红黑树是怎样通过代码实现的
时间: 2023-10-13 17:12:56 浏览: 85
红黑树是一种自平衡二叉查找树,其通过节点的颜色来维护平衡性。具体实现时,可以定义节点颜色为红色或黑色,然后通过一系列旋转和着色操作来保持树的平衡。
红黑树的具体实现可以采用面向对象的方式,定义一个节点类,节点包含键值、颜色、左右子节点等属性。然后定义一个红黑树类,包含插入、删除、查找等操作。在插入和删除操作中,需要根据红黑树的性质对节点进行旋转和着色,以保证树的平衡性。
下面是一个简单的红黑树实现的示例代码(使用Python语言):
```python
class Node:
def __init__(self, val):
self.val = val
self.color = 'red'
self.left = None
self.right = None
self.parent = None
class RedBlackTree:
def __init__(self):
self.root = None
def insert(self, val):
node = Node(val)
if self.root is None:
self.root = node
self.root.color = 'black'
else:
curr = self.root
parent = None
while curr is not None:
parent = curr
if node.val < curr.val:
curr = curr.left
else:
curr = curr.right
node.parent = parent
if node.val < parent.val:
parent.left = node
else:
parent.right = node
self._fix_insert(node)
def _fix_insert(self, node):
while node.parent is not None and node.parent.color == 'red':
if node.parent == node.parent.parent.left:
uncle = node.parent.parent.right
if uncle is not None and uncle.color == 'red':
node.parent.color = 'black'
uncle.color = 'black'
node.parent.parent.color = 'red'
node = node.parent.parent
else:
if node == node.parent.right:
node = node.parent
self._rotate_left(node)
node.parent.color = 'black'
node.parent.parent.color = 'red'
self._rotate_right(node.parent.parent)
else:
uncle = node.parent.parent.left
if uncle is not None and uncle.color == 'red':
node.parent.color = 'black'
uncle.color = 'black'
node.parent.parent.color = 'red'
node = node.parent.parent
else:
if node == node.parent.left:
node = node.parent
self._rotate_right(node)
node.parent.color = 'black'
node.parent.parent.color = 'red'
self._rotate_left(node.parent.parent)
self.root.color = 'black'
def _rotate_left(self, node):
temp = node.right
node.right = temp.left
if temp.left is not None:
temp.left.parent = node
temp.parent = node.parent
if node.parent is None:
self.root = temp
elif node == node.parent.left:
node.parent.left = temp
else:
node.parent.right = temp
temp.left = node
node.parent = temp
def _rotate_right(self, node):
temp = node.left
node.left = temp.right
if temp.right is not None:
temp.right.parent = node
temp.parent = node.parent
if node.parent is None:
self.root = temp
elif node == node.parent.right:
node.parent.right = temp
else:
node.parent.left = temp
temp.right = node
node.parent = temp
```
这段代码实现了红黑树的插入操作,其中`_fix_insert`函数实现了对节点的旋转和着色操作,以保证树的平衡性。
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