先决条件：异或链表
一个普通的双向链表需要两个地址字段的空间来存储前后节点的地址。双向链表的内存效率的版本可以只使用一个与每个节点的地址栏中空间中创建。这种内存高效的双向链表称为 XOR 链表或内存高效，因为该列表使用按位异或运算为一个地址节省空间。在异或链表中，每个节点都存储前后节点地址的异或，而不是存储实际的内存地址。
Python的异或链表实现没有多大用处，因为Python垃圾收集器不允许保存地址被异或的节点。
以下程序中实现的功能是：
- InsertAtStart()：方法在开头插入一个节点。
- InsertAtEnd()：在末尾插入一个节点的方法。
- DeleteAtStart()：方法在开始处删除一个节点。
- DeleteAtEnd()：方法在末尾删除一个节点。
- Print()：从头到尾遍历链表的方法。
- ReversePrint()：从头到尾遍历链表的方法。
- Length()：返回链表大小的方法。
- PrintByIndex()：返回由特定索引指定的链表节点的数据值的方法。
- isEmpty()：检查链表是否为空的方法。
- __type_cast()：返回指向同一内存块的新类型实例的方法。
以下是使用上述方法实现异或链表的完整Python程序：
Python3
# import required module
import ctypes
# create node class
class Node:
def __init__(self, value):
self.value = value
self.npx = 0
# create linked list class
class XorLinkedList:
# constructor
def __init__(self):
self.head = None
self.tail = None
self.__nodes = []
# method to insert node at beginning
def InsertAtStart(self, value):
node = Node(value)
if self.head is None: # If list is empty
self.head = node
self.tail = node
else:
self.head.npx = id(node) ^ self.head.npx
node.npx = id(self.head)
self.head = node
self.__nodes.append(node)
# method to insert node at end
def InsertAtEnd(self, value):
node = Node(value)
if self.head is None: # If list is empty
self.head = node
self.tail = node
else:
self.tail.npx = id(node) ^ self.tail.npx
node.npx = id(self.tail)
self.tail = node
self.__nodes.append(node)
# method to remove node at beginning
def DeleteAtStart(self):
if self.isEmpty(): # If list is empty
return "List is empty !"
elif self.head == self.tail: # If list has 1 node
self.head = self.tail = None
elif (0 ^ self.head.npx) == id(self.tail): # If list has 2 nodes
self.head = self.tail
self.head.npx = self.tail.npx = 0
else: # If list has more than 2 nodes
res = self.head.value
x = self.__type_cast(0 ^ self.head.npx) # Address of next node
y = (id(self.head) ^ x.npx) # Address of next of next node
self.head = x
self.head.npx = 0 ^ y
return res
# method to remove node at end
def DeleteAtEnd(self):
if self.isEmpty(): # If list is empty
return "List is empty !"
elif self.head == self.tail: # If list has 1 node
self.head = self.tail = None
elif self.__type_cast(0 ^ self.head.npx) == (self.tail): # If list has 2 nodes
self.tail = self.head
self.head.npx = self.tail.npx = 0
else: # If list has more than 2 nodes
prev_id = 0
node = self.head
next_id = 1
while next_id:
next_id = prev_id ^ node.npx
if next_id:
prev_id = id(node)
node = self.__type_cast(next_id)
res = node.value
x = self.__type_cast(prev_id).npx ^ id(node)
y = self.__type_cast(prev_id)
y.npx = x ^ 0
self.tail = y
return res
# method to traverse linked list
def Print(self):
"""We are printing values rather than returning it bacause
for returning we have to append all values in a list
and it takes extra memory to save all values in a list."""
if self.head != None:
prev_id = 0
node = self.head
next_id = 1
print(node.value, end=' ')
while next_id:
next_id = prev_id ^ node.npx
if next_id:
prev_id = id(node)
node = self.__type_cast(next_id)
print(node.value, end=' ')
else:
return
else:
print("List is empty !")
# method to traverse linked list in reverse order
def ReversePrint(self):
# Print Values is reverse order.
"""We are printing values rather than returning it bacause
for returning we have to append all values in a list
and it takes extra memory to save all values in a list."""
if self.head != None:
prev_id = 0
node = self.tail
next_id = 1
print(node.value, end=' ')
while next_id:
next_id = prev_id ^ node.npx
if next_id:
prev_id = id(node)
node = self.__type_cast(next_id)
print(node.value, end=' ')
else:
return
else:
print("List is empty !")
# method to get length of linked list
def Length(self):
if not self.isEmpty():
prev_id = 0
node = self.head
next_id = 1
count = 1
while next_id:
next_id = prev_id ^ node.npx
if next_id:
prev_id = id(node)
node = self.__type_cast(next_id)
count += 1
else:
return count
else:
return 0
# method to get node data value by index
def PrintByIndex(self, index):
prev_id = 0
node = self.head
for i in range(index):
next_id = prev_id ^ node.npx
if next_id:
prev_id = id(node)
node = self.__type_cast(next_id)
else:
return "Value dosn't found index out of range."
return node.value
# method to check if the liked list is empty or not
def isEmpty(self):
if self.head is None:
return True
return False
# method to return a new instance of type
def __type_cast(self, id):
return ctypes.cast(id, ctypes.py_object).value
# Driver Code
# create object
obj = XorLinkedList()
# insert nodes
obj.InsertAtEnd(2)
obj.InsertAtEnd(3)
obj.InsertAtEnd(4)
obj.InsertAtStart(0)
obj.InsertAtStart(6)
obj.InsertAtEnd(55)
# display length
print("\nLength:", obj.Length())
# traverse
print("\nTraverse linked list:")
obj.Print()
print("\nTraverse in reverse order:")
obj.ReversePrint()
# display data values by index
print('\nNodes:')
for i in range(obj.Length()):
print("Data value at index", i, 'is', obj.PrintByIndex(i))
# removing nodes
print("\nDelete Last Node: ", obj.DeleteAtEnd())
print("\nDelete First Node: ", obj.DeleteAtStart())
# new length
print("\nUpdated length:", obj.Length())
# display data values by index
print('\nNodes:')
for i in range(obj.Length()):
print("Data value at index", i, 'is', obj.PrintByIndex(i))
# traverse
print("\nTraverse linked list:")
obj.Print()
print("\nTraverse in reverse order:")
obj.ReversePrint()输出：
Length: 6
Traverse linked list:
6 0 2 3 4 55
Traverse in reverse order:
55 4 3 2 0 6
Nodes:
Data value at index 0 is 6
Data value at index 1 is 0
Data value at index 2 is 2
Data value at index 3 is 3
Data value at index 4 is 4
Data value at index 5 is 55
Delete Last Node: 55
Delete First Node: 6
Updated length: 4
Nodes:
Data value at index 0 is 0
Data value at index 1 is 2
Data value at index 2 is 3
Data value at index 3 is 4
Traverse linked list:
0 2 3 4
Traverse in reverse order:
4 3 2 0
Python垃圾收集器收集节点并在节点对象被异或时减少节点对象的引用计数， Python认为无法访问该节点所以我们使用__in来存储节点对象只是为了防止它变成垃圾。
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