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Update avl_tree.py (#2145)
* Update avl_tree.py it's true definition of AVL tree,change left and right rotation,and add avl_tree doctest * Update avl_tree.py * Update data_structures/binary_tree/avl_tree.py Co-authored-by: Christian Clauss <cclauss@me.com> * Update data_structures/binary_tree/avl_tree.py Co-authored-by: Christian Clauss <cclauss@me.com> * Update data_structures/binary_tree/avl_tree.py Co-authored-by: Christian Clauss <cclauss@me.com> * Update data_structures/binary_tree/avl_tree.py Co-authored-by: Christian Clauss <cclauss@me.com> * Update data_structures/binary_tree/avl_tree.py Co-authored-by: Christian Clauss <cclauss@me.com> * Update data_structures/binary_tree/avl_tree.py Co-authored-by: Christian Clauss <cclauss@me.com> * Update data_structures/binary_tree/avl_tree.py Co-authored-by: Christian Clauss <cclauss@me.com> * Update data_structures/binary_tree/avl_tree.py Co-authored-by: Christian Clauss <cclauss@me.com> * Update data_structures/binary_tree/avl_tree.py Co-authored-by: Christian Clauss <cclauss@me.com> * Update data_structures/binary_tree/avl_tree.py Co-authored-by: Christian Clauss <cclauss@me.com> * Update data_structures/binary_tree/avl_tree.py Co-authored-by: Christian Clauss <cclauss@me.com> * Update avl_tree.py update some function name and update doctest * Update avl_tree.py change some code format to fit flake8 review Co-authored-by: Christian Clauss <cclauss@me.com>
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Markgolzh
GitHub
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@ -1,6 +1,11 @@
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"""
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An auto-balanced binary tree!
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Implementation of an auto-balanced binary tree!
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For doctests run following command:
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python3 -m doctest -v avl_tree.py
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For testing run:
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python avl_tree.py
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"""
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import math
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import random
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@ -11,7 +16,7 @@ class my_queue:
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self.head = 0
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self.tail = 0
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def isEmpty(self):
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def is_empty(self):
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return self.head == self.tail
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def push(self, data):
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@ -39,39 +44,39 @@ class my_node:
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self.right = None
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self.height = 1
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def getdata(self):
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def get_data(self):
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return self.data
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def getleft(self):
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def get_left(self):
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return self.left
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def getright(self):
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def get_right(self):
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return self.right
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def getheight(self):
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def get_height(self):
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return self.height
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def setdata(self, data):
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def set_data(self, data):
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self.data = data
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return
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def setleft(self, node):
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def set_left(self, node):
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self.left = node
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return
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def setright(self, node):
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def set_right(self, node):
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self.right = node
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return
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def setheight(self, height):
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def set_height(self, height):
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self.height = height
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return
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def getheight(node):
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def get_height(node):
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if node is None:
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return 0
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return node.getheight()
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return node.get_height()
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def my_max(a, b):
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@ -80,7 +85,7 @@ def my_max(a, b):
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return b
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def leftrotation(node):
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def right_rotation(node):
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r"""
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A B
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/ \ / \
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@ -89,138 +94,171 @@ def leftrotation(node):
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Bl Br UB Br C
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/
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UB
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UB = unbalanced node
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"""
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print("left rotation node:", node.getdata())
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ret = node.getleft()
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node.setleft(ret.getright())
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ret.setright(node)
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h1 = my_max(getheight(node.getright()), getheight(node.getleft())) + 1
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node.setheight(h1)
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h2 = my_max(getheight(ret.getright()), getheight(ret.getleft())) + 1
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ret.setheight(h2)
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print("left rotation node:", node.get_data())
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ret = node.get_left()
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node.set_left(ret.get_right())
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ret.set_right(node)
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h1 = my_max(get_height(node.get_right()), get_height(node.get_left())) + 1
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node.set_height(h1)
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h2 = my_max(get_height(ret.get_right()), get_height(ret.get_left())) + 1
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ret.set_height(h2)
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return ret
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def rightrotation(node):
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def left_rotation(node):
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"""
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a mirror symmetry rotation of the leftrotation
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a mirror symmetry rotation of the left_rotation
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"""
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print("right rotation node:", node.getdata())
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ret = node.getright()
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node.setright(ret.getleft())
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ret.setleft(node)
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h1 = my_max(getheight(node.getright()), getheight(node.getleft())) + 1
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node.setheight(h1)
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h2 = my_max(getheight(ret.getright()), getheight(ret.getleft())) + 1
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ret.setheight(h2)
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print("right rotation node:", node.get_data())
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ret = node.get_right()
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node.set_right(ret.get_left())
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ret.set_left(node)
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h1 = my_max(get_height(node.get_right()), get_height(node.get_left())) + 1
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node.set_height(h1)
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h2 = my_max(get_height(ret.get_right()), get_height(ret.get_left())) + 1
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ret.set_height(h2)
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return ret
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def rlrotation(node):
