Python中的树形数据结构: AVL-T树
AVL树是一种自平衡二叉查找树。它的基本思想是对于每个节点，其左右子树的高度差不超过1，通过旋转操作来保持树的平衡。
T树是一种类似于B树的数据结构，它的每个节点可以有多个子节点，且节点存储的数据是有序的。T树中，每个节点保存了一组(key, value)键值对，其中key是用于比较节点大小的标准。
将两种树结合起来，就得到了AVL-T树，是一种自平衡的多叉查找树，既能够支持快速插入和删除操作，又能够保持数据有序。它的主要优点是在执行插入、删除和查找操作时，时间复杂度为O(log n)。
下面是AVL-T树的Python实现代码：
class AVLTreeNode: def __init__(self, key=None, value=None): self.key = key self.value = value self.height = 1 self.left = None self.right = None class AVLTree: def __init__(self): self.root = None def insert(self, key, value): self.root = self._insert(self.root, key, value) def _insert(self, node, key, value): if node is None: return AVLTreeNode(key, value) elif key < node.key: node.left = self._insert(node.left, key, value) else: node.right = self._insert(node.right, key, value) node.height = 1 + max(self.get_height(node.left), self.get_height(node.right)) balance_factor = self.get_balance_factor(node) if balance_factor > 1 and key < node.left.key: return self.rotate_right(node) if balance_factor < -1 and key > node.right.key: return self.rotate_left(node) if balance_factor > 1 and key > node.left.key: node.left = self.rotate_left(node.left) return self.rotate_right(node) if balance_factor < -1 and key < node.right.key: node.right = self.rotate_right(node.right) return self.rotate_left(node) return node def delete(self, key): self.root = self._delete(self.root, key) def _delete(self, node, key): if node is None: return node elif key < node.key: node.left = self._delete(node.left, key) elif key > node.key: node.right = self._delete(node.right, key) else: if node.left is None: temp = node.right node = None return temp elif node.right is None: temp = node.left node = None return temp temp = self.get_min_value_node(node.right) node.key = temp.key node.value = temp.value node.right = self._delete(node.right, temp.key) if node is None: return node node.height = 1 + max(self.get_height(node.left), self.get_height(node.right)) balance_factor = self.get_balance_factor(node) if balance_factor > 1 and self.get_balance_factor(node.left) >= 0: return self.rotate_right(node) if balance_factor < -1 and self.get_balance_factor(node.right) <= 0: return self.rotate_left(node) if balance_factor > 1 and self.get_balance_factor(node.left) < 0: node.left = self.rotate_left(node.left) return self.rotate_right(node) if balance_factor < -1 and self.get_balance_factor(node.right) > 0: node.right = self.rotate_right(node.right) return self.rotate_left(node) return node def get_min_value_node(self, node): if node is None or node.left is None: return node return self.get_min_value_node(node.left) def get_height(self, node): if node is None: return 0 return node.height def get_balance_factor(self, node): if node is None: return 0 return self.get_height(node.left) - self.get_height(node.right) def rotate_left(self, node): new_root = node.right node.right = new_root.left new_root.left = node node.height = 1 + max(self.get_height(node.left), self.get_height(node.right)) new_root.height = 1 + max(self.get_height(new_root.left), self.get_height(new_root.right)) return new_root def rotate_right(self, node): new_root = node.left node.left = new_root.right new_root.right = node node.height = 1 + max(self.get_height(node.left), self.get_height(node.right)) new_root.height = 1 + max(self.get_height(new_root.left), self.get_height(new_root.right)) return new_root
使用范例：
avl_tree = AVLTree() avl_tree.insert("pidancode.com", "1") avl_tree.insert("皮蛋编程", "2") avl_tree.insert("google.com", "3") avl_tree.insert("apple.com", "4") avl_tree.insert("microsoft.com", "5") avl_tree.delete("google.com") print(avl_tree.root.key) # "pidancode.com" print(avl_tree.root.left.key) # "apple.com" print(avl_tree.root.right.key) # "microsoft.com"
相关文章