Python/data_structures/binary_tree/avl_tree.py

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"""
Implementation of an auto-balanced binary tree!
For doctests run following command:
python3 -m doctest -v avl_tree.py
For testing run:
python avl_tree.py
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"""
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import math
import random
from typing import Any, List, Optional
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class my_queue:
def __init__(self) -> None:
self.data: List[Any] = []
self.head: int = 0
self.tail: int = 0
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def is_empty(self) -> bool:
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return self.head == self.tail
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def push(self, data: Any) -> None:
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self.data.append(data)
self.tail = self.tail + 1
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def pop(self) -> Any:
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ret = self.data[self.head]
self.head = self.head + 1
return ret
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def count(self) -> int:
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return self.tail - self.head
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def print(self) -> None:
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print(self.data)
print("**************")
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print(self.data[self.head : self.tail])
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class my_node:
def __init__(self, data: Any) -> None:
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self.data = data
self.left: Optional[my_node] = None
self.right: Optional[my_node] = None
self.height: int = 1
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def get_data(self) -> Any:
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return self.data
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def get_left(self) -> Optional["my_node"]:
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return self.left
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def get_right(self) -> Optional["my_node"]:
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return self.right
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def get_height(self) -> int:
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return self.height
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def set_data(self, data: Any) -> None:
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self.data = data
return
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def set_left(self, node: Optional["my_node"]) -> None:
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self.left = node
return
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def set_right(self, node: Optional["my_node"]) -> None:
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self.right = node
return
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def set_height(self, height: int) -> None:
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self.height = height
return
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def get_height(node: Optional["my_node"]) -> int:
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if node is None:
return 0
return node.get_height()
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def my_max(a: int, b: int) -> int:
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if a > b:
return a
return b
def right_rotation(node: my_node) -> my_node:
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r"""
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A B
/ \ / \
B C Bl A
/ \ --> / / \
Bl Br UB Br C
/
UB
UB = unbalanced node
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"""
print("left rotation node:", node.get_data())
ret = node.get_left()
assert ret is not None
node.set_left(ret.get_right())
ret.set_right(node)
h1 = my_max(get_height(node.get_right()), get_height(node.get_left())) + 1
node.set_height(h1)
h2 = my_max(get_height(ret.get_right()), get_height(ret.get_left())) + 1
ret.set_height(h2)
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return ret
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def left_rotation(node: my_node) -> my_node:
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"""
a mirror symmetry rotation of the left_rotation
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"""
print("right rotation node:", node.get_data())
ret = node.get_right()
assert ret is not None
node.set_right(ret.get_left())
ret.set_left(node)
h1 = my_max(get_height(node.get_right()), get_height(node.get_left())) + 1
node.set_height(h1)
h2 = my_max(get_height(ret.get_right()), get_height(ret.get_left())) + 1
ret.set_height(h2)
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return ret
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def lr_rotation(node: my_node) -> my_node:
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r"""
A A Br
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/ \ / \ / \
B C LR Br C RR B A
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/ \ --> / \ --> / / \
Bl Br B UB Bl UB C
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\ /
UB Bl
RR = right_rotation LR = left_rotation
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"""
left_child = node.get_left()
assert left_child is not None
node.set_left(left_rotation(left_child))
return right_rotation(node)
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def rl_rotation(node: my_node) -> my_node:
right_child = node.get_right()
assert right_child is not None
node.set_right(right_rotation(right_child))
return left_rotation(node)
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def insert_node(node: Optional["my_node"], data: Any) -> Optional["my_node"]:
