数据结构之二叉查找树的代码实现
定义
- 二叉查找树（Binary Search Tree，BST），是一种内存中特殊的树类型的存储结构，它允许对存储在其结点的数据进行增删改查，或者用作动态的数据集合，或是通过key查找对应value的查找表；
创建结点
- 设计：可以使用顺序表或链表实现二叉树，这里使用链表实现，在学习堆时再使用顺序表实现
使用链表结点设计：
class Node:def __init__(self, key=None, value=None):self.key = keyself.value = valueself.left = Noneself.right = None
left和right分别代表左右子结点，key是可比较的，用于进行顺序匹配；value储存值
实现的功能
- 构造方法__init__()，root为根结点，默认为None，len为树的大小
- size()获取BST中元素个数
- put(_key, _value)向树中添加键值对元素，元素按key排序，返回添加元素后的新树
- get(_key)通过键获取树中对应元素的值
- delete(_key)通过键删除树中对应的元素
- min_key()获取最小的key
- max_key()获取最大的key
Python代码实现
import operatorclass Node:def __init__(self, key=None, value=None):self.key = keyself.value = valueself.left = Noneself.right = Noneclass BinarySearchTree:def __init__(self):self.root = Noneself.len = 0def size(self):return self.lendef put(self, _key, _value):"""Put an element into this tree and generate a new BST"""def put_into(node, _key, _value):"""Adjust position of new inserted nodeby BST character:left > root > right"""if not node:self.len += 1return Node(_key, _value)if operator.lt(_key, node.key):node.left = put_into(node.left, _key, _value)elif operator.gt(_key, node.key):node.right = put_into(node.right, _key, _value)elif operator.eq(_key, node.key):node.value = _valuereturn nodeself.root = put_into(self.root, _key, _value)return self.rootdef get(self, _key):"""Get a value responding to the given _key from this tree"""def get_value_by_key(node, _key):if not node:returnif operator.lt(_key, node.key):return get_value_by_key(node.left, _key)elif operator.gt(_key, node.key):return get_value_by_key(node.right, _key)else:return node.valuereturn get_value_by_key(self.root, _key)def delete(self, _key):"""Delete a node responding to the giving key(_key)"""def delete_value_by_key(node, _key):if not node:returnif operator.lt(_key, node.key):node.left = delete_value_by_key(node.left, _key)elif operator.gt(_key, node.key):node.right = delete_value_by_key(node.right, _key)else:self.len -= 1to_delete_node = nodeif node == self.root:self.root = Nonereturn# node = Noneif not to_delete_node.left:return to_delete_node.rightelif not to_delete_node.right:return to_delete_node.leftelse:min_right_tree = to_delete_node.rightpre = min_right_treewhile min_right_tree.left:pre = min_right_treemin_right_tree = min_right_tree.leftpre.left = Nonemin_right_tree.left = to_delete_node.leftmin_right_tree.right = to_delete_node.rightreturn min_right_treereturn delete_value_by_key(self.root, _key)def min_key(self):"""Find the minimum key"""def min_node(node):while node.left:node = node.leftreturn nodereturn min_node(self.root).keydef max_key(self):"""Find the maximum key"""def max_node(node):while node.right:node = node.rightreturn nodereturn max_node(self.root).keydef max_depth(self):"""Calculate the max depth of this tree"""def max_depth(node):max_left, max_right = 0, 0if not node:return 0if node.left:max_left = max_depth(node.left)if node.right:max_right = max_depth(node.right)return max(max_left, max_right) + 1return max_depth(self.root)
主要代码解释：
put()插入元素：使用递归，按照从上到下从左到右的顺序，依次和插入的元素比较
- 1.如果当前树中没有任何一个结点，则直接把新结点当做根结点使用并返回
- 2.如果当前树不为空, 则从根结点开始与传入的元素的key进行比较：
2.1如果新结点的key小于当前结点的key ,则继续找当前结点的左子结点;
2.2如果新结点的key大于当前结点的key ,则继续找当前结点的右子结点;
2.3如果新结点的key等于当前结点的key ,则树中已经存在这样的结点,替换该结点的value值即可。
delete()删除元素：跟插入元素类似，也是使用递归，寻找的顺序按照从上到下从左到右的顺序，依次和插入的元素比较，如果找到key相等的元素则做删除动作
- 如果找到key相等的元素，则只需要往这个结点的右子树的左边最深处寻找，根据排序的规律，找到的元素与key相等的元素交换位置即可
代码测试
if __name__ == '__main__':BST = BinarySearchTree()BST.put('e', '5')BST.put('b', '2')BST.put('g', '7')BST.put('a', '1')BST.put('d', '4')BST.put('f', '6')BST.put('h', '8')BST.put('c', '3')print(f"The size of this binary tree now is {BST.size()}\n")key = 'a'print(f"\nGet element by key[{key}]: {BST.get(key)}")key = 'b'BST.delete(key)print(f"After deleting an node ({key}), the size of this tree: {BST.size()}")print(f"Get the deleted value (key[{key}]), it should be none: {BST.get(key)}")print(f"Get the value (key[{'a'}]), it should be {1}: {BST.get('a')}")
测试结果
The size of this binary tree now is 8Get element by key[a]: 1
After deleting an node (b), the size of this tree: 7
Get the deleted value (key[b]), it should be none: None
Get the value (key[a]), it should be 1: 1Process finished with exit code 0
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