Python Program to Find Nth Node of Inorder Traversal

This is a Python program to find the Nth node in the in-order traversal of a binary tree.

Problem Description

The program creates a binary tree and presents a menu to the user to perform operations on the tree including printing the Nth term in its in-order traversal.

Problem Solution

1. Create a class BinaryTree with instance variables key, left and right.
2. Define methods set_root, insert_left, insert_right, inorder_nth, inorder_nth_helper and search.
3. The method set_root takes a key as argument and sets the variable key equal to it.
4. The methods insert_left and insert_right insert a node as the left and right child respectively.
5. The method search returns a node with a specified key.
6. The method inorder_nth displays the nth element in the in-order traversal of the tree. It calls the recursive method inorder_nth_helper.

Program/Source Code

Here is the source code of a Python program to find the Nth node in the in-order traversal of a binary tree. The program output is shown below.

class BinaryTree:
    def __init__(self, key=None):
        self.key = key
        self.left = None
        self.right = None
 
    def set_root(self, key):
        self.key = key
 
    def inorder_nth(self, n):
        return self.inorder_nth_helper(n, [])
 
    def inorder_nth_helper(self, n, inord):
        if self.left is not None:
            temp = self.left.inorder_nth_helper(n, inord)
            if temp is not None:
                return temp
        inord.append(self)
        if n == len(inord):
            return self
        if self.right is not None:
            temp = self.right.inorder_nth_helper(n, inord)
            if temp is not None:
                return temp
 
    def insert_left(self, new_node):
        self.left = new_node
 
    def insert_right(self, new_node):
        self.right = new_node
 
    def search(self, key):
        if self.key == key:
            return self
        if self.left is not None:
            temp =  self.left.search(key)
            if temp is not None:
                return temp
        if self.right is not None:
            temp =  self.right.search(key)
            return temp
        return None
 
 
btree = None
 
print('Menu (this assumes no duplicate keys)')
print('insert <data> at root')
print('insert <data> left of <data>')
print('insert <data> right of <data>')
print('inorder <index>')
print('quit')
 
while True:
    do = input('What would you like to do? ').split()
 
    operation = do[0].strip().lower()
    if operation == 'insert':
        data = int(do[1])
        new_node = BinaryTree(data)
        suboperation = do[2].strip().lower() 
        if suboperation == 'at':
                btree = new_node
        else:
            position = do[4].strip().lower()
            key = int(position)
            ref_node = None
            if btree is not None:
                ref_node = btree.search(key)
            if ref_node is None:
                print('No such key.')
                continue
            if suboperation == 'left':
                ref_node.insert_left(new_node)
            elif suboperation == 'right':
                ref_node.insert_right(new_node)
 
    elif operation == 'inorder':
        if btree is not None:
            index = int(do[1].strip().lower())
            node = btree.inorder_nth(index)
            if node is not None:
                print('nth term of inorder traversal: {}'.format(node.key))
            else:
                print('index exceeds maximum possible index.')
        else:
            print('Tree is empty.')
 
    elif operation == 'quit':
        break

Program Explanation

1. A variable is created to store the binary tree.
2. The user is presented with a menu to perform operations on the binary tree.
3. The corresponding methods are called to perform each operation.
4. The method inorder_nth is called to display the nth element in the in-order traversal of the tree.

Runtime Test Cases

Case 1:
Menu (this assumes no duplicate keys)
insert <data> at root
insert <data> left of <data>
insert <data> right of <data>
inorder <index>
quit
What would you like to do? insert 1 at root
What would you like to do? insert 2 left of 1
What would you like to do? insert 3 right of 1
What would you like to do? inorder 1
nth term of inorder traversal: 2
What would you like to do? inorder 2
nth term of inorder traversal: 1
What would you like to do? inorder 3
nth term of inorder traversal: 3
What would you like to do? inorder 4
index exceeds maximum possible index.
What would you like to do? quit
 
Case 2:
Menu (this assumes no duplicate keys)
insert <data> at root
insert <data> left of <data>
insert <data> right of <data>
inorder <index>
quit
What would you like to do? insert 1 at root
What would you like to do? insert 3 left of 1
What would you like to do? insert 7 right of 1
What would you like to do? insert 5 right of 3
What would you like to do? insert 6 left of 5
What would you like to do? inorder 1
nth term of inorder traversal: 3
What would you like to do? inorder 2
nth term of inorder traversal: 6
What would you like to do? inorder 3
nth term of inorder traversal: 5
What would you like to do? inorder 4
nth term of inorder traversal: 1
What would you like to do? inorder 5
nth term of inorder traversal: 7
What would you like to do? inorder 6
index exceeds maximum possible index.
What would you like to do? quit

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