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Here is the lecture on general trees and binary trees by Prof Naveen Garg.

Some very important properties of a binary tree assuming that the height of the tree is h are:

1. The maximum number of nodes at each level of a binary tree is: 2^{l} where l is the level number.

2. The number of nodes n in a full binary tree are: 2^{h+1}-1
This is because a binary tree of height h has h levels. So we add the number of nodes at each level
(2^{0}+2^{1}+2^{2}…2^{h})

3. The number of leaf nodes in a full binary tree is: 2^{h}

Here is the python implementation of a binary tree:

class BinaryTree:
#binary tree constructor
def __init__(self, root):
self.root = root
self.leftChild = None #initializing left child of a binary tree
self.rightChild = None #initializing right child of a binary tree
#method for setting the root of a binary tree
def setRoot(self, root):
self.root = root
#method for getting the root of a binary tree
def getRoot(self):
return self.root
#method for getting the left child of the binary tree
def getLeftChild(self):
return self.leftChild
#method for getting the right child of the binary tree
def getRightChild(self):
return self.rightChild
#method for inserting the left child of the binary tree
def insertLeftChild(self, newNode):
if self.leftChild == None:
self.leftChild = BinaryTree(newNode)
else:
t = BinaryTree(newNode)
t.leftChild = self.leftChild
self.leftChild = t
#method for inserting the right child of the binary tree
def insertRightChild(self, newNode):
if self.rightChild == None:
self.rightChild = BinaryTree(newNode)
else:
t = BinaryTree(newNode)
t.rightChild = self.rightChild
self.rightChild = t

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