Prerequisite: XOR Linked List
An ordinary Doubly Linked List requires space for two address fields to store the addresses of previous and next nodes. A memory-efficient version of Doubly Linked List can be created using only one space for the address field with every node. This memory efficient Doubly Linked List is called XOR Linked List or Memory Efficient as the list uses bitwise XOR operation to save space for one address. In the XOR linked list, instead of storing actual memory addresses, every node stores the XOR of addresses of previous and next nodes.
The XOR Linked List implementation in Python is not of much use because the Python garbage collector doesn’t allow to save the node whose address is being XORed.
The functions that are implemented in the below program are:
- InsertAtStart(): Method to insert a node at the beginning.
- InsertAtEnd(): Method to insert a node at the end.
- DeleteAtStart(): Method to delete a node at the beginning.
- DeleteAtEnd(): Method to delete a node at the end.
- Print(): Method to traverse through the linked list from beginning to end.
- ReversePrint(): Method to traverse through the linked list from end to the beginning.
- Length(): Method to return the size of the linked list.
- PrintByIndex(): Method to return the data value of the node of the linked list specified by a particular index.
- isEmpty(): Method to check if the linked list is empty or not.
- __type_cast(): Method to return a new instance of type which points to the same memory block.
Below is the complete Python program to implement XOR Linked List with the above methods:
Python3
# import required moduleimport ctypes# create node classclass Node: def __init__(self, value): self.value = value self.npx = 0 # create linked list classclass 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 because 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 because 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 doesn't found index out of range." return node.value # method to check if the linked 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 objectobj = XorLinkedList()# insert nodesobj.InsertAtEnd(2)obj.InsertAtEnd(3)obj.InsertAtEnd(4)obj.InsertAtStart(0)obj.InsertAtStart(6)obj.InsertAtEnd(55)# display lengthprint("\nLength:", obj.Length())# traverseprint("\nTraverse linked list:")obj.Print()print("\nTraverse in reverse order:")obj.ReversePrint()# display data values by indexprint('\nNodes:')for i in range(obj.Length()): print("Data value at index", i, 'is', obj.PrintByIndex(i))# removing nodesprint("\nDelete Last Node: ", obj.DeleteAtEnd())print("\nDelete First Node: ", obj.DeleteAtStart())# new lengthprint("\nUpdated length:", obj.Length())# display data values by indexprint('\nNodes:')for i in range(obj.Length()): print("Data value at index", i, 'is', obj.PrintByIndex(i))# traverseprint("\nTraverse linked list:")obj.Print()print("\nTraverse in reverse order:")obj.ReversePrint() |
Output:
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
In Python garbage collector collect nodes and decrease the reference count of the object of a node when the object of the node is XORed, Python thinks there is no way to access the node so we used the __in which we store objects of node just for preventing it to become garbage.
