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

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.

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.

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

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.

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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