散列表

Posted 2020-11-20 yu-liang

一.散列表（Hash Table）

1.用来实现字典操作的一组有效数据结构

2.直接寻址表（直接寻址）：数组T[0...m-1]，可以存放动态集合的元素

 1 class direct_address_table:
 2     ‘‘‘直接寻址表‘‘‘
 3     def __init__(self, T=[], size=0):
 4         if len(T) == 0:
 5             self.T = [None for i in range(size)]
 6         else:
 7             self.T = T
 8         self.size = size
 9     ‘‘‘对于节点‘‘‘
10     def search(self, k):
11         return self.T[k]
12 
13     def insert(self, x):
14         self.T[x.key] = x
15 
16     def delete(self, x):
17         self.T[x.key] = None
18 
19 class Node:
20     def __init__(self, key):
21         self.key = key
22 
23 T=[]
24 dat=direct_address_table(T,10)
25 x=Node(2)
26 print(dat.insert(x))

直接寻址表

 

3.散列表：利用散列函数（hash function）h，把原来具有关键字k的元素存放在槽k中变成该元素放在h(k)中

冲突：两个关键字映射到同一个槽中

 解决（1）链接法：把散列到同一槽中的所有元素都放在一个链表中

 1 class chained_hash:
 2     ‘‘‘链接法散列，查找和插入时都要判断槽中有没有元素‘‘‘
 3     def __init__(self, T=[], size=0):
 4         if len(T) == 0:
 5             self.T = [None for i in range(size)]
 6         else:
 7             self.T = T
 8         self.size = size
 9     def search(self, k):
10         if self.T[self.hash_h(k)] != None:
11             x = self.T[self.hash_h(k)].list_search(k)
12             return x
13         return None
14     def insert(self, x):
15         if self.T[self.hash_h(x.key)] == None:
16             self.T[self.hash_h(x.key)] = DoublyLinkedList(x)
17         else:
18             self.T[self.hash_h(x.key)].list_insert(x)
19     def delete(self, x):
20         self.T[self.hash_h(x.key)].list_delete(x)
21     def hash_h(self, key):
22         ‘‘‘hash函数‘‘‘
23         return key % 12
24 
25 class Node:
26     def __init__(self, key):
27         self.key = key
28 class DoublyNode:
29     def __init__(self, n_prev, n_next, key):
30         self.prev = n_prev
31         self.next = n_next
32         self.key = key
33 
34 class DoublyLinkedList:
35     def __init__(self, head):
36         self.head = head
37 
38     def list_search(self, k):
39         x = self.head
40         while x != None and x.key != k:
41             x = x.next
42         return x
43 
44     def list_insert(self, x):
45         x.next = self.head
46         if self.head != None:
47             self.head.prev = x
48         self.head = x
49         x.prev = None
50 
51     def list_delete(self, x):
52         if x.prev != None:
53             x.prev.next = x.next
54         else:
55             self.head = x.next
56         if x.next != None:
57             x.next.prev = x.prev
58 
59 T=[]
60 x=DoublyNode(None,None,13)
61 ch=chained_hash(T,12)
62 ch.insert(x)
63 x=DoublyNode(None,None,25)
64 ch.insert(x)
65 y=ch.search(25)
66 print(y.key)
67 
68 ch.delete(y)
69 print(ch.T[1].head)
70 print(ch.T[1].head.key)
71 print(ch.T[1].head.next)
72 -----------------------------------------
73 25
74 <__main__.DoublyNode object at 0x039C78B0>
75 13
76 None

链接法散列

散列函数的选择：1）除法散列法：h(k)=k mod m ;2)乘法散列法：h(k)=[m(kA mod 1)] ; 3)全域散列法

（2）开放寻址法：所有元素都存放在散列表中，通过探查，找到空槽放置关键字

 1 class open_address_hash:
 2     ‘‘‘开放寻址散列，散列表T和一个关键字k‘‘‘
 3     def __init__(self, T=[], size=0):
 4         if len(T) == 0:
 5             self.T = [None for i in range(size)]
 6         else:
 7             self.T = T
 8         self.size = size
 9 
10     def hash_insert(self, k):
11         ‘‘‘插入关键字k，返回k的插槽或已满标志‘‘‘
12         i = 0
13         while i < self.size:
14             j = self.hash_h1_h2(k, i)#搜寻空槽并插入
15             if self.T[j] == None:
16                 self.T[j] = k
17                 return j
18             else:
19                 i += 1
20         return "hash table overflow"
21 
22     def hash_search(self, k):
23         ‘‘‘查找，如果槽j包含了关键字k，则返回j，否则返回NOne‘‘‘
24         i = 0
25         j = self.hash_h1_h2(k, i)
26         while self.T[j] != None and i < self.size:
27             j = self.hash_h1_h2(k, i)
28             if self.T[j] == k:
29                 return j
30             else:
31                 i += 1
32         return None
33 
34     def hash_h1_h2(self, k, i):
35         ‘‘‘hash 函数‘‘‘
36         return ((k % self.size + i * (1 + k % (self.size - 2)))) % self.size
37 
38 T=[]
39 oah=open_address_hash(T,13)
40 print(oah.hash_insert(79))
41 print(oah.hash_insert(69))
42 print(oah.hash_search(50))
43 ------------------------------
44 1
45 4
46 None

开放地址散列