Add Merge Sort Linked List algorithm

DIRECTORY.md

@@ -261,6 +261,7 @@
     * [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)
+    * [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)
     * [Print Reverse](data_structures/linked_list/print_reverse.py)

data_structures/linked_list/merge_sort_linked_list.py

@@ -0,0 +1,174 @@
+class Node:
+    """
+    A class representing a node in a linked list.
+
+    Attributes:
+        data (int): The data stored in the node.
+        next (Node | None): A reference to the next node in the linked list.
+
+    >>> head = Node(4)
+    >>> head.next = Node(2)
+    >>> head.next.next = Node(1)
+    >>> head.next.next.next = Node(3)
+    >>> sorted_head = merge_sort_linked_list(head)
+    >>> print_linked_list(sorted_head)
+    1 2 3 4
+    """
+
+    def __init__(self, data: int):
+        self.data = data
+        self.next: Node | None = None
+
+
+def get_middle(head: Node) -> Node:
+    """
+    Find the middle node of the linked list using the slow and fast pointer technique.
+
+    Parameters:
+        head: The head node of the linked list.
+
+    Returns:
+        The middle node of the linked list.
+
+    Example:
+    >>> head = Node(1)
+    >>> head.next = Node(2)
+    >>> head.next.next = Node(3)
+    >>> get_middle(head).data
+    2
+    """
+
+    if head is None:
+        return head
+
+    slow = head  # one node at a time
+    fast = head  # two nodes at a time
+    while fast.next and fast.next.next:
+        slow = slow.next
+        fast = fast.next.next
+    return slow
+
+
+def merge(left: Node | None, right: Node | None) -> Node | None:
+    """
+    Merge two sorted linked lists into one sorted linked list.
+
+    Parameters:
+        left: The head of the first sorted linked list.
+        right: The head of the second sorted linked list.
+
+    Returns:
+        The head of the merged sorted linked list.
+
+    Example:
+    >>> left = Node(1)
+    >>> left.next = Node(3)
+    >>> right = Node(2)
+    >>> right.next = Node(4)
+    >>> merged = merge(left, right)
+    >>> print_linked_list(merged)
+    1 2 3 4
+    """
+
+    if left is None:
+        return right
+    if right is None:
+        return left
+
+    if left.data <= right.data:
+        result = left
+        result.next = merge(left.next, right)
+    else:
+        result = right
+        result.next = merge(left, right.next)
+
+    return result
+
+
+def print_linked_list(head: Node | None) -> None:
+    """
+    Print the linked list in a single line.
+
+    Parameters:
+        head: The head node of the linked list.
+
+    Example:
+    >>> head = Node(1)
+    >>> head.next = Node(2)
+    >>> head.next.next = Node(3)
+    >>> print_linked_list(head)
+    1 2 3
+    """
+
+    current = head
+    first = True  # To avoid printing space before the first element
+    while current:
+        if not first:
+            print(" ", end="")
+        print(current.data, end="")
+        first = False
+        current = current.next
+    print()
+
+
+def merge_sort_linked_list(head: Node | None) -> Node | None:
+    """
+    Sort a linked list using the Merge Sort algorithm.
+
+    Parameters:
+        head: The head node of the linked list to be sorted.
+
+    Returns:
+        The head node of the sorted linked list.
+
+    Example:
+    >>> head = Node(4)
+    >>> head.next = Node(2)
+    >>> head.next.next = Node(1)
+    >>> head.next.next.next = Node(3)
+    >>> sorted_head = merge_sort_linked_list(head)
+    >>> print_linked_list(sorted_head)
+    1 2 3 4
+
+    >>> head = Node(1)
+    >>> head.next = Node(2)
+    >>> head.next.next = Node(3)
+    >>> head.next.next.next = Node(4)
+    >>> sorted_head = merge_sort_linked_list(head)
+    >>> print_linked_list(sorted_head)
+    1 2 3 4
+
+    >>> head = Node(10)
+    >>> head.next = Node(3)
+    >>> head.next.next = Node(5)
+    >>> head.next.next.next = Node(1)
+    >>> sorted_head = merge_sort_linked_list(head)
+    >>> print_linked_list(sorted_head)
+    1 3 5 10
+    """
+
+    # Base Case: 0 or 1 node
+    if head is None or head.next is None:
+        return head
+
+    # Split the linked list into two halves
+    middle = get_middle(head)
+    next_to_middle = middle.next
+    middle.next = None  # Split the list into two parts
+
+    left = merge_sort_linked_list(head)  # Sort left half
+    right = merge_sort_linked_list(next_to_middle)  # Sort right half
+
+    # Merge sorted halves
+    if left is None:
+        return right
+    if right is None:
+        return left
+    sorted_list = merge(left, right)
+    return sorted_list
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()