Problem:

  MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

Binary Search Tree I

 Search trees are data structures that support dynamic set operations including insert, search, delete and so on. Thus a search tree can be used both as a dictionary and as a priority queue. 

  Binary search tree is one of fundamental search trees. The keys in a binary search tree are always stored in such a way as to satisfy the following binary search tree property:

 Let $x$ be a node in a binary search tree. If $y$ is a node in the left subtree of $x$, then $y.key \leq x.key$. If $y$ is a node in the right subtree of $x$, then $x.key \leq y.key$.

  The following figure shows an example of the binary search tree.

  For example, keys of nodes which belong to the left sub-tree of the node containing 80 are less than or equal to 80, and keys of nodes which belong to the right sub-tree are more than or equal to 80. The binary search tree property allows us to print out all the keys in the tree in sorted order by an inorder tree walk.

  A binary search tree should be implemented in such a way that the binary search tree property continues to hold after modifications by insertions and deletions. A binary search tree can be represented by a linked data structure in which each node is an object. In addition to a key field and satellite data, each node contains fields left, right, and p that point to the nodes corresponding to its left child, its right child, and its parent, respectively.

  To insert a new value $v$ into a binary search tree $T$, we can use the procedure insert as shown in the following pseudo code. The insert procedure is passed a node $z$ for which $z.key = v$, $z.left = NIL$, and $z.right = NIL$. The procedure modifies $T$ and some of the fields of $z$ in such a way that $z$ is inserted into an appropriate position in the tree.

1 insert(T, z)
2     y = NIL // parent of x
3     x = 'the root of T'
4     while x &ne; NIL
5         y = x // set the parent
6         if z.key < x.key
7             x = x.left // move to the left child
8         else 
9             x = x.right // move to the right child
10    z.p = y
11
12    if y == NIL // T is empty
13        'the root of T' = z
14    else if z.key < y.key
15        y.left = z // z is the left child of y
16    else 
17        y.right = z // z is the right child of y

  Write a program which performs the following operations to a binary search tree $T$.

insert  $k$: Insert a node containing $k$ as key into $T$.

print: Print the keys of the binary search tree by inorder tree walk and  preorder tree walk respectively.

  You should use the above pseudo code to implement the insert operation. $T$ is empty at the initial state.

Input

  In the first line, the number of operations $m$ is given. In the following $m$ lines, operations represented by insert $k$ or print are given.

Output

  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

8
insert 30
insert 88
insert 12
insert 1
insert 20
insert 17
insert 25
print

Sample Output 1

 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.



Sample input:
8
insert 30
insert 88
insert 12
insert 1
insert 20
insert 17
insert 25
print


Sample output:
 1 12 17 20 25 30 88
 30 12 1 20 17 25 88

Submission status: Runtime Error

Solution code:
import sys

class TreeNode:
    def __init__(self, val):
        self.val = val
        self.left = self.right = None

class BST:
    def __init__(self):
        self.root = None
    
    def insert(self, node):
        def helper(root):
            if root is None:
                root = node
            elif node.val < root.val:
                lr = helper(root.left)
                root.left = lr
            else:
                rr = helper(root.right)
                root.right = rr
            return root
            
        self.root = helper(self.root)
    
    def inorder(self):
        def helper(root):
            if root is None:
                return []
            else:
                return helper(root.left) + [root.val] + helper(root.right)
        return helper(self.root)

if __name__ == '__main__':
    q = sys.stdin.readline()
    q = int(q)
    bst = BST()
    for i in range(q):
        tmp = sys.stdin.readline()
        if tmp.startswith('print'):
            print ' '.join(map(lambda x: str(x), bst.inorder()))
        else:
            _, val = tmp.split()
            node = TreeNode(int(val))
            sys.stdout.write(' '.join(map(lambda x: str(x), bst.insert(node)) + '\n'))

Submission status: Runtime Error

Solution code:
import sys

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

def insert(T, z): #z is node which you would like to insert                                
        #initialization                                                                    
    y = None #parent of x                                                                  
    x = T

