# Python Program to Count the Number of Nodes in Binary Tree

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This is a Python program to find the number of nodes in a binary tree.

Problem Description

The program creates a binary tree and counts the number of nodes in the tree.

Problem Solution

1. Create a class BinaryTree with instance variables key, left and right.
2. Define methods set_root, insert_left, insert_right, inorder 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 inorder displays the inorder traversal.
6. The method search returns a node with a specified key.
7. Define the function count_nodes which takes a binary tree as argument.
8. The recursive function count_nodes returns the number of nodes in the binary tree.

Program/Source Code

Here is the source code of a Python program to count the number of nodes in 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(self):
if self.left is not None:
self.left.inorder()
print(self.key, end=' ')
if self.right is not None:
self.right.inorder()

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

def count_nodes(node):
if node is None:
return 0
return 1 + count_nodes(node.left) + count_nodes(node.right)

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('count')
print('quit')

while True:
print('inorder traversal of binary tree: ', end='')
if btree is not None:
btree.inorder()
print()

do = input('What would you like to do? ').split()

operation = do.strip().lower()
if operation == 'insert':
data = int(do)
new_node = BinaryTree(data)
suboperation = do.strip().lower()
if suboperation == 'at':
btree = new_node
else:
position = do.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 == 'count':
print('Number of nodes in tree: {}'.format(count_nodes(btree)))

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 tree.
3. The corresponding methods are called to perform each operation.
4. The function count_nodes is called to count the number of nodes in the binary tree.

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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>
count
quit
inorder traversal of binary tree:
What would you like to do? insert 1 at root
inorder traversal of binary tree: 1
What would you like to do? insert 2 left of 1
inorder traversal of binary tree: 2 1
What would you like to do? insert 3 right of 1
inorder traversal of binary tree: 2 1 3
What would you like to do? insert 4 right of 2
inorder traversal of binary tree: 2 4 1 3
What would you like to do? count
Number of nodes in tree: 4
inorder traversal of binary tree: 2 4 1 3
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>
count
quit
inorder traversal of binary tree:
What would you like to do? count
Number of nodes in tree: 0
inorder traversal of binary tree:
What would you like to do? insert 1 at root
inorder traversal of binary tree: 1
What would you like to do? count
Number of nodes in tree: 1
inorder traversal of binary tree: 1
What would you like to do? insert 2 right of 1
inorder traversal of binary tree: 1 2
What would you like to do? count
Number of nodes in tree: 2
inorder traversal of binary tree: 1 2
What would you like to do? quit```

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