二叉搜索树

Posted 2020-11-20 yu-liang

二叉搜索树

 1 class Node:
 2     def __init__(self, key, right, left, p):
 3         ‘‘‘节点（关键字，左孩子，右孩子，父节点）‘‘‘
 4         self.key = key
 5         self.right = right
 6         self.left = left
 7         self.p = p
 8 
 9 class Binary_search_tree:
10     ‘‘‘二叉搜索树‘‘‘
11     def __init__(self, root):
12         ‘‘‘以根节点初始化一棵树‘‘‘
13         self.root = root
14     def tree_insert(self, z):
15         ‘‘‘在树中插入节点‘‘‘
16         y = None
17         x = self.root
18         while x != None:
19             y = x
20             if z.key < x.key:
21                 x = x.left
22             else:
23                 x = x.right
24         z.p = y
25         if y == None:
26             self.root = z
27         elif z.key < y.key:
28             y.left = z
29         else:
30             y.right = z
31 
32     def inorder_tree_walk(self, x):
33         ‘‘‘中序遍历‘‘‘
34         if x != None:
35             self.inorder_tree_walk(x.left)
36             print(x.key)
37             self.inorder_tree_walk(x.right)
38 
39 root=Node(6,None,None,None)
40 tree=Binary_search_tree(root)
41 List=[5,2,5,7,8]
42 for i in List:
43     node=Node(i,None,None,None)
44     tree.tree_insert(node)
45 print(tree)
46 print(tree.inorder_tree_walk(tree.root))
47 -------------------------------------------------------
48 <__main__.Binary_search_tree object at 0x032B7890>
49 2
50 5
51 5
52 6
53 7
54 8
55 None

二叉搜索树

 

 1 def tree_search(tree, x, k):
 2     ‘‘‘查找一个具有给定关键字的节点，x表示指向树根的指针‘‘‘
 3     if x == None or k == x.key:
 4         return x
 5     if k < x.key:
 6         return tree_search(tree,x.left, k)
 7     else:
 8         return tree_search(tree,x.right, k)
 9 
10 def iterative_tree_search(tree, x, k):
11     ‘‘‘迭代的树的搜索‘‘‘
12     while x != None and k != x.key:
13         if k < x.key:
14             x = x.left
15         else:
16             x = x.right
17     return x
18 
19 def tree_minimum(tree, x):
20     ‘‘‘最小关键字元素，最左边的节点‘‘‘
21     while x.left != None:
22         x = x.left
23     return x
24 
25 def tree_maximum(tree, x):
26     ‘‘‘最大关键字元素，最右边的节点‘‘‘
27     while x.right != None:
28         x = x.right
29     return x
30 
31 def tree_successor(tree, x):
32     ‘‘‘树的前继‘‘‘
33     if x.right != None:
34         return tree_minimum(tree,x.right)
35     y = x.p
36     while y != None and x == y.right:
37         x = y
38         y = y.p
39     return y
40 
41 root=Node(15,None,None,None)
42 tree=Binary_search_tree(root)
43 List=[6,18,3,7,17,20,2,4,13,9]
44 for i in List:
45     node=Node(i,None,None,None)
46     tree.tree_insert(node)
47 print(tree)
48 print(tree_search(tree, root, 13).key)
49 print(tree_maximum(tree,root).key)
50 print(tree_minimum(tree,root).key)
51 print(tree_successor(tree,tree_search(tree, root, 13)).key)
52 ---------------------------------------------------------------------
53 <__main__.Binary_search_tree object at 0x0391B530>
54 13
55 20
56 2
57 15

查找，最大最小值，前继

 删除节点

 1 def tree_delete(tree, z):
 2     ‘‘‘树的删除节点，分情况讨论‘‘‘
 3     if z.left == None:
 4         #1.z没有左孩子节点，用右孩子来替代他
 5         transplant(tree,z, z.right)
 6     elif z.right == None:
 7         #2.若z没有右孩子，用他的左孩子来替代他
 8         transplant(tree,z, z.left)
 9     else:
10         #如果有两个孩子，在z的右子树中找他的后继（最小关键字），并让y替代z的位置
11         y = tree_minimum(tree,z.right)
12         if y.p != z:
13             #若y不是z的左孩子，用y右孩子替换y并成为y的双亲的一个孩子，再将z的右孩子转换为y的右孩子
14             transplant(tree,y, y.right)
15             y.right = z.right
16             y.right.p = y
17         #用y替换z并成为z的双亲的一个孩子，再用z的左孩子替换为y的左孩子
18         transplant(tree,z, y)
19         y.left = z.left
20         y.left.p = y
21 
22 def transplant(tree, u, v):
23     ‘‘‘删除u后，树的替代，以一棵v为根的子树来替换一棵u为根的子树
24     结果：u的双亲变为v的双亲，v成为u的双亲的相应孩子‘‘‘
25     if u.p == None:
26         #1.若u是根节点，直接初始化一个v为根节点的树
27         tree.root = v
28     elif u == u.p.left:
29         #2.若u是他父节点的左孩子，更新他父节点的左孩子为v
30         u.p.left = v
31     else:
32         #3.若u是他父节点的右孩子，更新他父节点的右孩子为v
33         u.p.right = v
34     if v != None:
35         #如果v不为空，u的父节点变为v的父节点
36         v.p = u.p
37 
38 root=Node(15,None,None,None)
39 tree=Binary_search_tree(root)
40 List=[6,18,3,7,17,20,2,4,13,9]
41 for i in List:
42     node=Node(i,None,None,None)
43     tree.tree_insert(node)
44 
45 print(tree.inorder_tree_walk(tree.root))
46 print(‘#‘*30)
47 tree_delete(tree,tree_search(tree, root, 13))
48 print(tree.inorder_tree_walk(tree.root))
49 ------------------------------------------------------------------------
50 2
51 3
52 4
53 6
54 7
55 9
56 13
57 15
58 17
59 18
60 20
61 None
62 ##############################
63 2
64 3
65 4
66 6
67 7
68 9
69 15
70 17
71 18
72 20
73 None

节点的删除