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def lr_rotation(node):
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r"""
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A A Br
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/ \ / \ / \
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B C RR Br C LR B A
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B C LR Br C RR B A
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/ \ --> / \ --> / / \
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Bl Br B UB Bl UB C
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\ /
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UB Bl
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RR = rightrotation LR = leftrotation
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RR = right_rotation LR = left_rotation
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"""
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node.setleft(rightrotation(node.getleft()))
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return leftrotation(node)
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node.set_left(left_rotation(node.get_left()))
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return right_rotation(node)
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def lrrotation(node):
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node.setright(leftrotation(node.getright()))
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return rightrotation(node)
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def rl_rotation(node):
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node.set_right(right_rotation(node.get_right()))
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return left_rotation(node)
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def insert_node(node, data):
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if node is None:
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return my_node(data)
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if data < node.getdata():
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node.setleft(insert_node(node.getleft(), data))
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if data < node.get_data():
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node.set_left(insert_node(node.get_left(), data))
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if (
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getheight(node.getleft()) - getheight(node.getright()) == 2
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get_height(node.get_left()) - get_height(node.get_right()) == 2
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): # an unbalance detected
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if (
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data < node.getleft().getdata()
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data < node.get_left().get_data()
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): # new node is the left child of the left child
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node = leftrotation(node)
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node = right_rotation(node)
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else:
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node = rlrotation(node) # new node is the right child of the left child
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node = lr_rotation(node)
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else:
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node.setright(insert_node(node.getright(), data))
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if getheight(node.getright()) - getheight(node.getleft()) == 2:
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if data < node.getright().getdata():
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node = lrrotation(node)
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node.set_right(insert_node(node.get_right(), data))
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if get_height(node.get_right()) - get_height(node.get_left()) == 2:
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if data < node.get_right().get_data():
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node = rl_rotation(node)
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else:
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node = rightrotation(node)
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h1 = my_max(getheight(node.getright()), getheight(node.getleft())) + 1
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node.setheight(h1)
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node = left_rotation(node)
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h1 = my_max(get_height(node.get_right()), get_height(node.get_left())) + 1
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node.set_height(h1)
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return node
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def getRightMost(root):
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while root.getright() is not None:
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root = root.getright()
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return root.getdata()
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def get_rightMost(root):
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while root.get_right() is not None:
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root = root.get_right()
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return root.get_data()
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def getLeftMost(root):
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while root.getleft() is not None:
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root = root.getleft()
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return root.getdata()
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def get_leftMost(root):
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while root.get_left() is not None:
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root = root.get_left()
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return root.get_data()
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def del_node(root, data):
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if root.getdata() == data:
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if root.getleft() is not None and root.getright() is not None:
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temp_data = getLeftMost(root.getright())
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root.setdata(temp_data)
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root.setright(del_node(root.getright(), temp_data))
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elif root.getleft() is not None:
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root = root.getleft()
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if root.get_data() == data:
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if root.get_left() is not None and root.get_right() is not None:
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temp_data = get_leftMost(root.get_right())
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root.set_data(temp_data)
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root.set_right(del_node(root.get_right(), temp_data))
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elif root.get_left() is not None:
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root = root.get_left()
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else:
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root = root.getright()
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elif root.getdata() > data:
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if root.getleft() is None:
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root = root.get_right()
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elif root.get_data() > data:
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if root.get_left() is None:
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print("No such data")
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return root
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else:
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root.setleft(del_node(root.getleft(), data))
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elif root.getdata() < data:
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if root.getright() is None:
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root.set_left(del_node(root.get_left(), data))
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elif root.get_data() < data:
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if root.get_right() is None:
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return root
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else:
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root.setright(del_node(root.getright(), data))
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root.set_right(del_node(root.get_right(), data))
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if root is None:
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return root
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if getheight(root.getright()) - getheight(root.getleft()) == 2:
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if getheight(root.getright().getright()) > getheight(root.getright().getleft()):
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root = rightrotation(root)
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if get_height(root.get_right()) - get_height(root.get_left()) == 2:
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if get_height(root.get_right().get_right()) > \
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get_height(root.get_right().get_left()):
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root = left_rotation(root)
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else:
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root = lrrotation(root)
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elif getheight(root.getright()) - getheight(root.getleft()) == -2:
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if getheight(root.getleft().getleft()) > getheight(root.getleft().getright()):
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root = leftrotation(root)
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root = rl_rotation(root)
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elif get_height(root.get_right()) - get_height(root.get_left()) == -2:
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if get_height(root.get_left().get_left()) > \
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get_height(root.get_left().get_right()):
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root = right_rotation(root)
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else:
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root = rlrotation(root)
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height = my_max(getheight(root.getright()), getheight(root.getleft())) + 1
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root.setheight(height)
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root = lr_rotation(root)
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height = my_max(get_height(root.get_right()), get_height(root.get_left())) + 1
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root.set_height(height)
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return root
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class AVLtree:
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"""
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An AVL tree doctest
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Examples:
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>>> t = AVLtree()
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>>> t.insert(4)
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insert:4
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>>> print(str(t).replace(" \\n","\\n"))
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4
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*************************************
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>>> t.insert(2)
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insert:2
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>>> print(str(t).replace(" \\n","\\n").replace(" \\n","\\n"))
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4
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2 *
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*************************************
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>>> t.insert(3)
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insert:3
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right rotation node: 2
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left rotation node: 4
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>>> print(str(t).replace(" \\n","\\n").replace(" \\n","\\n"))
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3
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2 4
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*************************************
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>>> t.get_height()
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2
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>>> t.del_node(3)
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delete:3
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>>> print(str(t).replace(" \\n","\\n").replace(" \\n","\\n"))
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4
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2 *
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*************************************
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"""
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def __init__(self):
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self.root = None
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def getheight(self):
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def get_height(self):
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# print("yyy")
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return getheight(self.root)
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return get_height(self.root)
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def insert(self, data):
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print("insert:" + str(data))
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@ -233,56 +271,54 @@ class AVLtree:
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return
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self.root = del_node(self.root, data)
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def traversale(self): # a level traversale, gives a more intuitive look on the tree
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def __str__(self): # a level traversale, gives a more intuitive look on the tree
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output = ""
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q = my_queue()
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q.push(self.root)
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layer = self.getheight()
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layer = self.get_height()
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if layer == 0:
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return
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return output
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cnt = 0
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while not q.isEmpty():
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while not q.is_empty():
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node = q.pop()
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space = " " * int(math.pow(2, layer - 1))
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print(space, end="")
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output += space
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if node is None:
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print("*", end="")
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output += "*"
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q.push(None)
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q.push(None)
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else:
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print(node.getdata(), end="")
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q.push(node.getleft())
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q.push(node.getright())
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print(space, end="")
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output += str(node.get_data())
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q.push(node.get_left())
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q.push(node.get_right())
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output += space
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cnt = cnt + 1
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for i in range(100):
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if cnt == math.pow(2, i) - 1:
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layer = layer - 1
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if layer == 0:
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print()
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print("*************************************")
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return
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print()
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output += "\n*************************************"
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return output
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output += "\n"
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break
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print()
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print("*************************************")
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return
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output += "\n*************************************"
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return output
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def test(self):
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getheight(None)
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print("****")
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self.getheight()
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def _test():
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import doctest
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doctest.testmod()
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if __name__ == "__main__":
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_test()
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t = AVLtree()
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t.traversale()
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lst = list(range(10))
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random.shuffle(lst)
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for i in lst:
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t.insert(i)
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t.traversale()
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print(str(t))
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random.shuffle(lst)
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for i in lst:
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t.del_node(i)
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t.traversale()
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print(str(t))
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