        #search                                                                            
    while(x!=None):
        y = x
        if(z.key < x.key):
            x = x.left
        else:
            x = x.right

	#insert                                                                            
    if(y==None):
        T = z
    elif(z.key < y.key):
	y.left = z
    else:
        y.right = z

    return T

def inorder_walk(node):
    if node.left:
	inorder_walk(node.left)
    print('', node.key, end='')
    if node.right:
	inorder_walk(node.right)


def preorder_walk(node):
    print('', node.key, end='')
    if node.left:
        preorder_walk(node.left)
    if node.right:
	preorder_walk(node.right)


T = None
num = int(sys.stdin.readline())

for _ in range(num):
    cmd = sys.stdin.readline()
    if(cmd.startwith('i')):
        n = Node(int(cmd[:7]))
        T = insert(T, n)
    else:
        inorder_walk(T)
        preorder_walk(T)

Submission status: Runtime Error

Solution code:
import sys

#run by python3                                                                            

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

def insert(T, z): #z is node which you would like to insert                                
        #initialization                                                                    
    y = None #parent of x                                                                  
    x = T

	#search                                                                            
    while(x!=None):
        y = x
        if(z.key < x.key):
            x = x.left
        else:
            x = x.right

	#insert                                                                            
    if(y==None):
        T = z
    elif(z.key < y.key):
	y.left = z
    else:
        y.right = z

    return T

def inorder_walk(node):
    if node.left:
	inorder_walk(node.left)
    print ('', node.key, end='')
    if node.right:
	inorder_walk(node.right)


def preorder_walk(node):
    print ('', node.key,end='')
    if node.left:
        preorder_walk(node.left)
    if node.right:
	preorder_walk(node.right)


T = None
num = int(sys.stdin.readline())

for _ in range(num):
    cmd = sys.stdin.readline()
    if(cmd.startswith('i')):
	n = Node(int(cmd[7:]))
	T = insert(T, n)
    else:
        inorder_walk(T)
	print()
	preorder_walk(T)
	print()

Submission status: Runtime Error

Solution code:
import sys                                                                   

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

def insert(T, z):                                                                    
    y = None
    x = T
                                                                          
    while(x!=None):
        y = x
        if(z.key < x.key):
            x = x.left
        else:
            x = x.right

    if(y==None):
        T = z
    elif(z.key < y.key):
	y.left = z
    else:
        y.right = z

    return T

def inorder_walk(node):
    if node.left:
	inorder_walk(node.left)
    print ('', node.key, end='')
    if node.right:
	inorder_walk(node.right)


def preorder_walk(node):
    print ('', node.key,end='')
    if node.left:
        preorder_walk(node.left)
    if node.right:
	preorder_walk(node.right)


T = None
num = int(sys.stdin.readline())

for _ in range(num):
    cmd = sys.stdin.readline()
    if(cmd.startswith('i')):
	n = Node(int(cmd[7:]))
	T = insert(T, n)
    else:
        inorder_walk(T)
	print()
	preorder_walk(T)
	print()

Submission status: Runtime Error

Solution code:

def preorder_walk(node):
    print ('', node.key,end='')
    if node.left:
        preorder_walk(node.left)
    if node.right:
	preorder_walk(node.right)


T = None
num = int(sys.stdin.readline())

for _ in range(num):
    cmd = sys.stdin.readline()
    if(cmd.startswith('i')):
	n = Node(int(cmd[7:]))
	T = insert(T, n)
    else:
        inorder_walk(T)
	print()
	preorder_walk(T)
	print()

Submission status: Runtime Error

Solution code:
#!/usr/bin/env python3                                                                     
import sys

#run by python3                                                                            

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

def insert(T, z): #z is node which you would like to insert                                
        #initialization                                                                    
    y = None #parent of x                                                                  
    x = T

        #search                                                                            
    while(x!=None):
        y = x
        if(z.key < x.key):
            x = x.left
        else:
            x = x.right

