Problem:


Tree Walk

Binary trees are defined recursively. A binary tree T is a structure defined on a finite set of nodes that either

contains no nodes, or

is composed of three disjoint sets of nodes:

- a root node.

- a binary tree called its left subtree.

- a binary tree called its right subtree.

Your task is to write a program which perform tree walks (systematically traverse all nodes in a tree) based on the following algorithms:

Print the root, the left subtree and right subtree (preorder).

Print the left subtree, the root and right subtree (inorder).

Print the left subtree, right subtree and the root (postorder).

Here, the given binary tree consists of n nodes and evey node has a unique ID from 0 to n-1.

Input

The first line of the input includes an integer n, the number of nodes of the tree.

In the next n linen, the information of each node is given in the following format:

id left right

id is the node ID, left is ID of the left child and right is ID of the right child. If the node does not have the left (right) child, the left(right) is indicated by -1

Output

In the 1st line, print "Preorder", and in the 2nd line print a list of node IDs obtained by the preorder tree walk.

In the 3rd line, print "Inorder", and in the 4th line print a list of node IDs obtained by the inorder tree walk.

In the 5th line, print "Postorder", and in the 6th line print a list of node IDs obtained by the postorder tree walk.

Print a space character before each node ID.

Constraints

1 ≤ n ≤ 25

Sample Input 1

9
0 1 4
1 2 3
2 -1 -1
3 -1 -1
4 5 8
5 6 7
6 -1 -1
7 -1 -1
8 -1 -1

Sample Output 1

Preorder
 0 1 2 3 4 5 6 7 8
Inorder
 2 1 3 0 6 5 7 4 8
Postorder
 2 3 1 6 7 5 8 4 0

Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.



Sample input:
9
0 1 4
1 2 3
2 -1 -1
3 -1 -1
4 5 8
5 6 7
6 -1 -1
7 -1 -1
8 -1 -1


Sample output:
Preorder
 0 1 2 3 4 5 6 7 8
Inorder
 2 1 3 0 6 5 7 4 8
Postorder
 2 3 1 6 7 5 8 4 0

Submission status: WA: Presentation Error

Solution code:
n = int(input())
root = set(range(n))
nodes = [0 for i in range(n)]
for i in range(n):
    node = list(map(int, input().split()))
    children = node[1:3]
    root -= set(children)
    nodes[node[0]] = children

def preorder(id):
    if(id == -1):
        return
    order.append(id)
    preorder(nodes[id][0])
    preorder(nodes[id][1])

def inorder(id):
    if(id == -1):
        return
    inorder(nodes[id][0])
    order.append(id)
    inorder(nodes[id][1])

def postorder(id):
    if(id == -1):
        return
    postorder(nodes[id][0])
    postorder(nodes[id][1])
    order.append(id)

order = []
preorder(list(root)[0])
print('Preorder')
print(*order)
order = []
inorder(list(root)[0])
print('Inorder')
print(*order)
order = []
postorder(list(root)[0])
print('Postorder')
print(*order)

Submission status: WA: Presentation Error

Solution code:
class Tree:
    def __init__(self, ary):
        self.nodes = [
            Node(node, self) for node in sorted(ary, key=lambda x: x[0])
        ]
        [node.set() for node in self.nodes]
        for node in self.nodes:
            if node.parent == -1:
                self.root = node
                break
        self.root.set_depth(0)
        self.root.set_height()

    def output(self):
        [node.output() for node in self.nodes]

    def preorder(self):
        print('Preorder')
        self.root.preorder()

    def inorder(self):
        print('\nInorder')
        self.root.inorder()

    def postorder(self):
        print('\nPostorder')
        self.root.postorder()


class Node:
    def __init__(self, node, tree):
        self.tree = tree
        self.no = node[0]
        self.left = node[1]
        self.right = node[2]
        self.parent = -1
        self.sibling = -1
        self.degree = 0

    def set(self):
        if self.left > -1:
            self.tree.nodes[self.left].parent = self.no
            if self.right > -1:
                self.tree.nodes[self.right].sibling = self.left
            self.degree += 1

        if self.right > -1:
            self.tree.nodes[self.right].parent = self.no
            if self.left > -1:
                self.tree.nodes[self.left].sibling = self.right
            self.degree += 1

    def set_depth(self, d):
        self.depth = d
        if self.left > -1:
            self.tree.nodes[self.left].set_depth(d + 1)
        if self.right > -1:
            self.tree.nodes[self.right].set_depth(d + 1)

    def set_height(self):
        if self.degree == 0:
            self.height = 0
        else:
            self.tree.nodes[self.right].set_height()
            self.tree.nodes[self.left].set_height()
            self.height = 1 + max(self.tree.nodes[self.right].height,
                                  self.tree.nodes[self.left].height)

    def output(self):
        if self.parent == -1:
            kind = 'root'
        elif self.degree == 0:
            kind = 'leaf'
        else:
            kind = 'internal node'
        print(
            'node {}: parent = {}, sibling = {}, degree = {}, depth = {}, height = {}, {}'.
            format(self.no, self.parent, self.sibling, self.degree, self.depth,
                   self.height, kind))

