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python数据结构之二叉树的遍历实例

时间:2019-10-05 18:06:17      阅读:80      评论:0      收藏:0      [点我收藏+]

标签:实例   ini   二叉树   traversal   color   遍历   pytho   分组   后序   

遍历方案
    从二叉树的递归定义可知,一棵非空的二叉树由根结点及左、右子树这三个基本部分组成。因此,在任一给定结点上,可以按某种次序执行三个操作:
    1).访问结点本身(N)
    2).遍历该结点的左子树(L)
    3).遍历该结点的右子树(R)

有次序:
    NLR、LNR、LRN

遍历的命名

    根据访问结点操作发生位置命名:
NLR:前序遍历(PreorderTraversal亦称(先序遍历))  ——访问结点的操作发生在遍历其左右子树之前。
LNR:中序遍历(InorderTraversal)  ——访问结点的操作发生在遍历其左右子树之中(间)。
LRN:后序遍历(PostorderTraversal)    ——访问结点的操作发生在遍历其左右子树之后。

注:由于被访问的结点必是某子树的根,所以N(Node)、L(Left subtlee)和R(Right subtree)又可解释为根、根的左子树和根的右子树。NLR、LNR和LRN分别又称为先根遍历、中根遍历和后根遍历。

遍历算法

1).先序遍历的递归算法定义:
若二叉树非空,则依次执行如下操作:
a.访问根结点
b.遍历左子树
c.遍历右子树

2).中序遍历的递归算法定义:
若二叉树非空,则依次执行如下操作:
a.遍历左子树
b.访问根结点
c.遍历右子树

3).后序遍历得递归算法定义:
若二叉树非空,则依次执行如下操作:
a.遍历左子树
b.遍历右子树
c.访问根结点

一、二叉树的递归遍历:

# -*- 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 BTree(object):

    def __init__(self, root=0):
        self.root = root

    def is_empty(self):
        if self.root is 0:
            return True
        else:
            return False

    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)


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 = BTree(root)

print(u‘‘‘

#生成的二叉树

# ------------------------
#          root
#       7        8
#     6
#   2   5
# 1    3 4
#
# -------------------------

‘‘‘)
print(前序(pre-order,NLR)遍历 :\n)
bt.preorder(bt.root)

print(中序(in-order,LNR) 遍历 :\n)
bt.inorder(bt.root)

print(后序(post-order,LRN)遍历 :\n)
bt.postorder(bt.root)

输出:

#生成的二叉树

# ------------------------
#          root
#       7        8
#     6
#   2   5
# 1    3 4
#
# -------------------------


前序(pre-order,NLR)遍历 :

root
7
6
2
1
5
3
4
8
中序(in-order,LNR) 遍历 :

1
2
6
3
5
4
7
root
8
后序(post-order,LRN)遍历 :

1
2
3
4
5
6
7
8
root

二、.二叉树的非递归遍历

下面就用非递归的方式实现一遍。主要用到了 stack 和 queue维护一些数据节点:

# -*- 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 BTree(object):

    def __init__(self, root=0):
        self.root = root

    def is_empty(self):
        if self.root is 0:
            return True
        else:
            return False

    def preorder(self, treenode):
        前序(pre-order,NLR)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 inorder(self, treenode):
        中序(in-order,LNR) 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 postorder(self, treenode):
    #     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 postorder(self, treenode):
        后序(post-order,LRN)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 levelorder(self, treenode):
        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)


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 = BTree(root)

print(u‘‘‘

#生成的二叉树

# ------------------------
#          root
#       7        8
#     6
#   2   5
# 1    3 4
#
# -------------------------

‘‘‘)
print(前序(pre-order,NLR)遍历 :\n)
bt.preorder(bt.root)

print(中序(in-order,LNR) 遍历 :\n)
bt.inorder(bt.root)

print(后序(post-order,LRN)遍历 :\n)
bt.postorder(bt.root)

print(层序(level-order,LRN)遍历 :\n)
bt.levelorder(bt.root)

输出:

#生成的二叉树

# ------------------------
#          root
#       7        8
#     6
#   2   5
# 1    3 4
#
# -------------------------


前序(pre-order,NLR)遍历 :

root
7
6
2
1
5
3
4
8
中序(in-order,LNR) 遍历 :

1
2
6
3
5
4
7
root
8
后序(post-order,LRN)遍历 :

1
2
3
4
5
6
7
8
root
层序(level-order,LRN)遍历 :

root
7
8
6
2
5
1
3
4

 

python数据结构之二叉树的遍历实例

标签:实例   ini   二叉树   traversal   color   遍历   pytho   分组   后序   

原文地址:https://www.cnblogs.com/ceo-python/p/11625262.html

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