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if node is None:
return my_node(data)
if data < node.get_data():
node.set_left(insert_node(node.get_left(), data))
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if (
get_height(node.get_left()) - get_height(node.get_right()) == 2
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): # an unbalance detected
left_child = node.get_left()
assert left_child is not None
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if (
data < left_child.get_data()
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): # new node is the left child of the left child
node = right_rotation(node)
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else:
node = lr_rotation(node)
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else:
node.set_right(insert_node(node.get_right(), data))
if get_height(node.get_right()) - get_height(node.get_left()) == 2:
right_child = node.get_right()
assert right_child is not None
if data < right_child.get_data():
node = rl_rotation(node)
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else:
node = left_rotation(node)
h1 = my_max(get_height(node.get_right()), get_height(node.get_left())) + 1
node.set_height(h1)
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return node
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def get_rightMost(root: my_node) -> Any:
while True:
right_child = root.get_right()
if right_child is None:
break
root = right_child
return root.get_data()
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def get_leftMost(root: my_node) -> Any:
while True:
left_child = root.get_left()
if left_child is None:
break
root = left_child
return root.get_data()
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def del_node(root: my_node, data: Any) -> Optional["my_node"]:
left_child = root.get_left()
right_child = root.get_right()
if root.get_data() == data:
if left_child is not None and right_child is not None:
temp_data = get_leftMost(right_child)
root.set_data(temp_data)
root.set_right(del_node(right_child, temp_data))
elif left_child is not None:
root = left_child
elif right_child is not None:
root = right_child
else:
return None
elif root.get_data() > data:
if left_child is None:
print("No such data")
return root
else:
root.set_left(del_node(left_child, data))
else: # root.get_data() < data
if right_child is None:
return root
else:
root.set_right(del_node(right_child, data))
if get_height(right_child) - get_height(left_child) == 2:
assert right_child is not None
if get_height(right_child.get_right()) > get_height(right_child.get_left()):
root = left_rotation(root)
else:
root = rl_rotation(root)
elif get_height(right_child) - get_height(left_child) == -2:
assert left_child is not None
if get_height(left_child.get_left()) > get_height(left_child.get_right()):
root = right_rotation(root)
else:
root = lr_rotation(root)
height = my_max(get_height(root.get_right()), get_height(root.get_left())) + 1
root.set_height(height)
return root
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class AVLtree:
"""
An AVL tree doctest
Examples:
>>> t = AVLtree()
>>> t.insert(4)
insert:4
>>> print(str(t).replace(" \\n","\\n"))
4
*************************************
>>> t.insert(2)
insert:2
>>> print(str(t).replace(" \\n","\\n").replace(" \\n","\\n"))
4
2 *
*************************************
>>> t.insert(3)
insert:3
right rotation node: 2
left rotation node: 4
>>> print(str(t).replace(" \\n","\\n").replace(" \\n","\\n"))
3
2 4
*************************************
>>> t.get_height()
2
>>> t.del_node(3)
delete:3
>>> print(str(t).replace(" \\n","\\n").replace(" \\n","\\n"))
4
2 *
*************************************
"""
def __init__(self) -> None:
self.root: Optional[my_node] = None
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def get_height(self) -> int:
return get_height(self.root)
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def insert(self, data: Any) -> None:
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print("insert:" + str(data))
self.root = insert_node(self.root, data)
def del_node(self, data: Any) -> None:
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print("delete:" + str(data))
if self.root is None:
print("Tree is empty!")
return
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self.root = del_node(self.root, data)
def __str__(
self,
) -> str: # a level traversale, gives a more intuitive look on the tree
output = ""
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q = my_queue()
q.push(self.root)
layer = self.get_height()
if layer == 0:
return output
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cnt = 0
while not q.is_empty():
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node = q.pop()
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space = " " * int(math.pow(2, layer - 1))
output += space
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if node is None:
output += "*"
q.push(None)
q.push(None)
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else:
output += str(node.get_data())
q.push(node.get_left())
q.push(node.get_right())
output += space
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cnt = cnt + 1
for i in range(100):
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if cnt == math.pow(2, i) - 1:
layer = layer - 1
if layer == 0:
output += "\n*************************************"
return output
output += "\n"
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break
output += "\n*************************************"
return output
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def _test() -> None:
import doctest
doctest.testmod()
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if __name__ == "__main__":
_test()
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t = AVLtree()
lst = list(range(10))
random.shuffle(lst)
for i in lst:
t.insert(i)
print(str(t))
random.shuffle(lst)
for i in lst:
t.del_node(i)
print(str(t))