Python TreeNode如何實(shí)現(xiàn)樹的AVL樹

小樊
83
2024-08-17 16:30:42

在Python中實(shí)現(xiàn)AVL樹，需要定義一個(gè)TreeNode類來(lái)表示樹的節(jié)點(diǎn)，然后定義一個(gè)AVLTree類來(lái)實(shí)現(xiàn)AVL樹的操作。

class TreeNode:
    def __init__(self, key):
        self.key = key
        self.left = None
        self.right = None
        self.height = 1

class AVLTree:
    def __init__(self):
        self.root = None

    def insert(self, key):
        self.root = self._insert(self.root, key)

    def _insert(self, node, key):
        if not node:
            return TreeNode(key)
        
        if key < node.key:
            node.left = self._insert(node.left, key)
        else:
            node.right = self._insert(node.right, key)

        node.height = 1 + max(self._get_height(node.left), self._get_height(node.right))
        
        balance = self._get_balance(node)

        # 左旋
        if balance > 1 and key < node.left.key:
            return self._rotate_right(node)
        # 右旋
        if balance < -1 and key > node.right.key:
            return self._rotate_left(node)
        # 左右旋
        if balance > 1 and key > node.left.key:
            node.left = self._rotate_left(node.left)
            return self._rotate_right(node)
        # 右左旋
        if balance < -1 and key < node.right.key:
            node.right = self._rotate_right(node.right)
            return self._rotate_left(node)

        return node

    def _get_height(self, node):
        if not node:
            return 0
        return node.height

    def _get_balance(self, node):
        if not node:
            return 0
        return self._get_height(node.left) - self._get_height(node.right)

    def _rotate_left(self, z):
        y = z.right
        T2 = y.left

        y.left = z
        z.right = T2

        z.height = 1 + max(self._get_height(z.left), self._get_height(z.right))
        y.height = 1 + max(self._get_height(y.left), self._get_height(y.right))

        return y

    def _rotate_right(self, z):
        y = z.left
        T3 = y.right

        y.right = z
        z.left = T3

        z.height = 1 + max(self._get_height(z.left), self._get_height(z.right))
        y.height = 1 + max(self._get_height(y.left), self._get_height(y.right))

        return y

以上是AVL樹的Python實(shí)現(xiàn)代碼，包括了插入節(jié)點(diǎn)和旋轉(zhuǎn)操作。可以根據(jù)需要進(jìn)一步實(shí)現(xiàn)刪除節(jié)點(diǎn)、查找節(jié)點(diǎn)等操作。

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