        #insert                                                                            
    if(y==None):
        T = z
    elif(z.key < y.key):
        y.left = z
    else:
        y.right = z

    return T

def inorder_walk(node):
    if node.left:
        inorder_walk(node.left)
    print ('', node.key, end='')
    if node.right:
        inorder_walk(node.right)


def preorder_walk(node):
    print ('', node.key,end='')
    if node.left:
        preorder_walk(node.left)
    if node.right:
	preorder_walk(node.right)


T = None
num = int(sys.stdin.readline())

for _ in range(num):
    cmd = sys.stdin.readline()
    if(cmd.startswith('i')):
        n = Node(int(cmd[7:]))
	T = insert(T, n)
    else:
        inorder_walk(T)
        print()
        preorder_walk(T)
        print()

Submission status: Runtime Error

Solution code:
#!/usr/bin/env python3                                                                     
import sys

#run by python3                                                                            

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

def insert(T, z): #z is node which you would like to insert                                
        #initialization                                                                    
    y = None #parent of x                                                                  
    x = T

        #search                                                                            
    while(x!=None):
        y = x
        if(z.key < x.key):
            x = x.left
        else:
            x = x.right

        #insert                                                                            
    if(y==None):
        T = z
    elif(z.key < y.key):
        y.left = z
    else:
        y.right = z

    return T


def inorder_walk(node):
    if node.left:
        inorder_walk(node.left)
    print ('', node.key, end='')
    if node.right:
	inorder_walk(node.right)


def preorder_walk(node):
    print ('', node.key,end='')
    if node.left:
        preorder_walk(node.left)
    if node.right:
	preorder_walk(node.right)

if __name__ == '__main__':

    T = None
    num = int(sys.stdin.readline())

    for _ in range(num):
        cmd = sys.stdin.readline()
        if(cmd.startswith('i')):
            n = Node(int(cmd[7:]))
            T = insert(T, n)
        else:
            inorder_walk(T)
            print()
            preorder_walk(T)
            print()

Submission status: Runtime Error

Solution code:
def inorder_walk(node):
    if node.left:
        inorder_walk(node.left)
    print ('', node.key, end='')
    if node.right:
	inorder_walk(node.right)


def preorder_walk(node):
    print ('', node.key,end='')
    if node.left:
        preorder_walk(node.left)
    if node.right:
	preorder_walk(node.right)

if __name__ == '__main__':

    T = None
    num = int(sys.stdin.readline())

    for _ in range(num):
        cmd = sys.stdin.readline()
        if(cmd.startswith('i')):
            n = Node(int(cmd[7:]))
            T = insert(T, n)
        else:
            inorder_walk(T)
            print()
            preorder_walk(T)
            print()

Submission status: Runtime Error

Solution code:
File Edit Options Buffers Tools Python Help                                                
#!/usr/bin/env python3                                                                     
#run by python3                                                                            

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

def insert(T, z): #z is node which you would like to insert                                
        #initialization                                                                    
    y = None #parent of x                                                                  
    x = T

        #search                                                                            
    while(x!=None):
        y = x
        if(z.key < x.key):
            x = x.left
        else:
            x = x.right

        #insert                                                                            
    if(y==None):
	T = z
    elif(z.key < y.key):
        y.left = z
    else:
        y.right = z

    return T


def inorder_walk(node):
    if node.left:
        inorder_walk(node.left)
    print ('', node.key, end='')
    if node.right:
        inorder_walk(node.right)


def preorder_walk(node):
    print ('', node.key,end='')
    if node.left:
        preorder_walk(node.left)
    if node.right:
        preorder_walk(node.right)

if __name__ == '__main__':

    T = None
    num = int(input())

    for _ in range(num):
        cmd = input()
        if(cmd.startswith('i')):
            n = Node(int(cmd[7:]))
            T = insert(T, n)
        else:
            inorder_walk(T)
            print()
            preorder_walk(T)
            print()

Submission status: Runtime Error

Solution code:
#!/usr/bin/env python3                                                                     
#run by python3                                                                            

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

def insert(T, z): #z is node which you would like to insert                                
        #initialization                                                                    
    y = None #parent of x                                                                  
    x = T

