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AVL_Tree.py
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AVL_Tree.py
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"""
AVL tree is a self-balancing Binary Search Tree (BST) where the difference between heights of left and right subtrees cannot be more than one for
all nodes and if at any time they differ by more than one, rebalancing is done to restore this property. Each node maintains extra information
called a balance factor whose value is either -1, 0 or +1 where balance factor of a node in an AVL tree is the difference between the height of
the left subtree and that of the right subtree of that node.
"""
class avlnode:
def __init__(self, value):
self.left = None
self.right = None
self.value = value
class avltree():
def __init__(self):
self.node = None
self.height = -1
self.balancefactor = 0
"""
Insert new value into AVL Tree
"""
def insert(self, value):
tree = self.node
new_node = avlnode(value)
if tree is None:
self.node = new_node
self.node.left = avltree()
self.node.right = avltree()
elif value < tree.value:
self.node.left.insert(value)
elif value > tree.value:
self.node.right.insert(value)
self.rebalance()
def get_height(self):
if self.node:
return self.node.height
else:
return 0
# Rotate left (RL)
def rotate_left(self):
old_root = self.node
new_root = self.node.right.node
new_right = new_root.left.node
self.node = new_root
old_root.right.node = new_right
new_root.left.node = old_root
#Rotate right (RR)
def rotate_right(self):
old_root = self.node
new_root = self.node.left.node
new_left = new_root.right.node
self.node = new_root
old_root.left.node = new_left
new_root.right.node = old_root
"""
Rebalance a tree after insertion or deletion of a node
"""
def rebalance(self):
self.compute_height(recursive=False)
self.balance(recursive=False)
# For each node if balance is -1, 0 or 1 no rotation is required
while self.balancefactor < -1 or self.balancefactor > 1:
# Left subtree is bigger than right subtree
if self.balancefactor > 1:
if self.node.left.balancefactor < 0:
self.node.left.rotate_left()
self.compute_height()
self.balance()
self.rotate_right()
self.compute_height()
self.balance()
# Right subtree is bigger than left subtree
if self.balancefactor < -1:
if self.node.right.balancefactor > 0:
self.node.right.rotate_right()
self.compute_height()
self.balance()
self.rotate_left()
self.compute_height()
self.balance()
def compute_height(self, recursive=True):
# Height is max height of either left or right subtree =1 for root
if self.node:
if recursive:
if self.node.left:
self.node.left.compute_height()
if self.node.right:
self.node.right.compute_height()
self.height = 1 + max(self.node.left.height,
self.node.right.height)
else:
self.height = -1
"""
balance - Balance = height (left subtee ) - height (right subtree)
"""
def balance(self, recursive=True):
if self.node:
if recursive:
if self.node.left:
self.node.left.balance()
if self.node.right:
self.node.right.balance()
self.balancefactor = self.node.left.height - self.node.right.height
else:
self.balancefactor = 0
def inorder_traversal(self):
"""
Left tree nodes , root , right tree nodes
"""
if not self.node:
return []
result = []
left_nodes = self.node.left.inorder_traversal()
for lnode in left_nodes:
result.append(lnode)
result.append(self.node.value)
right_nodes = self.node.right.inorder_traversal()
for rnode in right_nodes:
result.append(rnode)
return result
def preorder_traversal(self):
"""
root, Left tree nodes , right tree nodes
"""
if not self.node:
return []
result = []
result.append(self.node.value)
left_nodes = self.node.left.preorder_traversal()
for lnode in left_nodes:
result.append(lnode)
right_nodes = self.node.right.preorder_traversal()
for rnode in right_nodes:
result.append(rnode)
return result
def postorder_traversal(self):
"""
Left tree nodes , root , right tree nodes
"""
if not self.node:
return []
result = []
left_nodes = self.node.left.postorder_traversal()
for lnode in left_nodes:
result.append(lnode)
right_nodes = self.node.right.postorder_traversal()
for rnode in right_nodes:
result.append(rnode)
result.append(self.node.value)
return result
if __name__ == "__main__":
tree = avltree()
data = []
i=0
print("Enter the number of nodes in a tree -")
num = int(input())
print("Enter the values of the nodes - ")
for i in range(0,num):
val = int(input())
data.append(val)
for value in data:
tree.insert(value)
print('In order traversal ', tree.inorder_traversal())
print('Preorder traversal ', tree.preorder_traversal())
print('Postorder traversal ', tree.postorder_traversal())
'''
Enter the number of nodes in a tree -
10
Enter the values of the nodes -
10
20
40
30
80
60
50
44
22
18
('In order traversal ', [10, 18, 20, 22, 30, 40, 44, 50, 60, 80])
('Preorder traversal ', [40, 20, 10, 18, 30, 22, 60, 50, 44, 80])
('Postorder traversal ', [18, 10, 22, 30, 20, 44, 50, 80, 60, 40])
--------------------------------
Space Complexity :
O(n) in all the cases
Time Complexity :
O(log n) in all the cases
'''