# 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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