Python实现完全二叉树

一、二叉树的存储结构

对于线性表、栈、队列等数据结构，数据都可以使用物理有序和逻辑有序的方式存储，二叉树也可以使用这两种方式存储。然而，二叉树的特点决定了其存储结构与传统线性数据结构有所不同。

物理有序将数据存储在连续的内存空间中，例如存储在一个列表中，这种方式在遍历速度上有一定优势。然而，二叉树的节点通过父子关系连接，直接使用线性列表存储不容易体现树的结构。因此，二叉树通常以链式方式存储，反映其层次结构。

二、实现完全二叉树类

完全二叉树是一种特殊的二叉树，其节点按从上到下、从左到右的顺序依次排列，且不存在空隙。为了从简到繁地实现完全二叉树，我们先定义一个节点类Node。

class Node(object):    def __init__(self, data):        self.data = data        self.parent = None        self.left_child = None        self.right_child = None

节点类中，data属性存储节点的值，parent属性指向父节点，left_child和right_child属性分别指向左、右子节点。

接下来，我们定义一个完全二叉树类PerfectBinaryTree。

class PerfectBinaryTree(object):    def __init__(self):        self.__root = None        self.prefix_branch = '├'        self.prefix_trunk = '|'        self.prefix_leaf = '└'        self.prefix_empty = ''        self.prefix_left = '─L─'        self.prefix_right = '─R─'    def is_empty(self):        return not self.__root

三、实现完全二叉树的遍历和添加节点

为了在完全二叉树中添加节点，我们需要找到添加的位置。我们使用队列来实现层次遍历，确保从上到下、从左到右依次找到空位。

class TreeQueue(object):    def __init__(self):        self.__members = list()    def is_empty(self):        return not len(self.__members)    def enter(self, data):        self.__members.insert(0, data)    def outer(self):        if self.is_empty():            return        return self.__members.pop()

接下来实现append方法，用于将节点添加到完全二叉树中。

def append(self, data):    node = Node(data)    if self.is_empty():        self.__root = node        return    queue = TreeQueue()    queue.enter(self.__root)    while not queue.is_empty():        cur = queue.outer()        if cur.left_child is None:            cur.left_child = node            node.parent = cur            return        queue.enter(cur.left_child)        if cur.right_child is None:            cur.right_child = node            node.parent = cur            return        queue.enter(cur.right_child)

四、实现完全二叉树的其他方法

为了方便展示数据，我们实现show方法。

def show(self):    if self.is_empty():        print('空二叉树')        return    queue = TreeQueue()    queue.enter(self.__root)    while not queue.is_empty():        cur = queue.outer()        print(cur.data, end=' ')        if cur.left_child is not None:            queue.enter(cur.left_child)        if cur.right_child is not None:            queue.enter(cur.right_child)    print()

为了判断节点是否存在，我们实现is_exist方法。

def is_exist(self, data):    if self.is_empty():        return False    queue = TreeQueue()    queue.enter(self.__root)    while not queue.is_empty():        cur = queue.outer()        if cur.data == data:            return True        if cur.left_child is not None:            queue.enter(cur.left_child)        if cur.right_child is not None:            queue.enter(cur.right_child)    return False

为了展示树形结构，我们实现show_tree方法。

def show_tree(self):    if self.is_empty():        print('空二叉树')        return    print(self.__root.data)    self.__print_tree(self.__root)

def __print_tree(self, node, prefix=None):    if prefix is None:        prefix = ''        prefix_left_child = ''    else:        prefix = prefix.replace(self.prefix_branch, self.prefix_trunk)        prefix = prefix.replace(self.prefix_leaf, self.prefix_empty)        prefix_left_child = prefix.replace(self.prefix_leaf, self.prefix_empty)    if self.has_child(node):        if node.right_child is not None:            print(prefix + self.prefix_branch + self.prefix_right + str(node.right_child.data))            if self.has_child(node.right_child):                self.__print_tree(node.right_child, prefix + self.prefix_branch + ' ')        else:            print(prefix + self.prefix_branch + self.prefix_right)        if node.left_child is not None:            print(prefix + self.prefix_leaf + self.prefix_left + str(node.left_child.data))            if self.has_child(node.left_child):                prefix_left_child += '  '                self.__print_tree(node.left_child, self.prefix_leaf + prefix_left_child)        else:            print(prefix + self.prefix_leaf + self.prefix_left)def has_child(self, node):    return node.left_child is not None or node.right_child is not None