    def preorder(self):
        print(' {}'.format(self.no), end='')
        if self.left > -1:
            self.tree.nodes[self.left].preorder()
        if self.right > -1:
            self.tree.nodes[self.right].preorder()

    def inorder(self):
        if not self.left > -1:
            print(' {}'.format(self.no), end='')
        else:
            self.tree.nodes[self.left].inorder()
            print(' {}'.format(self.no), end='')
            if self.right > -1:
                self.tree.nodes[self.right].inorder()

    def postorder(self):
        if not self.left > -1:
            print(' {}'.format(self.no), end='')
        else:
            self.tree.nodes[self.left].postorder()
            if self.right > -1:
                self.tree.nodes[self.right].postorder()
            print(' {}'.format(self.no), end='')


n = int(input())
ary = [[int(_) for _ in input().split()] for i in range(n)]
tree = Tree(ary)
tree.preorder()
tree.inorder()
tree.postorder()

Submission status: WA: Presentation Error

Solution code:
def preorder(tree, now):
    if now == -1:
        return []
    else:
        left = tree[now][0]
        right = tree[now][1]
        return [now] + preorder(tree, left) + preorder(tree, right)


def inorder(tree, now):
    if now == -1:
        return []
    else:
        left = tree[now][0]
        right = tree[now][1]
        return inorder(tree, left) + [now] + inorder(tree, right)


def postorder(tree, now):
    if now == -1:
        return []
    else:
        left = tree[now][0]
        right = tree[now][1]
        return postorder(tree, left) + postorder(tree, right) + [now]


def print_list_split_whitespace(a):
    for x in a[:-1]:
        print(x, end=" ")
    print(a[-1])


n = int(input())
tree = [[] for _ in range(n)]
ps = [-1 for _ in range(n)]
ss = [-1 for _ in range(n)]
for _ in range(n):
    s = input().split()
    id = int(s[0])
    left = int(s[1])
    right = int(s[2])
    tree[id] = [left, right]
    if left >= 0:
        ps[left] = id
        ss[left] = right
    if right >= 0:
        ps[right] = id
        ss[right] = left

root = ps.index(-1)

print("Preorder")
pre_list = preorder(tree, root)
print_list_split_whitespace(pre_list)

print("Inorder")
in_list = inorder(tree, root)
print_list_split_whitespace(in_list)

print("Postorder")
post_list = postorder(tree, root)
print_list_split_whitespace(post_list)

Submission status: WA: Presentation Error

Solution code:
n = int(input())
tree = [[-1, -1, True] for i in range(n)]
for i in range(n):
    id, left, right = map(int, input().split())
    if left != -1:
        tree[id][0] = left
        tree[left][2] = False
    if right != -1:
        tree[id][1] = right
        tree[right][2] = False

def preoder(id):
    if id == -1:
        return
    print(' ' + str(id), end='')
    preoder(tree[id][0])
    preoder(tree[id][1])

def inorder(id):
    if id == -1:
        return
    inorder(tree[id][0])
    print(' ' + str(id), end='')
    inorder(tree[id][1])

def postorder(id):
    if id == -1:
        return
    postorder(tree[id][0])
    postorder(tree[id][1])
    print(' ' + str(id), end='')

root = 0
for i, node in enumerate(tree):
    if node[2] == True:
        root = i

print('Preorder')
preoder(root)
print('')
print('Inorder')
inorder(root)
print('')
print('Postorder')
postorder(root)

Submission status: WA: Presentation Error

Solution code:
#coding:utf-8
N = int(input())
T = [None for i in range(N)]
class Tree:
    def __init__(self, ID,p=-1):
        self.ID = ID

    def makeTree(self, tree):
        ID = tree.ID
        if ID == -1:
            return
        else:
            for i in range(N):
                if trees[i][0] == ID:
                    [ID,l,r] = trees[i]
                    tree.l = Tree(l)
                    tree.r = Tree(r)
                    treeL = tree.l
                    treeR = tree.r
                    treeL.p = tree
                    treeR.p = tree

                    self.makeTree(self,treeL)
                    self.makeTree(self,treeR)

def preParse(tree):
    ID = tree.ID
    if ID == -1:
        return
    else:
        global preList
        preList.append(ID)
        treeL = tree.l
        treeR = tree.r
        preParse(treeL)
        preParse(treeR)
        
def inParse(tree):
    ID = tree.ID
    if ID == -1:
        return
    else:
        global inList
        treeL = tree.l
        treeR = tree.r
        inParse(treeL)
        inList.append(ID)
        inParse(treeR)

def posParse(tree):
    ID = tree.ID
    if ID == -1:
        return
    else:
        global posList
        treeL = tree.l
        treeR = tree.r
        posParse(treeL)
        posParse(treeR)
        posList.append(ID)
        
    
trees = [list(map(int,input().split())) for i in range(N)]
ID = trees[0][0]
tree = Tree(ID)
Tree.makeTree(Tree,tree)

preList = []
inList = []
posList = []
preParse(tree)
inParse(tree)
posParse(tree)

def convert(List, order):
    a =  " ".join([str(num) for num in List])
    print("{}".format(order))
    print(a)
convert(preList, "Preorder")
convert(inList, "Inorder")
convert(posList, "Postorder")