树和二叉树的Python实现

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本文详细介绍了如何构建二叉树结构，并提供了先序、中序、后序及层序遍历的递归与非递归实现，同时展示了二叉树的反转操作。

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树

树节点构建

首先先定义一个二叉树的节点类，一个二叉树节点应该包括，数据，左子树信息，右子树信息。

class BinTreeNode(object):
    def __init__(self, data, left=None, right=None):
        self.data, self.left, self.right = data, left, right

树构建

下面再建立一个树的类，首先默认一个根节点root

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

下面定义一个构建树结构的函数，把树的节点放到树里面。构造一个字典，包含：data、left、right、is_root三个Key值，后面分别表示其状态。提前将一个包含树的各个信息的字典（node_list）作为输入,来构造。第一个循环将构造node节点，将每个数据构造成build_node的节点，放入node_dict里面，第二次循环，给root和孩子节点赋值，最后用root初始化这个类并返回一个对象。

   def build_from(cls, node_list):
        """build_from

        :param node_list: {'data': 'A', 'left': None, 'right': None, 'is_root': False}
        """
        node_dict = {}
        for node_data in node_list:
            data = node_data['data']
            node_dict[data] = BinTreeNode(data)
        for node_data in node_list:
            data = node_data['data']
            node = node_dict[data]
            if node_data['is_root']:
                root = node
            node.left = node_dict.get(node_data['left'])
            node.right = node_dict.get(node_data['right'])
        return cls(root)

用递归的思想去遍历它

先序遍历

先（根）序遍历（根->左->右）

 def preorder_trav(self, subtree):
        if subtree is not None:
            print(subtree.data)
            self.preorder_trav(subtree.left)
            self.preorder_trav(subtree.right)

中序遍历

（左->根->右）

    def inorder_trav(self, subtree):
        if subtree is not None:
            self.inorder_trav(subtree.left)
            print(subtree.data)
            self.inorder_trav(subtree.right)

后序遍历

（左->右->根）

    def back_trav(self, subtree):
        if subtree is not None:
            self.back_trav(subtree.left)
            self.back_trav(subtree.right)
            print(subtree.data)

遍历输出每个节点

    def yield_inorder(self, subtree):  # for val in yield_inorder(root): print(val)
        if subtree:
            yield from self.inorder(subtree.left)
            yield subtree.val
            yield from self.inorder(subtree.right)

二叉树的反转

    def reverse(self, subtree):
        if subtree is not None:
            subtree.left, subtree.right = subtree.right, subtree.left
            self.reverse(subtree.left)
            self.reverse(subtree.right)

用非递归的方式模拟树的遍历

    def layer_trav(self, subtree):
        cur_nodes = [subtree]
        next_nodes = []
        while cur_nodes or next_nodes:
            for node in cur_nodes:
                print(node.data)
                if node.left:
                    next_nodes.append(node.left)
                if node.right:
                    next_nodes.append(node.right)
            cur_nodes = next_nodes  # 继续遍历下一层
            next_nodes = []

完整代码

# -*- coding: utf-8 -*-


from collections import deque


class Queue(object):  # 借助内置的 deque 我们可以迅速实现一个 Queue
    def __init__(self):
        self._items = deque()

    def append(self, value):
        return self._items.append(value)

    def pop(self):
        return self._items.popleft()

    def empty(self):
        return len(self._items) == 0


class Stack(object):
    def __init__(self):
        self._items = deque()

    def push(self, value):
        return self._items.append(value)

    def pop(self):
        return self._items.pop()

    def empty(self):
        return len(self._items) == 0


class BinTreeNode(object):
    def __init__(self, data, left=None, right=None):
        self.data, self.left, self.right = data, left, right


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

    @classmethod
    def build_from(cls, node_list):
        """build_from

        :param node_list: {'data': 'A', 'left': None, 'right': None, 'is_root': False}
        """
        node_dict = {}
        for node_data in node_list:
            data = node_data['data']
            node_dict[data] = BinTreeNode(data)
        for node_data in node_list:
            data = node_data['data']
            node = node_dict[data]
            if node_data['is_root']:
                root = node
            node.left = node_dict.get(node_data['left'])
            node.right = node_dict.get(node_data['right'])
        return cls(root)

    def preorder_trav(self, subtree):
        if subtree is not None:
            print(subtree.data)
            self.preorder_trav(subtree.left)
            self.preorder_trav(subtree.right)

    def preorder_trav_use_stack(self, subtree):
        """递归的方式其实是计算机帮我们实现了栈结构，我们可以自己显示的用栈来实现"""
        s = Stack()
        if subtree:
            s.push(subtree)
            while not s.empty():
                top_node = s.pop()
                print(top_node.data)    # 注意这里我用了 print，你可以用 yield 产出值然后在调用的地方转成 list
                if top_node.right:
                    s.push(top_node.right)
                if top_node.left:
                    s.push(top_node.left)

    def inorder_trav(self, subtree):
        if subtree is not None:
            self.inorder_trav(subtree.left)
            print(subtree.data)
            self.inorder_trav(subtree.right)

    def yield_inorder(self, subtree):  # for val in yield_inorder(root): print(val)
        if subtree:
            yield from self.inorder(subtree.left)
            yield subtree.val
            yield from self.inorder(subtree.right)

    def reverse(self, subtree):
        if subtree is not None:
            subtree.left, subtree.right = subtree.right, subtree.left
            self.reverse(subtree.left)
            self.reverse(subtree.right)

    def layer_trav(self, subtree):
        cur_nodes = [subtree]
        next_nodes = []
        while cur_nodes or next_nodes:
            for node in cur_nodes:
                print(node.data)
                if node.left:
                    next_nodes.append(node.left)
                if node.right:
                    next_nodes.append(node.right)
            cur_nodes = next_nodes  # 继续遍历下一层
            next_nodes = []

    def layer_trav_use_queue(self, subtree):
        q = Queue()
        q.append(subtree)
        while not q.empty():
            cur_node = q.pop()
            print(cur_node.data)
            if cur_node.left:
                q.append(cur_node.left)
            if cur_node.right:
                q.append(cur_node.right)


node_list = [
    {'data': 'A', 'left': 'B', 'right': 'C', 'is_root': True},
    {'data': 'B', 'left': 'D', 'right': 'E', 'is_root': False},
    {'data': 'D', 'left': None, 'right': None, 'is_root': False},
    {'data': 'E', 'left': 'H', 'right': None, 'is_root': False},
    {'data': 'H', 'left': None, 'right': None, 'is_root': False},
    {'data': 'C', 'left': 'F', 'right': 'G', 'is_root': False},
    {'data': 'F', 'left': None, 'right': None, 'is_root': False},
    {'data': 'G', 'left': 'I', 'right': 'J', 'is_root': False},
    {'data': 'I', 'left': None, 'right': None, 'is_root': False},
    {'data': 'J', 'left': None, 'right': None, 'is_root': False},
]


btree = BinTree.build_from(node_list)
print('====先序遍历=====')
btree.preorder_trav(btree.root)

print('====使用 stack 实现先序遍历=====')
btree.preorder_trav_use_stack(btree.root)

print('====层序遍历=====')
btree.layer_trav(btree.root)
print('====用队列层序遍历=====')
btree.layer_trav_use_queue(btree.root)

btree.reverse(btree.root)
print('====反转之后的结果=====')
btree.preorder_trav(btree.root)