就是二叉树最后的层次，如下图：

实现代码：

代码如下:

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

代码如下:

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

代码如下:

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

代码如下:

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：

代码如下:

# -*- 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

-------------------------

'''