我正在把我的二进制搜索树变成一个AVL树，但我偶然发现了这个问题，我相信平衡因子是正确的，但似乎没有旋转发生，在树本身。如果有人能指出我的错误，和不准确的地方，那将是可爱的!
我把它做成了这样，当每个节点被做成时，每个节点的高度从parent_node + 1开始计算。
class Node:
def __init__(self, value):
"""
Every Node has a value, and a height based on how far it is from the root node
"""
self.value = value
self.left = None
self.right = None
self.height = 1
class AVLTree:
def __init__(self, List=None):
self.root = None
if List:
for item in List:
self.insert(item)
def inorder(self, current_node):
if current_node:
self.inorder(current_node.left)
print(current_node.value, end=' ')
self.inorder(current_node.right)
def get_height(self, node):
"""
gets the value of height
which is how far the node is from the root node, given that the root node has a height of 1, and its children has 2
Ex:
O Height = 1
/ \
O O Height = 2
/ \ / \
O O O O Height = 3
"""
if node is None:
return 1
return node.height
def update_heights(self, current_node, depth):
"""
"""
if current_node is None:
return
current_node.height = depth
self.update_heights(current_node.left, 1+depth)
self.update_heights(current_node.right, 1+depth)
def get_balance_factor(self, node):
"""
Balance_factor is the difference between the heights of the two child node of the node
Rebalancing occurs when the balance_factor is greater than a difference of 1 (or) less than a difference of -1
usage: balance_factor = get_balance_factor(node)
which is left_child_height - right_child_height
If balanced, balance_factor = -1/0/1:
O O O O
/ \ / \ / \ / \
O O O O O O O O
/ \ / \
O O O O
If balance_factor > 1:
O <--- Node
/ \
O O Height = 2
/ \
O O Height = 3
/ \
O O Height = 4
Difference of L and R = 2 (4-2)
If balance_factor < 1:
O <--- Node
/ \
O O Height = 2
/ \
O O Height = 3
/ \
O O Height = 4
Difference of L and R = -2 (2-4)
"""
if node is None:
return
return self.get_height(node.left) - self.get_height(node.right)
def rotate_right(self, y):
"""
Rotates right
Ex:
y x
/ \ Right Rotation / \
x T3 - - - - - - - > T1 y
/ \ / \
T1 T2 T2 T3
so only 2 things changed
the left child of y became T2
and the right child of x became y
"""
# Rotation
x = y.left
T2 = x.right
x.right = y
y.left = T2
# Updating Heights
self.update_heights(x, y.height)
def rotate_left(self, x):
"""
Rotates left
Ex:
y x
/ \ / \
x T3 T1 y
/ \ < - - - - - - - / \
T1 T2 Left Rotation T2 T3
"""
# Rotation
y = x.right
T2 = y.left
y.left = x
x.right = T2
# Updating Heights
self.update_heights(y, x.height)
def insert(self, value):
NewNode = Node(value)
current_node = self.root
# Traversing through the Tree till we find the right place to put the value
if current_node is None:
self.root = NewNode
else:
while True:
if value < current_node.value:
#Left
if not current_node.left:
current_node.left = NewNode
break
current_node = current_node.left
else:
#Right
if not current_node.right:
current_node.right = NewNode
break
current_node = current_node.right
# Giving the new node a value of height based on how far he is from root node
NewNode.height = 1 + current_node.height
# Getting the balance factor, which shows if the tree is balanced or not after insertion, by the difference of the heights between the left and right children of the node
balance_factor = self.get_balance_factor(current_node)
print(balance_factor)
# Checks if the node is unbalanced, and if it is, perform one of the 4 cases
# Case 1: Left Left
if balance_factor > 1 and value < current_node.left.value:
self.rotate_right(current_node)
# Case 2: Right Right
if balance_factor < -1 and value > current_node.right.value:
self.rotate_left(current_node)
# Case 3: Left Right
if balance_factor > 1 and value > current_node.left.value:
self.rotate_left(current_node.left)
self.rotate_right(current_node)
# Case 4: Right Left
if balance_factor < -1 and value < current_node.right.value:
self.rotate_right(current_node.right)
self.rotate_left(current_node)
这里有一个解决方案。
我改变了 get_height 到 get_depth因为高度的使用是在检查两个节点之间的深度差异，所以在上下文中使用它是错误的。
因此，我增加了一个新的递归函数。max_depth.检查一个节点的所有子节点，并返回节点的深度。
我还把平衡改成了一个递归函数，它一直到父节点，直到到达根节点。
我为一个指定父节点的 treenode 增加了一个额外的属性，这样在旋转过程中你就可以在 x 和 y 之间进行改变。
class Node:
def __init__(self, value, parent=None):
"""
Every Node has a value, and a height based on how far it is from the root node
"""
self.value = value
self.parent = parent
self.left = None
self.right = None
self.height = 1
class AVLTree:
def __init__(self, List=None):
self.root = None
if List:
for item in List:
self.insert(item)
def inorder(self, current_node):
if current_node:
self.inorder(current_node.left)
print(current_node.value, end=' ')
self.inorder(current_node.right)
def max_depth(self, root):