        #search                                                                            
    while(x!=None):
        y = x
        if(z.key < x.key):
            x = x.left
        else:
            x = x.right

        #insert                                                                            
    if(y==None):
	T = z
    elif(z.key < y.key):
        y.left = z
    else:
        y.right = z

    return T


def inorder_walk(node):
    if node.left:
        inorder_walk(node.left)
    print ('', node.key, end='')
    if node.right:
        inorder_walk(node.right)


def preorder_walk(node):
    print ('', node.key,end='')
    if node.left:
        preorder_walk(node.left)
    if node.right:
        preorder_walk(node.right)

if __name__ == '__main__':

    T = None
    num = int(input())

    for _ in range(num):
        cmd = input()
        if(cmd.startswith('i')):
            n = Node(int(cmd[7:]))
            T = insert(T, n)
        else:
            inorder_walk(T)
            print()
            preorder_walk(T)
            print()

Submission status: Runtime Error

Solution code:
#!/usr/bin/env python3                                                                        

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

def insert(T, z):                     
    #initialization                                                                    
    y = None #parent of x                                                                  
    x = T

    #search                                                                            
    while(x!=None):
        y = x
        if(z.key < x.key):
            x = x.left
        else:
            x = x.right

    #insert                                                                            
    if(y==None):
	T = z
    elif(z.key < y.key):
        y.left = z
    else:
        y.right = z

    return T


def inorder_walk(node):
    if node.left:
        inorder_walk(node.left)
    print ('', node.key, end='')
    if node.right:
        inorder_walk(node.right)


def preorder_walk(node):
    print ('', node.key,end='')
    if node.left:
        preorder_walk(node.left)
    if node.right:
        preorder_walk(node.right)

if __name__ == '__main__':

    T = None
    num = int(input())

    for _ in range(num):
        cmd = input()
        if(cmd.startswith('i')):
            n = Node(int(cmd[7:]))
            T = insert(T, n)
        else:
            inorder_walk(T)
            print()
            preorder_walk(T)
            print()

Submission status: Runtime Error

Solution code:
import sys

class binarySearchTree:
    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

        if y is None:
            self.root = z
        elif z.key < y.key:
            y.left = z
        else:
            y.right = z

    def printBT(self):
        print self.root.inorderTreeWalk()
        print self.root.preorderTreeWalk()

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

    def inorderTreeWalk(self):
        ret = ""
        if self.left:
            ret += self.left.inorderTreeWalk()
        ret += " " + str(self.key)
        if self.right:
            ret += self.right.inorderTreeWalk()

        return ret

    def preorderTreeWalk(self):
        ret = " " + str(self.key)
        if self.left:
            ret += self.left.preorderTreeWalk()
        if self.right:
            ret += self.right.preorderTreeWalk()

        return ret

if __name__ == "__main__":
    lines = sys.stdin.readlines()
    del lines[0]

    bt = binarySearchTree()
    for line in lines:
        if line[0] == "i":
            bt.insert(int(line.split()[1])
        else:
            bt.printBT()

Submission status: Runtime Error

Solution code:
import sys

class binarySearchTree:
    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

        if y is None:
            self.root = z
        elif z.key < y.key:
            y.left = z
        else:
            y.right = z

    def printBT(self):
        print inorderTreeWalk(self.root)
        print preorderTreeWalk(self.root)

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

def inorderTreeWalk(node):
    if node:
        return inorderTreeWalk(node.left) + " " + str(node.key) + inorderTreeWalk(node.right)
    return ""

def preorderTreeWalk(node):
    if node:
        return " " + str(node.key) + preorderTreeWalk(node.left) + preorderTreeWalk(node.right)
    return ""

if __name__ == "__main__":
    m = int(raw_input())
    bt = binarySearchTree()
    for i in range(m):
        line = map(str, raw_input())
        if line[0] == "i":
            bt.insert(int(line[i].split()[1]))
        else:
            bt.printBT()

