PYTHON - AVL TREES CODE

JAVA PYTHON GO KOTLIN C# RUBY C++ Java Script

Example :

class Node:
	def __init__(self, value):
		self.data = value
		self.left = None
		self.right = None
		self.height = 1
		self.size = 0

class TreeTraversal:
	def __init__(self):
		self.root = None

	def inOrder(self, node):
		if (node != None):
			self.inOrder(node.left)
			print(node.data, end = "  ")
			self.inOrder(node.right)


def leftRotate(rootNode):
	newRoot = rootNode.right
	rootNode.right = rootNode.right.left
	newRoot.left = rootNode
	rootNode.height = setHeight(rootNode)
	rootNode.size = setSize(rootNode)
	newRoot.height = setHeight(newRoot)
	newRoot.size = setSize(newRoot)
	return newRoot

def rightRotate(rootNode):
	newRoot = rootNode.left
	rootNode.left = rootNode.left.right
	newRoot.right = rootNode
	rootNode.height = setHeight(rootNode)
	rootNode.size = setSize(rootNode)
	newRoot.height = setHeight(newRoot)
	newRoot.size = setSize(newRoot)
	return newRoot;

def setSize(rootNode):
	if(rootNode == None):
		return 0
	return 1 + max((rootNode.left.size if rootNode.left != None else 0), (rootNode.right.size if rootNode.right != None else 0));

def insert(rootNode, data):
	if (rootNode == None):
		rootNode = Node(data)
		return rootNode

	if (data < rootNode.data):
		rootNode.left = insert(rootNode.left, data)
	elif (data > rootNode.data):
		rootNode.right = insert(rootNode.right, data)

	balanceFactor = balance(rootNode.left, rootNode.right)

	if(balanceFactor > 1):
		if(height(rootNode.left.left) >= height(rootNode.left.right)):
			rootNode = rightRotate(rootNode);
		else:
			rootNode.left = leftRotate(rootNode.left)
			rootNode = rightRotate(rootNode)
	elif(balanceFactor < -1):
		if(height(rootNode.right.right) >= height(rootNode.right.left)):
			rootNode = leftRotate(rootNode);
		else:
			rootNode.right = rightRotate(rootNode.right)
			rootNode = leftRotate(rootNode);
	else:
		rootNode.height = setHeight(rootNode)
		rootNode.size = setSize(rootNode)
	return rootNode;

def balance(rootNodeLeft, rootNodeRight):
	return height(rootNodeLeft) - height(rootNodeRight)

def setHeight(rootNode):
	if(rootNode == None):
		return 0
	return 1 + max((rootNode.left.height if rootNode.left != None else 0), (rootNode.right.height if rootNode.right != None else 0))

def height(rootNode):
	if(rootNode == None):
		return 0
	else:
		return rootNode.height


root = None
root = insert(root, 16)
root = insert(root, 10)
root = insert(root, 25)
root = insert(root, 2)
root = insert(root, 13)
root = insert(root, 18)
root = insert(root, 30)
root = insert(root, 7)
root = insert(root, 8)

tt = TreeTraversal()
print("Inorder Traversal : \n")
tt.inOrder(root)

print()

Output :

Inorder Traversal :

2 7 8 10 13 16 18 25 30

Code Explanation

So, we will constructing the below Balanced Binary Search Tree, by inserting the elements one by one.

And we have the below methods :

def insert(root, key)

This method is used to insert a new Node to the Binary Search Tree. Then balance it as per the rules of AVL Tree.

def leftRotate(rootNode)

This method is used to Left Rotate the Binary Search Tree in order to balance it as per the rules of AVL Tree.

def rightRotate(rootNode)

This method is used to Right Rotate the Binary Search Tree in order to balance it as per the rules of AVL Tree.

def balance(rootNodeLeft, rootNodeRight)

As the name suggests, this method is used to balance the Binary Search Tree as per the rules of AVL Tree.

def setHeight(rootNode) and def height(rootNode)

As we know an AVL Tree is a height balanced Binary Search Tree. And the setHeight(...) and height(...) are the methods where the height of the AVL Tree is calculated.

Code explanation for AVL Tree :

Firstly, we would be constructing the above Binary Search Tree, with the help of insert method.

root = None
root = insert(root, 16)

Initially, the variable root is None. So, we take the element i.e. 16 in this case. And pass the root and the element 16 to the insert method.

