Add XOR Linked List implementation with doctests

data_structures/linked_list/xor_linked_list.py

@@ -0,0 +1,58 @@
+"""
+XOR Linked List implementation
+
+A memory-efficient doubly linked list using XOR of node addresses.
+Each node stores one pointer that is the XOR of previous and next node addresses.
+
+Example:
+>>> xor_list = XORLinkedList()
+>>> xor_list.insert(10)
+>>> xor_list.insert(20)
+>>> xor_list.insert(30)
+>>> xor_list.to_list()
+[10, 20, 30]
+"""
+
+from typing import Optional
+
+
+class Node:
+    def __init__(self, value: int):
+        self.value = value
+        self.both: int = 0  # XOR of prev and next node ids
+
+
+class XORLinkedList:
+    def __init__(self):
+        self.head: Optional[Node] = None
+        self.tail: Optional[Node] = None
+        self._nodes = {}  # id → node map to simulate pointer references
+
+    def _xor(self, a: Optional[Node], b: Optional[Node]) -> int:
+        return (id(a) if a else 0) ^ (id(b) if b else 0)
+
+    def insert(self, value: int) -> None:
+        node = Node(value)
+        self._nodes[id(node)] = node
+        if self.head is None:
+            self.head = self.tail = node
+        else:
+            node.both = id(self.tail)
+            self.tail.both ^= id(node)
+            self.tail = node
+
+    def to_list(self) -> list[int]:
+        result = []
+        prev_id = 0
+        current = self.head
+        while current:
+            result.append(current.value)
+            next_id = prev_id ^ current.both
+            prev_id = id(current)
+            current = self._nodes.get(next_id)
+        return result
+
+
+if __name__ == "__main__":
+    import doctest
+    doctest.testmod()