Add merge sort for linked list

data_structures/linked_list/merge_sort_linked_list.py

@@ -0,0 +1,143 @@
+"""
+Merge sort for a singly linked list.
+
+https://en.wikipedia.org/wiki/Merge_sort
+"""
+
+from data_structures.linked_list.singly_linked_list import Node
+
+
+def split_middle(node: Node) -> tuple[Node | None, Node | None]:
+    """
+    Find the middle node of a linked list using the fast/slow pointer method.
+
+    Returns a tuple containing:
+    - the node before the middle
+    - the middle node
+
+    >>> head = Node(1)
+    >>> head.next_node = Node(2)
+    >>> head.next_node.next_node = Node(3)
+    >>> head.next_node.next_node.next_node = Node(4)
+    >>> previous, middle = split_middle(head)
+    >>> previous is not None
+    True
+    >>> middle is not None
+    True
+    >>> previous.data
+    2
+    >>> middle.data
+    3
+    """
+    fast = slow = node
+    previous: Node | None = None
+
+    while fast and fast.next_node:
+        fast = fast.next_node.next_node if fast.next_node else None
+        previous = slow
+        slow = slow.next_node
+
+    return previous, slow
+
+
+def sort_list(head: Node | None) -> Node | None:
+    """
+    Sort a linked list using merge sort.
+
+    >>> head = Node(4)
+    >>> head.next_node = Node(2)
+    >>> head.next_node.next_node = Node(1)
+    >>> head.next_node.next_node.next_node = Node(3)
+    >>> sorted_head = sort_list(head)
+    >>> sorted_head is not None
+    True
+    >>> sorted_head.data
+    1
+    >>> sorted_head.next_node is not None
+    True
+    >>> sorted_head.next_node.data
+    2
+    >>> sorted_head.next_node.next_node is not None
+    True
+    >>> sorted_head.next_node.next_node.data
+    3
+    >>> sorted_head.next_node.next_node.next_node is not None
+    True
+    >>> sorted_head.next_node.next_node.next_node.data
+    4
+    >>> sort_list(None) is None
+    True
+    """
+    if head is None:
+        return head
+
+    if head.next_node is None:
+        return head
+
+    previous, middle_node = split_middle(head)
+    if previous:
+        previous.next_node = None
+
+    left = head
+    right = middle_node
+
+    left = sort_list(left)
+    right = sort_list(right)
+
+    dummy_head = current = Node(0)
+
+    while left and right:
+        if left.data < right.data:
+            current.next_node = left
+            left = left.next_node
+        else:
+            current.next_node = right
+            right = right.next_node
+
+        current = current.next_node
+
+    while left:
+        current.next_node = left
+        next_node = left.next_node
+        left.next_node = None
+        left = next_node
+        current = current.next_node
+
+    while right:
+        current.next_node = right
+        next_node = right.next_node
+        right.next_node = None
+        right = next_node
+        current = current.next_node
+
+    return dummy_head.next_node
+
+
+def test_merge_sort() -> None:
+    """
+    >>> test_merge_sort()
+    """
+    head = Node(4)
+    head.next_node = Node(2)
+    head.next_node.next_node = Node(5)
+    head.next_node.next_node.next_node = Node(1)
+    head.next_node.next_node.next_node.next_node = Node(3)
+
+    sorted_head = sort_list(head)
+
+    assert sorted_head is not None
+    assert sorted_head.data == 1
+    assert sorted_head.next_node is not None
+    assert sorted_head.next_node.data == 2
+    assert sorted_head.next_node.next_node is not None
+    assert sorted_head.next_node.next_node.data == 3
+    assert sorted_head.next_node.next_node.next_node is not None
+    assert sorted_head.next_node.next_node.next_node.data == 4
+    assert sorted_head.next_node.next_node.next_node.next_node is not None
+    assert sorted_head.next_node.next_node.next_node.next_node.data == 5
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()