'def insert(rootNode, data)' method

def insert(rootNode, data):
	if (rootNode == None):
		rootNode = Node(data)
		return rootNode

	if (data < rootNode.data):
		rootNode.left = insert(rootNode.left, data)
	elif (data > rootNode.data):
		rootNode.right = insert(rootNode.right, data)

	balanceFactor = balance(rootNode.left, rootNode.right)

	if(balanceFactor > 1):
		if(height(rootNode.left.left) >= height(rootNode.left.right)):
			rootNode = rightRotate(rootNode);
		else:
			rootNode.left = leftRotate(rootNode.left)
			rootNode = rightRotate(rootNode)
	elif(balanceFactor < -1):
		if(height(rootNode.right.right) >= height(rootNode.right.left)):
			rootNode = leftRotate(rootNode);
		else:
			rootNode.right = rightRotate(rootNode.right)
			rootNode = leftRotate(rootNode);
	else:
		rootNode.height = setHeight(rootNode)
		rootNode.size = setSize(rootNode)
	return rootNode

The first line of the insert(...) checks if the rootNode is None or not.

if (rootNode == None):
	rootNode = Node(data)
	return rootNode

And in this case rootNode is None. So, we create a new Node object with the data i.e. 16. And the Node object is created with the below constructor.

def __init__(self, value):
	self.data = value
	self.left = None
	self.right = None
	self.height = 1
	self.size = 0

Then assign it to the Node object root.

And return the Node root.

return root

In the next line we try to insert the element 13 in the Binary Search Tree using the insert(...) method.

root = insert(root, 10)

And the insert(...) method is called.

And in the similar way we check,

if (data < rootNode.data):
	rootNode.left = insert(rootNode.left, data)
elif (data > rootNode.data):
	rootNode.right = insert(rootNode.right, data)

If the data i.e. 13 is less than the root element root.data. And the first condition matches.

if (data < rootNode.data):
	rootNode.left = insert(rootNode.left, data)

And a recursive call is made to insert(...) method.

rootNode.left = insert(rootNode.left, data)

So, the method executes and sets the value of rootNode.left with this Node that contains 13.

And since we are dealing with AVL tree, it is time to calculate the Balance Factor.

balanceFactor = balance(rootNode.left, rootNode.right)

And the balance(...) method is called.

def balance(rootNodeLeft, rootNodeRight):
	return height(rootNodeLeft) - height(rootNodeRight)

And the balance(...) method is quite simple to understand. It calls the height(...) method for the Left Node and Right Node and calculates the difference between Left and Right Node.

And as we know, Balance Factor is the difference of Left and Right Node.

And now since we got the Balance Factor, we need to perform Left or Right rotation if the value of Balance Factor is other than -1, 0 or 1.

if(balanceFactor > 1):
	if(height(rootNode.left.left) >= height(rootNode.left.right)):
		rootNode = rightRotate(rootNode);
	else:
		rootNode.left = leftRotate(rootNode.left)
		rootNode = rightRotate(rootNode)
elif(balanceFactor < -1):
	if(height(rootNode.right.right) >= height(rootNode.right.left)):
		rootNode = leftRotate(rootNode);
	else:
		rootNode.right = rightRotate(rootNode.right)
		rootNode = leftRotate(rootNode);
else:
	rootNode.height = setHeight(rootNode)
	rootNode.size = setSize(rootNode)

So, if the Balance Factor is greater than 1.

if(balanceFactor > 1):
	if(height(rootNode.left.left) >= height(rootNode.left.right)):
		rootNode = rightRotate(rootNode)
	else:
		rootNode.left = leftRotate(rootNode.left)
		rootNode = rightRotate(rootNode)

We go to the left child of the rootNode and try checking, if the height of the left child of the left node is greater than the height of the right child of the left node.

if(height(rootNode.left.left) >= height(rootNode.left.right)):
	rootNode = rightRotate(rootNode)

If the above condition satisfies, then we can assume that we need to right rotate the tree.

And the rightRotate(...) method is called to balance the tree.

def rightRotate(rootNode):
	newRoot = rootNode.left
	rootNode.left = rootNode.left.right
	newRoot.right = rootNode
	rootNode.height = setHeight(rootNode)
	rootNode.size = setSize(rootNode)
	newRoot.height = setHeight(newRoot)
	newRoot.size = setSize(newRoot)
	return newRoot

Let us take the below example to understand the rightRotate(...) method.

Say, rootNode has the element 13.

Now, we create a Node named newNode and assign the Node rootNode.left to it.

newRoot = rootNode.left

And as we can see in the above diagram rootNode.left has the element 7 in it.

Then we take the rootNode.left.right (i.e. The right child of 7, which is None in the above case) and assign it to rootNode.left.

rootNode.left = rootNode.left.right

And the below tree looks like,

Next, we take the rootNode and assign it as the right child of the newly created Node newRoot.

newRoot.right = rootNode

So, the right rotation is performed,

The rest few lines of the method is quite easy to understand.

The height is set by calling the setHeight(...) method.

rootNode.height = setHeight(rootNode)

And finally, the Node newRoot is returned.

return newRoot;

And continuing this way we get the below AVL tree.

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