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avl_tree.py
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from queue import Queue
# AVL Tree node
class Node:
def __init__(self, data):
self.data = data
self.height = 0 # Keeps track of height for each node
self.left = None
self.right = None
class AVLTree:
# Threshold is commonly set to 1 by default
def __init__(self, threshold = 1):
self.root = None
self.threshold = threshold
def insert(self, items):
if not items: # If empty
return None
for i in range(len(items)): # Add each element
self.root = self.__insert(self.root, items[i], self.threshold)
def __insert(self, root, data, threshold):
if not root:
return Node(data)
elif data < root.data:
root.left = self.__insert(root.left, data, threshold)
else:
root.right = self.__insert(root.right, data, threshold)
# Get the height for root
# H(r) = 1 + max(h[r.left], h[r.right])
root.height = 1 + max(self.get_height(root.left), self.get_height(root.right))
# Get balance
# For AVL trees, -1 <= balance <= 1
balance = self.get_balance(root)
# If balance is greater than 1, then left side is heavy so we must rotate right
if balance > threshold:
if self.get_balance(root.left) >= 0: # Node left correctly balanced
root = self.rotate_right(root)
else:
root = self.rotate_left_right(root) # For node left right heavy
# If balance is less than 1, right side is heavy
elif balance < -threshold:
if self.get_balance(root.right) <= 0:
root = self.rotate_left(root)
else:
root = self.rotate_right_left(root) # For node right left heavy
return root
# Rotate right for left-heavy rebalance
'''
z y
/ \ / \
y T4 Right Rotate (z) x z
/ \ - - - - - - - - -> / \ / \
x T3 T1 T2 T3 T4
/ \
T1 T2
'''
def rotate_right(self, root):
left_temp = root.left # Keep track of left node
root.left = left_temp.right # Change node left
left_temp.right = root # Update left_temp right, now left_temp comes to root position
# Update heights of rotated nodes
# Order of updating height is important, height value comes form bottom root
# If root is changes and comes below left_temp first root should be updated
root.height = 1 + max(self.get_height(root.left), self.get_height(root.right))
left_temp.height = 1 + max(self.get_height(left_temp.left), self.get_height(left_temp.right))
return left_temp
# Rotate left for rigt-heavy rebalance
'''
z y
/ \ / \
T1 y Left Rotate(z) z x
/ \ - - - - - - - -> / \ / \
T2 x T1 T2 T3 T4
/ \
T3 T4
'''
def rotate_left(self, root):
right_temp = root.right
root.right = right_temp.left
right_temp.left = root
# Update heights of rotated nodes
# Order of updating height is important, height value comes form bottom root
# If root is changes and comes below right_temp first root should be updated
root.height = 1 + max(self.get_height(node.left), self.get_height(node.right))
right_temp.height = 1 + max(self.get_height(right_temp.left), self.get_height(right_temp.right))
return right_temp
# For right node left heavy rebalance
'''
z z x
/ \ / \ / \
y T4 Left Rotate (y) x T4 Right Rotate(z) y z
/ \ - - - - - - - - -> / \ - - - - - - - -> / \ / \
T1 x y T3 T1 T2 T3 T4
/ \ / \
T2 T3 T1 T2
'''
def rotate_left_right(self, root):
root.left = self.rotate_left(root.left)
return self.rotate_right(root)
# For left node right heavy rebalance
'''
z z x
/ \ / \ / \
T1 y Right Rotate (y) T1 x Left Rotate(z) z y
/ \ - - - - - - - - -> / \ - - - - - - - -> / \ / \
x T4 T2 y T1 T2 T3 T4
/ \ / \
T2 T3 T3 T4
'''
def rotate_right_left(self, root):
root.right = self.rotate_right(root.right)
return self.rotate_left(root)
def get_height(self, root):
if not root:
return -1
return root.height
def get_balance(self, root):
if not root:
return 0
return self.get_height(root.left) - self.get_height(root.right)
def preorder(self):
self.__preorder(self.root)
print()
def __preorder(self, root):
if root:
print(root.data, end=" ")
self.__preorder(root.left)
self.__preorder(root.right)
def level_order_traversal(self):
if self.root is None:
return
q = Queue()
q.put(self.root)
while(not q.empty()):
count = q.qsize()
while(count > 0):
node = q.get()
print(node.data, end=" ")
if node.left is not None:
q.put(node.left)
if node.right is not None:
q.put(node.right)
count -= 1
print()
if __name__ == "__main__":
avl = AVLTree()
avl.insert([5,4,3,2,1])
avl.preorder()
avl.level_order_traversal()
'''
Output
Preorder -> 4 2 1 3 5
Level Order Traversal -> 4
2 5
1 3
'''
#Comparison with tree
class Tree:
def __init__(self):
self.root = None
def insert(self, items):
if not items:
return None
for i in range(len(items)):
self.root = self.__insert(self.root, items[i])
def __insert(self, root, data):
if not root:
return Node(data)
elif data < root.data:
root.left = self.__insert(root.left, data)
else:
root.right = self.__insert(root.right, data)
return root
def level_order_traversal(self):
if self.root is None:
return
q = Queue()
q.put(self.root)
while(not q.empty()):
count = q.qsize()
while(count > 0):
node = q.get()
print(node.data, end=" ")
if node.left is not None:
q.put(node.left)
if node.right is not None:
q.put(node.right)
count -= 1
print()
if __name__ == "__main__":
tree = Tree()
tree.insert([5,4,3,2,1])
tree.level_order_traversal()
'''
Output
5
4
3
2
1
'''