python数据结构之二叉树的统计与转换实例

一、获取二叉树的深度

就是二叉树最后的层次，如下图：

实现代码：

def getheight(self):
        ''' 获取二叉树深度 '''
        return self.__get_tree_height(self.root)    def __get_tree_height(self, root):
        if root is 0:
            return 0
        if root.left is 0 and root.right is 0:
            return 1
        else:
            left = self.__get_tree_height(root.left)
            right = self.__get_tree_height(root.right)
            if left < right:
                return right + 1
            else:
                return left + 1

二、叶子的统计

叶子就是二叉树的节点的 left 指针和 right 指针分别指向空的节点

def getleafcount(self):
        ''' 获取二叉树叶子数 '''
        return self.__count_leaf_node(self.root)    def __count_leaf_node(self, root):
        res = 0
        if root is 0:
            return res
        if root.left is 0 and root.right is 0:
            res += 1
            return res
        if root.left is not 0:
            res += self.__count_leaf_node(root.left)
        if root.right is not 0:
            res += self.__count_leaf_node(root.right)
        return res

三、统计叶子的分支节点

与叶子节点相对的其他节点 left 和 right 的指针指向其他节点

def getbranchcount(self):
        ''' 获取二叉树分支节点数 '''
        return self.__get_branch_node(self.root)    def __get_branch_node(self, root):
        if root is 0:
            return 0
        if root.left is 0 and root.right is 0:
            return 0
        else:
            return 1 + self.__get_branch_node(root.left) + self.__get_branch_node(root.right)

四、二叉树左右树互换

def replacelem(self):
        ''' 二叉树所有结点的左右子树相互交换 '''
        self.__replace_element(self.root)    def __replace_element(self, root):
        if root is 0:
            return
        root.left, root.right = root.right, root.left
        self.__replace_element(root.left)
        self.__replace_element(root.right)

这些方法和操作，都是运用递归。其实二叉树的定义也是一种递归。附上最后的完整代码：

# -*- coding: utf - 8 - *-    
class TreeNode(object):
    def __init__(self, left=0, right=0, data=0):
        self.left = left
        self.right = right
        self.data = data
    
class BinaryTree(object):
    def __init__(self, root=0):
        self.root = root
    def is_empty(self):
        if self.root is 0:
            return True
        else:
            return False
    def create(self):
        temp = input('enter a value:')
        if temp is '#':
            return 0
        treenode = TreeNode(data=temp)
        if self.root is 0:
            self.root = treenode
        treenode.left = self.create()
        treenode.right = self.create()
    def preorder(self, treenode):
        '前序（pre-order，NLR）遍历'
        if treenode is 0:
            return
        print treenode.data
        self.preorder(treenode.left)
        self.preorder(treenode.right)
    def inorder(self, treenode):
        '中序（in-order，LNR'
        if treenode is 0:
            return
        self.inorder(treenode.left)
        print treenode.data
        self.inorder(treenode.right)
    def postorder(self, treenode):
        '后序（post-order，LRN）遍历'
        if treenode is 0:
            return
        self.postorder(treenode.left)
        self.postorder(treenode.right)
        print treenode.data
    def preorders(self, treenode):
        '前序（pre-order，NLR）非递归遍历'
        stack = []
        while treenode or stack:
            if treenode is not 0:
                print treenode.data
                stack.append(treenode)
                treenode = treenode.left
            else:
                treenode = stack.pop()
                treenode = treenode.right
    def inorders(self, treenode):
        '中序（in-order，LNR) 非递归遍历'
        stack = []
        while treenode or stack:
            if treenode:
                stack.append(treenode)
                treenode = treenode.left
            else:
                treenode = stack.pop()
                print treenode.data
                treenode = treenode.right
    def postorders(self, treenode):
        '后序（post-order，LRN）非递归遍历'
        stack = []
        pre = 0
        while treenode or stack:
            if treenode:
                stack.append(treenode)
                treenode = treenode.left
            elif stack[-1].right != pre:
                treenode = stack[-1].right
                pre = 0
            else:
                pre = stack.pop()
                print pre.data
    # def postorders(self, treenode):
    #     '后序（post-order，LRN）非递归遍历'
    #     stack = []
    #     queue = []
    #     queue.append(treenode)
    #     while queue:
    #         treenode = queue.pop()
    #         if treenode.left:
    #             queue.append(treenode.left)
    #         if treenode.right:
    #             queue.append(treenode.right)
    #         stack.append(treenode)
    #     while stack:
    #         print stack.pop().data
    def levelorders(self, treenode):
        '层序（post-order，LRN）非递归遍历'
        from collections import deque
        if not treenode:
            return
        q = deque([treenode])
        while q:
            treenode = q.popleft()
            print treenode.data
            if treenode.left:
                q.append(treenode.left)
            if treenode.right:
                q.append(treenode.right)
    def getheight(self):
        ''' 获取二叉树深度 '''
        return self.__get_tree_height(self.root)
    def __get_tree_height(self, root):
        if root is 0:
            return 0
        if root.left is 0 and root.right is 0:
            return 1
        else:
            left = self.__get_tree_height(root.left)
            right = self.__get_tree_height(root.right)
            if left < right:
                return right + 1
            else:
                return left + 1
    def getleafcount(self):
        ''' 获取二叉树叶子数 '''
        return self.__count_leaf_node(self.root)
    def __count_leaf_node(self, root):
        res = 0
        if root is 0:
            return res
        if root.left is 0 and root.right is 0:
            res += 1
            return res
        if root.left is not 0:
            res += self.__count_leaf_node(root.left)
        if root.right is not 0:
            res += self.__count_leaf_node(root.right)
        return res
    def getbranchcount(self):
        ''' 获取二叉树分支节点数 '''
        return self.__get_branch_node(self.root)
    def __get_branch_node(self, root):
        if root is 0:
            return 0
        if root.left is 0 and root.right is 0:
            return 0
        else:
            return 1 + self.__get_branch_node(root.left) + self.__get_branch_node(root.right)
    def replacelem(self):
        ''' 二叉树所有结点的左右子树相互交换 '''
        self.__replace_element(self.root)
    def __replace_element(self, root):
        if root is 0:
            return
        root.left, root.right = root.right, root.left
        self.__replace_element(root.left)
        self.__replace_element(root.right)
node1 = TreeNode(data=1)
node2 = TreeNode(node1, 0, 2)
node3 = TreeNode(data=3)
node4 = TreeNode(data=4)
node5 = TreeNode(node3, node4, 5)
node6 = TreeNode(node2, node5, 6)
node7 = TreeNode(node6, 0, 7)
node8 = TreeNode(data=8)
root = TreeNode(node7, node8, 'root')
    
bt = BinaryTree(root)
print u'''
生成的二叉树
------------------------
         root
      7        8
    6
  2   5
1    3 4
-------------------------
'''