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328 lines (278 loc) · 8.4 KB
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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
"""
import math
import random
class my_queue:
def __init__(self):
self.data = []
self.head = 0
self.tail = 0
def is_empty(self):
return self.head == self.tail
def push(self, data):
self.data.append(data)
self.tail = self.tail + 1
def pop(self):
ret = self.data[self.head]
self.head = self.head + 1
return ret
def count(self):
return self.tail - self.head
def print(self):
print(self.data)
print("**************")
print(self.data[self.head : self.tail])
class my_node:
def __init__(self, data):
self.data = data
self.left = None
self.right = None
self.height = 1
def get_data(self):
return self.data
def get_left(self):
return self.left
def get_right(self):
return self.right
def get_height(self):
return self.height
def set_data(self, data):
self.data = data
return
def set_left(self, node):
self.left = node
return
def set_right(self, node):
self.right = node
return
def set_height(self, height):
self.height = height
return
def get_height(node):
if node is None:
return 0
return node.get_height()
def my_max(a, b):
if a > b:
return a
return b
def right_rotation(node):
r"""
A B
/ \ / \
B C Bl A
/ \ --> / / \
Bl Br UB Br C
/
UB
UB = unbalanced node
"""
print("left rotation node:", node.get_data())
ret = node.get_left()
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)
return ret
def left_rotation(node):
"""
a mirror symmetry rotation of the left_rotation
"""
print("right rotation node:", node.get_data())
ret = node.get_right()
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)
return ret
def lr_rotation(node):
r"""
A A Br
/ \ / \ / \
B C LR Br C RR B A
/ \ --> / \ --> / / \
Bl Br B UB Bl UB C
\ /
UB Bl
RR = right_rotation LR = left_rotation
"""
node.set_left(left_rotation(node.get_left()))
return right_rotation(node)
def rl_rotation(node):
node.set_right(right_rotation(node.get_right()))
return left_rotation(node)
def insert_node(node, data):
if node is None:
return my_node(data)
if data < node.get_data():
node.set_left(insert_node(node.get_left(), data))
if (
get_height(node.get_left()) - get_height(node.get_right()) == 2
): # an unbalance detected
if (
data < node.get_left().get_data()
): # new node is the left child of the left child
node = right_rotation(node)
else:
node = lr_rotation(node)
else:
node.set_right(insert_node(node.get_right(), data))
if get_height(node.get_right()) - get_height(node.get_left()) == 2:
if data < node.get_right().get_data():
node = rl_rotation(node)
else:
node = left_rotation(node)
h1 = my_max(get_height(node.get_right()), get_height(node.get_left())) + 1
node.set_height(h1)
return node
def get_rightMost(root):
while root.get_right() is not None:
root = root.get_right()
return root.get_data()
def get_leftMost(root):
while root.get_left() is not None:
root = root.get_left()
return root.get_data()
def del_node(root, data):
if root.get_data() == data:
if root.get_left() is not None and root.get_right() is not None:
temp_data = get_leftMost(root.get_right())
root.set_data(temp_data)
root.set_right(del_node(root.get_right(), temp_data))
elif root.get_left() is not None:
root = root.get_left()
else:
root = root.get_right()
elif root.get_data() > data:
if root.get_left() is None:
print("No such data")
return root
else:
root.set_left(del_node(root.get_left(), data))
elif root.get_data() < data:
if root.get_right() is None:
return root
else:
root.set_right(del_node(root.get_right(), data))
if root is None:
return root
if get_height(root.get_right()) - get_height(root.get_left()) == 2:
if get_height(root.get_right().get_right()) > get_height(
root.get_right().get_left()
):
root = left_rotation(root)
else:
root = rl_rotation(root)
elif get_height(root.get_right()) - get_height(root.get_left()) == -2:
if get_height(root.get_left().get_left()) > get_height(
root.get_left().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
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):
self.root = None
def get_height(self):
# print("yyy")
return get_height(self.root)
def insert(self, data):
print("insert:" + str(data))
self.root = insert_node(self.root, data)
def del_node(self, data):
print("delete:" + str(data))
if self.root is None:
print("Tree is empty!")
return
self.root = del_node(self.root, data)
def __str__(self): # a level traversale, gives a more intuitive look on the tree
output = ""
q = my_queue()
q.push(self.root)
layer = self.get_height()
if layer == 0:
return output
cnt = 0
while not q.is_empty():
node = q.pop()
space = " " * int(math.pow(2, layer - 1))
output += space
if node is None:
output += "*"
q.push(None)
q.push(None)
else:
output += str(node.get_data())
q.push(node.get_left())
q.push(node.get_right())
output += space
cnt = cnt + 1
for i in range(100):
if cnt == math.pow(2, i) - 1:
layer = layer - 1
if layer == 0:
output += "\n*************************************"
return output
output += "\n"
break
output += "\n*************************************"
return output
def _test():
import doctest
doctest.testmod()
if __name__ == "__main__":
_test()
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))
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