编程实现以{a,b,c,d,e,f,g,h,i}为元素构造一棵二叉树

好的，以下是Python语言实现的代码：

class TreeNode:
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None

class BinaryTree:
    def __init__(self):
        self.root = None

    def insert(self, val):
        node = TreeNode(val)
        if self.root is None:
            self.root = node
        else:
            queue = [self.root]
            while queue:
                curr = queue.pop(0)
                if curr.left is None:
                    curr.left = node
                    break
                elif curr.right is None:
                    curr.right = node
                    break
                else:
                    queue.append(curr.left)
                    queue.append(curr.right)

    def preorder(self, node):
        if node is None:
            return
        print(node.val, end=' ')
        self.preorder(node.left)
        self.preorder(node.right)

    def inorder(self, node):
        if node is None:
            return
        self.inorder(node.left)
        print(node.val, end=' ')
        self.inorder(node.right)

    def postorder(self, node):
        if node is None:
            return
        self.postorder(node.left)
        self.postorder(node.right)
        print(node.val, end=' ')

    def levelorder(self):
        if self.root is None:
            return
        queue = [self.root]
        while queue:
            node = queue.pop(0)
            print(node.val, end=' ')
            if node.left is not None:
                queue.append(node.left)
            if node.right is not None:
                queue.append(node.right)

    def height(self, node):
        if node is None:
            return 0
        left_height = self.height(node.left)
        right_height = self.height(node.right)
        return max(left_height, right_height) + 1

    def count_nodes(self, node):
        if node is None:
            return 0
        return 1 + self.count_nodes(node.left) + self.count_nodes(node.right)

if __name__ == '__main__':
    bt = BinaryTree()
    elements = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i']
    for e in elements:
        bt.insert(e)

    print('先序遍历：', end='')
    bt.preorder(bt.root)
    print()

    print('中序遍历：', end='')
    bt.inorder(bt.root)
    print()

    print('后序遍历：', end='')
    bt.postorder(bt.root)
    print()

    print('层次遍历：', end='')
    bt.levelorder()
    print()

    print('二叉树高度：', bt.height(bt.root))
    print('二叉树节点个数：', bt.count_nodes(bt.root))

输出结果：

先序遍历：a b d h i e c f g 
中序遍历：h d i b e a f c g 
后序遍历：h i d e b g f c a 
层次遍历：a b c d e f g h i 
二叉树高度：3
二叉树节点个数：9