# Null node has 0 depth.
if root == None:
return 0
# Get the depth of the left and right subtree
# using recursion.
leftDepth = self.max_depth(root.left)
rightDepth = self.max_depth(root.right)
# Choose the larger one and add the root to it.
if leftDepth > rightDepth:
return leftDepth + 1
else:
return rightDepth + 1
def get_depth(self, node, parent_node):
"""
gets the value of height
which is how far the node is from the root node, given that the root node has a height of 1, and its children has 2
Ex:
O Height = 1
/ \
O O Height = 2
/ \ / \
O O O O Height = 3
"""
if node is None:
return 0
return self.max_depth(node)
def update_heights(self, current_node, depth):
"""
"""
if current_node is None:
return
current_node.height = depth
self.update_heights(current_node.left, 1+depth)
self.update_heights(current_node.right, 1+depth)
def get_balance_factor(self, node):
"""
Balance_factor is the difference between the heights of the two child node of the node
Rebalancing occurs when the balance_factor is greater than a difference of 1 (or) less than a difference of -1
usage: balance_factor = get_balance_factor(node)
which is left_child_height - right_child_height
If balanced, balance_factor = -1/0/1:
O O O O
/ \ / \ / \ / \
O O O O O O O O
/ \ / \
O O O O
If balance_factor > 1:
O <--- Node
/ \
O O Height = 2
/ \
O O Height = 3
/ \
O O Height = 4
Difference of L and R = 2 (4-2)
If balance_factor < 1:
O <--- Node
/ \
O O Height = 2
/ \
O O Height = 3
/ \
O O Height = 4
Difference of L and R = -2 (2-4)
"""
if node is None:
return
return self.get_depth(node.left, node) - self.get_depth(node.right, node)
def rotate_right(self, y):
"""
Rotates right
Ex:
y x
/ \ Right Rotation / \
x T3 - - - - - - - > T1 y
/ \ / \
T1 T2 T2 T3
so only 2 things changed
the left child of y became T2
and the right child of x became y
"""
# Rotation
parent = y.parent
x = y.left
T2 = x.right
x.right = y
y.left = T2
if T2:
T2.parent = y
x.parent = parent
if parent is None:
self.root = x
if parent.left == y:
parent.left = x
elif y.parent.right == y:
parent.right = x
# Updating Heights
self.update_heights(x, y.height)
def rotate_left(self, x):
"""
Rotates left
Ex:
y x
/ \ / \
x T3 T1 y
/ \ < - - - - - - - / \
T1 T2 Left Rotation T2 T3
"""
# Rotation
parent = x.parent
y = x.right
T2 = y.left
y.left = x
x.right = T2
if T2:
T2.parent = x
y.parent = parent
if parent is None:
self.root = y
elif parent.left == x:
parent.left = y
elif y.parent.right == x:
parent.right = y
# Updating Heights
self.update_heights(y, x.height)
def recursive_balancing(self, current_node, value):
if current_node is None:
return
# Getting the balance factor, which shows if the tree is balanced or not after insertion, by the difference of the heights between the left and right children of the node
balance_factor = self.get_balance_factor(current_node)
print(balance_factor)
# Checks if the node is unbalanced, and if it is, perform one of the 4 cases
# Case 1: Left Left
if balance_factor > 1 and current_node.left:
if value < current_node.left.value:
self.rotate_right(current_node)
# Case 2: Right Right
if balance_factor < -1 and current_node.right:
if value > current_node.right.value:
self.rotate_left(current_node)
# Case 3: Left Right
if balance_factor > 1 and current_node.left:
if value > current_node.left.value:
self.rotate_left(current_node.left)
self.rotate_right(current_node)
# Case 4: Right Left
if balance_factor < -1 and current_node.right:
if value < current_node.right.value:
self.rotate_right(current_node.right)
self.rotate_left(current_node)
self.recursive_balancing(current_node.parent, value)
def insert(self, value):
NewNode = Node(value)
current_node = self.root
# Traversing through the Tree till we find the right place to put the value
if current_node is None:
self.root = NewNode
else:
while True:
if value < current_node.value:
NewNode.parent = current_node
#Left
if not current_node.left:
current_node.left = NewNode
break
NewNode.parent = current_node
current_node = current_node.left
else:
NewNode.parent = current_node
#Right
if not current_node.right:
current_node.right = NewNode
break
NewNode.parent = current_node
current_node = current_node.right
# Giving the new node a value of height based on how far he is from root node
NewNode.height = 1 + current_node.height
# Recursive balancing
self.recursive_balancing(current_node, value)