五、完整代码

class Node(object):    def __init__(self, data):        self.data = data        self.parent = None        self.left_child = None        self.right_child = Noneclass TreeQueue(object):    def __init__(self):        self.__members = list()    def is_empty(self):        return not len(self.__members)    def enter(self, data):        self.__members.insert(0, data)    def outer(self):        if self.is_empty():            return        return self.__members.pop()class PerfectBinaryTree(object):    def __init__(self):        self.__root = None        self.prefix_branch = '├'        self.prefix_trunk = '|'        self.prefix_leaf = '└'        self.prefix_empty = ''        self.prefix_left = '─L─'        self.prefix_right = '─R─'    def is_empty(self):        return not self.__root    def append(self, data):        node = Node(data)        if self.is_empty():            self.__root = node            return        queue = TreeQueue()        queue.enter(self.__root)        while not queue.is_empty():            cur = queue.outer()            if cur.left_child is None:                cur.left_child = node                node.parent = cur                return            queue.enter(cur.left_child)            if cur.right_child is None:                cur.right_child = node                node.parent = cur                return            queue.enter(cur.right_child)    def show(self):        if self.is_empty():            print('空二叉树')            return        queue = TreeQueue()        queue.enter(self.__root)        while not queue.is_empty():            cur = queue.outer()            print(cur.data, end=' ')            if cur.left_child is not None:                queue.enter(cur.left_child)            if cur.right_child is not None:                queue.enter(cur.right_child)        print()    def is_exist(self, data):        if self.is_empty():            return False        queue = TreeQueue()        queue.enter(self.__root)        while not queue.is_empty():            cur = queue.outer()            if cur.data == data:                return True            if cur.left_child is not None:                queue.enter(cur.left_child)            if cur.right_child is not None:                queue.enter(cur.right_child)        return False    def show_tree(self):        if self.is_empty():            print('空二叉树')            return        print(self.__root.data)        self.__print_tree(self.__root)    def __print_tree(self, node, prefix=None):        if prefix is None:            prefix = ''            prefix_left_child = ''        else:            prefix = prefix.replace(self.prefix_branch, self.prefix_trunk)            prefix = prefix.replace(self.prefix_leaf, self.prefix_empty)            prefix_left_child = prefix.replace(self.prefix_leaf, self.prefix_empty)        if self.has_child(node):            if node.right_child is not None:                print(prefix + self.prefix_branch + self.prefix_right + str(node.right_child.data))                if self.has_child(node.right_child):                    self.__print_tree(node.right_child, prefix + self.prefix_branch + ' ')            else:                print(prefix + self.prefix_branch + self.prefix_right)            if node.left_child is not None:                print(prefix + self.prefix_leaf + self.prefix_left + str(node.left_child.data))                if self.has_child(node.left_child):                    prefix_left_child += '  '                    self.__print_tree(node.left_child, self.prefix_leaf + prefix_left_child)            else:                print(prefix + self.prefix_leaf + self.prefix_left)    def has_child(self, node):        return node.left_child is not None or node.right_child is not Noneif __name__ == '__main__':    tree = PerfectBinaryTree()    print(tree)    print("is_empty: ", tree.is_empty())    tree.show()    for i in range(15):        tree.append(i)    tree.show()    print(tree.is_exist(2))    print(tree.is_exist(200))    tree.show_tree()

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