Title

Python实现二叉查找树

二叉查找树

• 所有 key 小于 V 的都被存储在 V 的左子树
• 所有 key 大于 V 的都存储在 V 的右子树

BST 的节点

class BSTNode(object):
    def __init__(self, key, value, left=None, right=None):
        self.key, self.value, self.left, self.right = key, value, left, right

二叉树查找

如何查找一个指定的节点呢，根据定义我们知道每个内部节点左子树的 key 都比它小，右子树的 key 都比它大，所以 对于带查找的节点 search_key，从根节点开始，如果 search_key 大于当前 key，就去右子树查找，否则去左子树查找

NODE_LIST = [
    {'key': 60, 'left': 12, 'right': 90, 'is_root': True},
    {'key': 12, 'left': 4, 'right': 41, 'is_root': False},
    {'key': 4, 'left': 1, 'right': None, 'is_root': False},
    {'key': 1, 'left': None, 'right': None, 'is_root': False},
    {'key': 41, 'left': 29, 'right': None, 'is_root': False},
    {'key': 29, 'left': 23, 'right': 37, 'is_root': False},
    {'key': 23, 'left': None, 'right': None, 'is_root': False},
    {'key': 37, 'left': None, 'right': None, 'is_root': False},
    {'key': 90, 'left': 71, 'right': 100, 'is_root': False},
    {'key': 71, 'left': None, 'right': 84, 'is_root': False},
    {'key': 100, 'left': None, 'right': None, 'is_root': False},
    {'key': 84, 'left': None, 'right': None, 'is_root': False},
]


class BSTNode(object):
    def __init__(self, key, value, left=None, right=None):
        self.key, self.value, self.left, self.right = key, value, left, right


class BST(object):
    def __init__(self, root=None):
        self.root = root

    @classmethod
    def build_from(cls, node_list):
        cls.size = 0
        key_to_node_dict = {}
        for node_dict in node_list:
            key = node_dict['key']
            key_to_node_dict[key] = BSTNode(key, value=key)   # 这里值和key一样的

        for node_dict in node_list:
            key = node_dict['key']
            node = key_to_node_dict[key]
            if node_dict['is_root']:
                root = node
            node.left = key_to_node_dict.get(node_dict['left'])
            node.right = key_to_node_dict.get(node_dict['right'])
            cls.size += 1
        return cls(root)

    def _bst_search(self, subtree, key):
        """
        subtree.key小于key则去右子树找  因为 左子树<subtree.key<右子树
        subtree.key大于key则去左子树找  因为 左子树<subtree.key<右子树
        :param subtree:
        :param key:
        :return:
        """
        if subtree is None:
            return None
        elif subtree.key < key:
            self._bst_search(subtree.right, key)
        elif subtree.key > key:
            self._bst_search(subtree.left, key)
        else:
            return subtree

    def get(self, key, default=None):
        """
        查找树
        :param key:
        :param default:
        :return:
        """
        node = self._bst_search(self.root, key)
        if node is None:
            return default
        else:
            return node.value

    def _bst_min_node(self, subtree):
        """
        查找最小值的树
        :param subtree:
        :return:
        """
        if subtree is None:
            return None
        elif subtree.left is None:
            # 找到左子树的头
            return subtree
        else:
            return self._bst_min_node(subtree.left)

    def bst_min(self):
        """
        获取最小树的value
        :return:
        """
        node = self._bst_min_node(self.root)
        if node is None:
            return None
        else:
            return node.value

    def _bst_max_node(self, subtree):
        """
        查找最大值的树
        :param subtree:
        :return:
        """
        if subtree is None:
            return None
        elif subtree.right is None:
            # 找到右子树的头
            return subtree
        else:
            return self._bst_min_node(subtree.right)

    def bst_max(self):
        """
        获取最大树的value
        :return:
        """
        node = self._bst_max_node(self.root)
        if node is None:
            return None
        else:
            return node.value

    def _bst_insert(self, subtree, key, value):
        """
        二叉查找树插入
        :param subtree:
        :param key:
        :param value:
        :return:
        """
        # 插入的节点一定是根节点，包括 root 为空的情况
        if subtree is None:
            subtree = BSTNode(key, value)
        elif subtree.key > key:
            subtree.left = self._bst_insert(subtree.left, key, value)
        elif subtree.key < key:
            subtree.right = self._bst_insert(subtree.right, key, value)
        return subtree

    def add(self, key, value):
        # 先去查一下看节点是否已存在
        node = self._bst_search(self.root, key)
        if node is not None:
            # 更新已经存在的 key
            node.value = value
            return False
        else:
            self.root = self._bst_insert(self.root, key, value)
            self.size += 1

    def _bst_remove(self, subtree, key):
        """
        删除并返回根节点
        :param subtree:
        :param key:
        :return:
        """
        if subtree is None:
            return None
        elif subtree.key > key:
            subtree.right = self._bst_remove(subtree.right, key)
            return subtree
        elif subtree.key < key:
            subtree.left = self._bst_remove(subtree.left, key)
            return subtree
        else:
            # 找到了需要删除的节点
            # 要删除的节点是叶节点 返回 None 把其父亲指向它的指针置为 None
            if subtree.left is None and subtree.right is None:
                return None
            # 要删除的节点有一个孩子
            elif subtree.left is None or subtree.right is None:
                # 返回它的孩子并让它的父亲指过去
                if subtree.left is not None:
                    return subtree.left
                else:
                    return subtree.right
            else:
                # 有两个孩子，寻找后继节点替换，并从待删节点的右子树中删除后继节点
                # 后继节点是待删除节点的右孩子之后的最小节点
                # 中(根)序得到的是一个排列好的列表 后继节点在待删除节点的后边
                successor_node = self._bst_min_node(subtree.right)
                # 用后继节点替换待删除节点即可保持二叉查找树的特性 左<根<右
                subtree.key, subtree.value = successor_node.key, successor_node.value
                # 从待删除节点的右子树中删除后继节点，并更新其删除后继节点后的右子树
                subtree.right = self._bst_remove(subtree.right, successor_node.key)
                return subtree

    def remove(self, key):
        assert key in self
        self.size -= 1
        return self._bst_remove(self.root, key)