Submission status: Runtime Error

Solution code:
import sys
import time

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

def insert(key):
    global root
    z = Node(key)
    y = None
    x = root
    while x:
        y = x
        if z.key < x.key:
            x = x.left
        else:
            x = x.right

    if y is None:
        root.key = key
    elif z.key < y.key:
        y.left = z
    else:
        y.right = z

def inorderTreeWalk(node):
    if node:
        return inorderTreeWalk(node.left) + " " + str(node.key) + inorderTreeWalk(node.right)
    return ""

def preorderTreeWalk(node):
    if node:
        return " " + str(node.key) + preorderTreeWalk(node.left) + preorderTreeWalk(node.right)
    return ""

if __name__ == "__main__":
    lines = sys.stdin.readlines()
    del lines[0]

    root = None
    for line in lines:
        if line[0] == "i":
            insert(int(line.split()[1]))
        else:
            print inorderTreeWalk(root)
            print preorderTreeWalk(root)

Submission status: Runtime Error

Solution code:
import sys
import time

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

def insert(key, z):
    global root
    y = None
    x = root
    while x:
        y = x
        if z.key < x.key:
            x = x.left
        else:
            x = x.right
    z.parent = y
    if y is None:
        root = z
    elif z.key < y.key:
        y.left = z
    else:
        y.right = z

def inorderTreeWalk(node):
    global In
    if node:
        inorderTreeWalk(node.left)
        In.append(str(node.key))
        inorderTreeWalk(node.right)

def preorderTreeWalk(node):
    global Pre
    if node:
        Pre.append(str(node.key))
        preorderTreeWalk(node.left)
        preorderTreeWalk(node.right)

if __name__ == "__main__":
    lines = sys.stdin.readlines()
    del lines[0]

    root = None
    for line in lines:
        if line[0] == "i":
            insert(Node(int(line.split()[1])))
        else:
            In = []
            Pre = []
            inorderTreeWalk(root)
            print " " + " ".join(map(str, In))
            preorderTreeWalk(root)
            print " " + " ".join(map(str, Pre))

Submission status: Runtime Error

Solution code:
#http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ALDS1_8_A
#????????????

def insert(root, insert_node):
    focus_node = root
    parent = None
    while not focus_node == None:
        parent = focus_node
        if focus_node["data"]  > insert_node["data"]:
            focus_node = focus_node["left"]
        else:
            focus_node = focus_node["right"]

    if parent["data"] > insert_node["data"]:
        parent["left"] = insert_node
    else:
        parent["right"] = insert_node

def get_preorder(node):
    if node == None:
        return []
    r = []
    r.append(str(node["data"]))
    r.extend(get_preorder(node["left"]))
    r.extend(get_preorder(node["right"]))

    return r
    
def get_inorder(node):
    if node == None:
        return []
    r = []
    r.extend(get_inorder(node["left"]))
    r.append(str(node["data"]))
    r.extend(get_inorder(node["right"]))

    return r
def print_tree(root):
    print(" " + " ".join(get_inorder(root)))
    print(" " + " ".join(get_preorder(root)))
def main():
    
    n_line = int(input())
    input_list = [input().split()[1] for i in range(n_line - 1)]
    root = {"left":None, "right": None, "data":int(input_list[0])}

    for s in input_list[1:]:
        node = {"left":None, "right": None, "data":int(s)}
        insert(root, node)

    print_tree(root)

    
if __name__ == "__main__":
    main()

Submission status: Runtime Error

Solution code:
import sys

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

    def prewalk(self):
        nodeList = [self.key]
        if self.left:
            nodeList += self.left.prewalk()
        if self.right:
            nodeList += self.right.prewalk()
        return nodeList

    def inwalk(self):
        nodeList = []
        if self.left:
            nodeList += self.left.inwalk()
        nodeList += [self.key]
        if self.right:
            nodeList += self.right.inwalk()
        return nodeList

    def print(self):
        print('', ' '.join(map(str, self.root.inwalk())))
        print('', ' '.join(map(str, self.root.prewalk())))

class Tree():
    def __init__(self):
        self.root = None
    def insert(self, key):
        Nz = Node(key)
        Ny = None #???????£?
        Nx = self.root
        while Nx:
            Ny = Nx
            if Nz.key < Ny.key:
                Nx = Nx.left
            else:
                Nx = Nx.right

