diff --git a/DIRECTORY.md b/DIRECTORY.md
index a6800acdac4a..a2de2029c773 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -181,6 +181,7 @@
 ## [Computer Vision](computer_vision)
   * [Cnn Classification](computer_vision/cnn_classification.py)
   * [Flip Augmentation](computer_vision/flip_augmentation.py)
+  * [Gramian](computer_vision/gramian.py)
   * [Haralick Descriptors](computer_vision/haralick_descriptors.py)
   * [Harris Corner](computer_vision/harris_corner.py)
   * [Horn Schunck](computer_vision/horn_schunck.py)
@@ -231,6 +232,7 @@
   * [Lempel Ziv](data_compression/lempel_ziv.py)
   * [Lempel Ziv Decompress](data_compression/lempel_ziv_decompress.py)
   * [Lz77](data_compression/lz77.py)
+  * [Move To Front](data_compression/move_to_front.py)
   * [Peak Signal To Noise Ratio](data_compression/peak_signal_to_noise_ratio.py)
   * [Run Length Encoding](data_compression/run_length_encoding.py)
 
@@ -324,9 +326,11 @@
     * [From Sequence](data_structures/linked_list/from_sequence.py)
     * [Has Loop](data_structures/linked_list/has_loop.py)
     * [Is Palindrome](data_structures/linked_list/is_palindrome.py)
+    * [Kth Element From End](data_structures/linked_list/kth_element_from_end.py)
     * [Merge Sort Linked List](data_structures/linked_list/merge_sort_linked_list.py)
     * [Merge Two Lists](data_structures/linked_list/merge_two_lists.py)
     * [Middle Element Of Linked List](data_structures/linked_list/middle_element_of_linked_list.py)
+    * [Partition Linked List](data_structures/linked_list/partition_linked_list.py)
     * [Print Reverse](data_structures/linked_list/print_reverse.py)
     * [Reverse K Group](data_structures/linked_list/reverse_k_group.py)
     * [Rotate To The Right](data_structures/linked_list/rotate_to_the_right.py)
@@ -334,6 +338,7 @@
     * [Skip List](data_structures/linked_list/skip_list.py)
     * [Sorted Linked List](data_structures/linked_list/sorted_linked_list.py)
     * [Swap Nodes](data_structures/linked_list/swap_nodes.py)
+    * [Xor Linked List](data_structures/linked_list/xor_linked_list.py)
   * Queues
     * [Circular Queue](data_structures/queues/circular_queue.py)
     * [Circular Queue Linked List](data_structures/queues/circular_queue_linked_list.py)
diff --git a/data_structures/linked_list/xor_linked_list.py b/data_structures/linked_list/xor_linked_list.py
new file mode 100644
index 000000000000..3de6e12c910e
--- /dev/null
+++ b/data_structures/linked_list/xor_linked_list.py
@@ -0,0 +1,85 @@
+"""
+XOR Linked List implementation
+A memory-efficient doubly linked list that uses the XOR of node addresses.
+Each node stores one pointer that is the XOR of the previous and next node addresses.
+https://en.wikipedia.org/wiki/XOR_linked_list
+Example:
+>>> xor_list = XORLinkedList()
+>>> xor_list.insert(10)
+>>> xor_list.insert(20)
+>>> xor_list.insert(30)
+>>> xor_list.to_list()
+[10, 20, 30]
+"""
+
+from dataclasses import dataclass
+
+
+@dataclass
+class Node:
+    value: int
+    both: int = 0  # XOR of prev and next node IDs
+
+
+class XORLinkedList:
+    def __init__(self) -> None:
+        """Initializes an empty XOR Linked List."""
+        # Use 'Node | None' instead of 'Optional[Node]' (per ruff UP045)
+        self.head: Node | None = None
+        self.tail: Node | None = None
+        # id -> node map to simulate pointer references
+        self._nodes: dict[int, Node] = {}
+
+    def _xor(self, node_a: Node | None, node_b: Node | None) -> int:
+        """
+        Helper function to get the XOR of two node IDs (simulated addresses).
+        Names 'node_a' and 'node_b' are used for descriptive parameters.
+        """
+        id_a = id(node_a) if node_a else 0
+        id_b = id(node_b) if node_b else 0
+        return id_a ^ id_b
+
+    def insert(self, value: int) -> None:
+        """Inserts a value at the end of the list."""
+        node = Node(value)
+        self._nodes[id(node)] = node
+        node_id = id(node)
+
+        if self.head is None:
+            # If the list is empty, head and tail are the new node
+            self.head = self.tail = node
+        else:
+            # If the list is not empty, append to the tail
+            # The new node's pointer is just the ID of the old tail
+            node.both = id(self.tail)
+            if self.tail:  # Type checker guard
+                # The old tail's pointer must be updated to XOR
+                # its previous node ID with the new node's ID.
+                # self.tail.both was (prev_id ^ 0)
+                # self.tail.both becomes (prev_id ^ new_node_id)
+                self.tail.both ^= node_id
+            self.tail = node
+
+    def to_list(self) -> list[int]:
+        """Converts the XOR list to a standard Python list (forward traversal)."""
+        result = []
+        prev_id = 0
+        current = self.head
+        while current:
+            result.append(current.value)
+            # Find next node's ID:
+            # current.both = prev_id ^ next_id
+            # so, next_id = prev_id ^ current.both
+            current_id = id(current)
+            next_id = prev_id ^ current.both
+
+            # Move forward
+            prev_id = current_id
+            current = self._nodes.get(next_id)
+        return result
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()