
        if find(root, num) != None:
            print('yes')
        else:
            print('no')

Solution (Python):
def insert(tree,k):
    y = None
    x = tree
    z = {'key':k, 'parent':None, 'left':None, 'right':None}
    while x != None:
        y = x
        if x['key'] > k:
            x = x['left']
        else:
            x = x['right']
    z['parent'] = y
    if y == None:
        tree = z
    elif y['key'] > k:
        y['left'] = z
    else:
        y['right'] = z
    return tree

def delete_leaf(p,x):
    if left(p,x):
        p['left'] = None
    else:
        p['right'] = None
    return p

def delete_half_leaf(p,x,y):
    if left(p,x):
        p['left'] = y
    else:
        p['right'] = y
    y['parent'] = p
    return p


def left(p,x):
    if p['left'] != None and p['left']['key'] == x['key']:
        return True
    else:
        return False

def delete_internal(p,x):
    y = x['right']
    while y['left'] != None:
        y = y['left']
    x['key'] = y['key']
    if y['right'] == None:
        y['parent'] = delete_leaf(y['parent'],y)
    else:
        y['parent'] = delete_half_leaf(y['parent'],y,y['left'])
    return p

def delete(tree,k):
    x = find(tree,k)
    if x == None: return
    p = x['parent']
    if p == None:
        pass
    else:
        if x['left'] == x['right'] == None:
            p = delete_leaf(p,x)
        elif x['right'] == None:
            p = delete_half_leaf(p,x,x['left'])
        elif x['left'] == None:
            p = delete_half_leaf(p,x,x['right'])
        else:
            p = delete_internal(p,x)
    return tree

def find(tree,k):
    x = tree
    while x != None:
        if x['key'] == k:
            return x
        elif x['key'] > k:
            x = x['left']
        else:
            x = x['right']
    return None

def middleorder(x):
    if x != None:
        middleorder(x['left'])
        print x['key'],
        middleorder(x['right'])

def preorder(x):
    if x != None:
        print x['key'],
        preorder(x['left'])
        preorder(x['right'])



tree = None
m = int(raw_input())
for i in range(m):
    c = raw_input().strip()
    if c[0] == 'i':
        tree = insert(tree, int(c[7:]))
    elif c[0] == 'f':
        x = find(tree, int(c[5:]))
        if x == None:
            print "no"
        else:
            print "yes"
    elif c[0] == 'd':
        tree = delete(tree, int(c[7:]))
    elif c[0] == 'p':
        print '',
        middleorder(tree)
        print
        print '',
        preorder(tree)
        print

Solution (Python):
def insert(tree,k):
    y = None
    x = tree
    z = {'key':k, 'parent':None, 'left':None, 'right':None}
    while x != None:
        y = x
        if x['key'] > k:
            x = x['left']
        else:
            x = x['right']
    z['parent'] = y
    if y == None:
        tree = z
    elif y['key'] > k:
        y['left'] = z
    else:
        y['right'] = z
    return tree

def get_successor(x):
    if x['right'] != None:
        return get_minimum(x['right'])
    else:
        y = x['parent']
        while y != None and x == y['left']:
            x = y
            y = y['parent']
        return y

def get_minimum(x):
    while x['left'] != None:
        x = x['left']
    return x

def delete_node(tree,z):
    if z['left'] == None or z['right'] == None:
        y = z
    else:
        y = get_successor(z)

    if y['left'] != None:
        x = y['left']
    else:
        x = y['right']

    if x != None:
        x['parent'] = y['parent']

    if y['parent'] == None:
        tree = x
    else:
        if y['parent']['left'] != None and y['parent']['left']['key'] == y['key']:
            y['parent']['left'] = x
        else:
            y['parent']['right'] = x

    z['key'] = y['key']

    return tree

def find(tree,k):
    x = tree
    while x != None:
        if x['key'] == k:
            return x
        elif x['key'] > k:
            x = x['left']
        else:
            x = x['right']
    return None

def middleorder(x):
    if x != None:
        middleorder(x['left'])
        print x['key'],
        middleorder(x['right'])

def preorder(x):
    if x != None:
        print x['key'],
        preorder(x['left'])
        preorder(x['right'])



tree = None
m = int(raw_input())
for i in range(m):
    c = raw_input().strip()
    if c[0] == 'i':
        tree = insert(tree, int(c[7:]))
    elif c[0] == 'f':
        x = find(tree, int(c[5:]))
        if x == None:
            print "no"
        else:
            print "yes"
    elif c[0] == 'd':
        z = find(tree, int(c[7:]))
        if not z == None: tree = delete_node(tree,z)
    elif c[0] == 'p':
        print '',
        middleorder(tree)
        print
        print '',
        preorder(tree)
        print