python-二叉树-先根-中根-后根-递归-非递归-实现方法

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二叉树之先根/中根/后根遍历:

# 感谢兄弟连姚老师(python-爬虫)

又叫先序后序中序遍历;三种都是从上到下从左到右依次近栈,唯一不同的就是出栈顺序:

先序(根)遍历(Python3中新式类的继承顺序,MRO,C3算法):

输出顺序: 根-左(上)-右(上)

出栈顺序:近栈后立马出栈(出栈顺序就是输出顺序)

中序(根)遍历(可看做是x轴投影的排序,y轴无重叠)():

输出顺序: 左(下)-根-右(下)

出栈顺序:游标左下方无分支立马出栈

后续(根)遍历(左右子树先输出再输出根节点.)(从左到右,从下到上;最好记忆的):

输出顺序:左(下)-右(下)-根

出栈顺序:游标右下方无分支立马出栈

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递归代码:

# 二叉树的先根,中根,后根遍历
# 建议使用递归的方法来实现树的遍历,其他实现不专业
class TreeNode(object):
    #python3新式类中object写不写都默认使用新式类的继承方式,都是继承object类
    def __init__(self,num):
        self.val = num
        # 类能够动态绑定属性,但是只可以使用类绑定,不能通过实例化对象
        # 绑定属性,因此可以在类里面写下面两行或者在后面写TreeNode.left=None;TreeNode.right=None;后才
        # 能够进行t1.left = t2的属性赋值操作
        # self.left=None
        # self.right=None

# 递归都可以看作是进栈出栈
# 先根遍历
def preRecursion(root):
    '''
        pre:previous
        Recursion:递归
        root:二叉树的根

        :param root:
        :return:
        '''
    if root == None:
        return None
    # 入栈就打印
    print(root.val,end='')
    preRecursion(root.left)
    preRecursion(root.right)
# 中根遍历
def midRecursion(root):
    if root == None:
        return None
    # 出左栈打印
    midRecursion(root.left)
    print(root.val,end='')
    midRecursion(root.right)
# 后根遍历
def afterRecursion(root):
    if root == None:
        return None
    # 出右栈打印
    afterRecursion(root.left)
    afterRecursion(root.right)
    print(root.val,end='')
if __name__ == '__main__':
    t1 = TreeNode(1)
    t2 = TreeNode(2)
    t3 = TreeNode(3)
    t4 = TreeNode(4)
    t5 = TreeNode(5)
    t6 = TreeNode(6)
    t7 = TreeNode(7)
    t8 = TreeNode(8)

    TreeNode.left = None
    TreeNode.right = None

    t1.left = t2
    t1.right = t3
    t2.left = t4
    t2.right = t5
    t3.left = t6
    t3.right = t7
    t6.right = t8

    '''
    形如:
                                1
                                
                        2                3
                        
                    4       5        6       7
                    
                                        8
    '''
    # 先根遍历
    preRecursion(t1)
    print()
    # 中根遍历
    midRecursion(t1)
    print()
    # 后根遍历
    afterRecursion(t1)
    '''
    结果:
        12453687
        42516837
        45286731
    '''

非递归写法:

# 二叉树的先根,中根,后根遍历
# 建议使用递归的方法来实现树的遍历,其他实现不专业
class TreeNode(object):
    #python3新式类中object写不写都默认使用新式类的继承方式,都是继承object类
    def __init__(self,num):
        self.val = num
        # 类能够动态绑定属性,但是只可以使用类绑定,不能通过实例化对象
        # 绑定属性,因此可以在类里面写下面两行或者在后面写TreeNode.left=None;TreeNode.right=None;后才
        # 能够进行t1.left = t2的属性赋值操作
        self.left=None
        self.right=None


# 递归本质上可以看出入栈和出栈的操作
def preOrder(root):
    '''

    :param root: 根
    :return:
    '''
    if root == None:
        return None
    # 使用列表表示栈
    stack = []
    tmpNode = root
    # 循环的头tmpNode/注意两个包含关系的while嵌套的重要性/while确定跳出条件,临界参数/
    while tmpNode or stack:
        while tmpNode:
            print(tmpNode.val,end='')
            # 入栈
            stack.append(tmpNode)
            tmpNode = tmpNode.left
        node = stack.pop()
        tmpNode = node.right

# 中根排序
def midOrder(root):
    if root == None:
        return None
    stack = []
    tmpNode = root
    while tmpNode or stack:
        while tmpNode:
            stack.append(tmpNode)
            tmpNode = tmpNode.left
        node = stack.pop()
        print(node.val,end='')
        tmpNode = node.right


# 后根排序
def aftOrder(root):
    if root == None:
        return None
    stack = []
    tmpNode = root
    while tmpNode or stack:
        while tmpNode:
            stack.append(tmpNode)
            tmpNode = tmpNode.left
        node = stack[-1]
        tmpNode = node.right
        if node.right == None:
            print(node.val,end='')
            node = stack.pop()
            while stack and node == stack[-1].right:
                node = stack.pop()
                print(node.val,end='')





if __name__ == '__main__':
    t1 = TreeNode(1)
    t2 = TreeNode(2)
    t3 = TreeNode(3)
    t4 = TreeNode(4)
    t5 = TreeNode(5)
    t6 = TreeNode(6)
    t7 = TreeNode(7)
    t8 = TreeNode(8)

    t1.left = t2
    t1.right = t3
    t2.left = t4
    t2.right = t5
    t3.left = t6
    t3.right = t7
    t6.right = t8

    preOrder(t1);print()
    midOrder(t1);print()
    aftOrder(t1)