        Nz.parent = Ny
        if Ny == None:
            self.root = Nz
        elif Nz.key < Ny.key:
            Ny.left = Nz
        else:
            Ny.right = Nz

tree = Tree()

n = sys.stdin.readline()
for line in sys.stdin:
    if line[0] == 'i':
        tree.insert(int(line.split()[1]))
    else:
        tree.print()

Submission status: Runtime Error

Solution code:
# -*- coding: utf-8 -*-

import random


class Tree:
    def __init__(self):
        self.root = None

    def __str__(self):
        if self.root == None:
            return None
        else:
            return "TODO"

    def print_inorder(self):
        self.__inorder(self.root)

    def __inorder(self, node):
        """
        :param node: Node
        :return:
        """
        if node is None:
            return
        else:
            self.__inorder(node.left)
            print(node.key, end=' ')
            self.__inorder(node.right)

    def print_preorder(self):
        self.__preorder(self.root)

    def __preorder(self, node):
        """
        :param node: Node
        :return:
        """
        if node is None:
            return
        else:
            print(node.key, end=' ')
            self.__preorder(node.left)
            self.__preorder(node.right)

    def insert(self, node):
        """
        :param node: Node
        :return:
        """
        if self.root is None:
            self.root = node
        else:
            x = self.root
            parent_candidate = x

            while x is not None:
                parent_candidate = x
                if x.key > node.key:
                    x = x.left
                else:
                    x = x.right

            # child to parent link
            x = node
            x.parent = parent_candidate

            # parent to child link
            if x.key < x.parent.key:
                x.parent.left = x
            else:
                x.parent.right = x

    def find(self, value):
        """
        :param value:
        :rtype: Node
        :return:
        """
        x = self.root
        while x is not None and x.key != value:
            if x.key > value:
                x = x.left
            else:
                x = x.right
        return x

    def delete(self, value):
        found_node = self.find(value)
        if found_node is None:
            print("value is nothing")
        else:
            # has no child
            if found_node.is_leaf():
                # delete link from parent
                print(found_node.parent.left.key)
                print(found_node.key)

                if found_node.parent.left.key == found_node.key:
                    found_node.parent.left = None
                else:
                    found_node.parent.right = None
            else:
                # has one child
                if found_node.has_one_child():
                    one_child = found_node.get_one_child()

                    # change link to parent
                    one_child.parent = found_node.parent

                    # chagne link from parent
                    if found_node.parent.left == found_node:
                        found_node.parent.left = one_child
                    else:
                        found_node.parent.right = one_child

                # has two child
                else:
                    next_section_point = found_node.get_next_section_point()
                    # ?¬???????????????????????????????????????????????¬?????????????????????? p217
                    # ????????????
                    key = next_section_point.key
                    self.delete(next_section_point.key)
                    found_node.key = key


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

    def has_one_child(self):
        if self.left is None and self.right is not None:
            return True
        elif self.left is not None and self.right is None:
            return True
        else:
            return False

    def get_one_child(self):
        if not self.has_one_child():
            return None
        else:
            if self.left is not None:
                return self.left
            else:
                return self.right

    def get_next_section_point(self):
        """?¬??????????????????????"""

        # ????????????????????´???
        if self.right is not None:
            return self.right.get_minimum()
        # ???????????????????????´???????¬???????????????´?????????
        else:
            # ?
            return self.parent

    def is_leaf(self):
        if self.left is None and self.right is None:
            return True
        else:
            return False

    def get_minimum(self):
        if self.left is None:
            return self
        else:
            return self.left.get_minimum()

n = int(input())
for _ in range(n):
    s = input()
    value = int(s.split(" "))
    tree.insert(value)

tree.print_preorder()
print('')
tree.print_inorder()