小鱼要学数据结构与算法（基于python)—Day20二叉查找树、实现及算法分析

二叉查找树

一、知识概览

本章主要讲二叉查找树、实现及算法分析

1.1 二叉查找树操作及性质

下面是主要操作及BST的性质：

1.2 二叉查找树实现及算法分析

算法复杂度和key的分布有关，性能O(log n)，极端情况O(n):

二、代码实现

本节以代码实现BST数据结构为主：

2.1 BST类及其方法

# 二叉搜索树的实现
class BinarySearchTree:def __init__(self):self.root = Noneself.size = 0def length(self):return self.sizedef __len__(self):return self.sizedef __iter__(self):return self.root.__iter__()def put(self, key, val):'''插入key构造BST,先看BST是否为空，如果一个节点都没有，那么key成为根节点root否则，就调用一个递归函数_put()来放置key'''if self.root:self._put(key, val, self.root)else:self.root = TreeNode(key, val)self.size = self.size + 1def _put(self, key, val, currentNode):'''如果key比currentNode小,那么_put到左子树，如果没有左子树，那么key就成为左子节点，反之亦然'''if key < currentNode.key:if currentNode.hasLeftChild():self._put(key, val, currentNode.leftChild)else:currentNode.leftChild = TreeNode(key, val, parent=currentNode)else:if currentNode.hasRightChild():self._put(key, val, currentNode.rightChild)else:currentNode.rightChild = TreeNode(key, val, parent=currentNode)def __setitem__(self, key, value):'''特殊方法实现索引赋值'''self.put(key, value)def get(self, key):'''在树中找到key所在节点取到payload'''if self.root:  # 是否为空树res = self._get(key, self.root)  # 找到节点if res:return res.payloadelse:return Noneelse:return Nonedef _get(self, key, currentNode):if not currentNode:  # ?return Noneelif currentNode.key == key:return currentNodeelif key < currentNode.key:return self._get(key, currentNode.leftChild)else:return self._get(key, currentNode.rightChild)def __getitem__(self, key):'''索引取值'''return self.get(key)def __contains__(self, key):'''归属判断'''if self._get(key, self.root):return Trueelse:return Falsedef delete(self, key):if self.size > 1:nodeToRemove = self._get(key, self.root)if nodeToRemove:self.remove(nodeToRemove)self.size = self.size - 1else:raise KeyError('Error,key not in tree')elif self.size == 1 and self.root.key == key:self.root = Noneself.size = self.size - 1else:raise KeyError('Error,key not in tree')def __delitem__(self, key):self.delete(key)

注：其中remove方法还未详细写

2.2 TreeNode类及其方法

class TreeNode:def __init__(self, key, val, left=None,right=None, parent=None):self.key = keyself.payload = valself.leftChild = leftself.rightChild = rightself.parent = parentdef hasLeftChild(self):return self.leftChilddef hasRightChild(self):return self.rightChilddef isLeftChild(self):  # 判断是否为父节点的左子节点return self.parent and \self.parent.leftChild == selfdef isRightChild(self):  # 判断是否为父节点的右子节点return self.parent and \self.parent.rightChild == selfdef isRoot(self):  # 判断是否是一个根节点return not self.parentdef isLeaf(self):  # 判断是否为叶节点return not (self.rightChild or self.leftChild)def hasAnyChildren(self):return self.rightChild or self.leftChilddef hasBothChildren(self):return self.rightChild and self.leftChilddef replaceNodeData(self, key, value, lc, rc):self.key = keyself.payload = valueself.leftChild = lcself.rightChild = rcif self.hasLeftChild():self.leftChild.parent = selfif self.hasRightChild():self.rightChild.parent = selfdef __iter__(self):'''左，根，右，中序遍历迭代'''if self:  # 根节点不是空——递归的基本结束条件if self.hasLeftChild():for elem in self.leftChild:  # 迭代yield elem  # 对每次迭代返回的值，类似于生成器yield self.keyif self.hasRightChild():for elem in self.rightChild:yield elem