feat(data-structures, linked-lists, remove cycle): utilities to detect and remove cycles

datastructures/linked_lists/__init__.py

@@ -2,6 +2,12 @@
 from abc import ABCMeta, abstractmethod
 
 from datastructures.linked_lists.exceptions import EmptyLinkedList
+from datastructures.linked_lists.linked_list_utils import (
+    has_cycle,
+    detect_node_with_cycle,
+    cycle_length,
+    remove_cycle,
+)
 
 T = TypeVar("T")
 
@@ -379,14 +385,7 @@ def has_cycle(self):
         :return: True if there is a cycle, False otherwise
         :rtype: bool
         """
-        fast_pointer = slow_pointer = self.head
-        while fast_pointer and slow_pointer and fast_pointer.next:
-            fast_pointer = fast_pointer.next.next
-            slow_pointer = slow_pointer.next
-
-            if slow_pointer == fast_pointer:
-                return True
-        return False
+        return has_cycle(self.head)
 
     def cycle_length(self) -> int:
         """
@@ -395,105 +394,25 @@ def cycle_length(self) -> int:
         Returns:
             int: length of the cycle or number of nodes in the cycle
         """
-        if not self.head:
-            return 0
-        slow_pointer = fast_pointer = self.head
-
-        while fast_pointer and fast_pointer.next:
-            slow_pointer = slow_pointer.next
-            fast_pointer = fast_pointer.next.next
-
-            # Cycle detected
-            if slow_pointer is fast_pointer:
-                length = 1
-                # Move slow pointer by one step to start counting
-                slow_pointer = slow_pointer.next
-
-                # Continue moving the slow pointer until it meets the fast pointer again
-                while slow_pointer != fast_pointer:
-                    length += 1
-                    slow_pointer = slow_pointer.next
-
-                return length
-
-        return 0
+        return cycle_length(self.head)
 
     def detect_node_with_cycle(self) -> Optional[Node]:
         """
         Detects the node with a cycle and returns it
         """
-        if not self.has_cycle():
-            return None
-        else:
-            slow_pointer = fast_pointer = self.head
-
-            while fast_pointer and slow_pointer and fast_pointer.next:
-                fast_pointer = fast_pointer.next.next
-                slow_pointer = slow_pointer.next
-
-                if slow_pointer == fast_pointer:
-                    break
-            else:
-                return None
-
-            while self.head != slow_pointer:
-                slow_pointer = slow_pointer.next
-                self.head = self.head.next
-            return self.head
+        return detect_node_with_cycle(self.head)
 
-    def remove_cycle(self):
+    def remove_cycle(self) -> Optional[Node]:
         """
         Removes cycle if there exists. This will use the same concept as has_cycle method to check if there is a loop
         and remove the cycle
-        if one is found.
-        1) Detect Loop using Floyd’s Cycle detection algo and get the pointer to a loop node.
-        2) Count the number of nodes in loop. Let the count be k.
-        3) Fix one pointer to the head and another to kth node from head.
-        4) Move both pointers at the same pace, they will meet at loop starting node.
-        5) Get pointer to the last node of loop and make next of it as NULL.
-        :return: True if the cycle has been removed, False otherwise
-        :rtype: bool
+        Returns:
+            Node: head node with cycle removed
         """
-        fast_pointer = slow_pointer = self.head
-
-        while fast_pointer and slow_pointer and fast_pointer.next:
-            fast_pointer = fast_pointer.next.next
-            slow_pointer = slow_pointer.next
-
-            if slow_pointer == fast_pointer:
-                pointer_1 = pointer_2 = slow_pointer
-
-                # Count the number of nodes in loop
-                k = 1
-                while pointer_1.next != pointer_2:
-                    pointer_1 = pointer_1.next
-                    k += 1
-
-            # Fix one pointer to head
-            pointer_1 = self.head
-
-            # And the other pointer to k nodes after head
-            pointer_2 = self.head
-            for _ in range(k):
-                pointer_2 = pointer_2.next
-
-            # Move both pointers at the same place
-            # they will meet at loop starting node
-            while pointer_2 != pointer_1:
-                pointer_1 = pointer_1.next
-                pointer_2 = pointer_2.next
-
-            # Get pointer to the last node
-            pointer_2 = pointer_2.next
-            while pointer_2.next != pointer_1:
-                pointer_2 = pointer_2.next
-
-            # Set the next node of the loop ending node
-            # to fix the loop
-            pointer_2.next = None
-            return True
+        if not self.head or not self.head.next:
+            return self.head
 
-        return False
+        return remove_cycle(self.head)
 
     @abstractmethod
     def alternate_split(self):

datastructures/linked_lists/linked_list_utils.py

@@ -1,4 +1,4 @@
-from typing import Optional
+from typing import Optional, Callable, Any
 from datastructures.linked_lists import Node
 
 
@@ -19,3 +19,157 @@ def find_middle_node(head: Optional[Node]) -> Optional[Node]:
         fast_pointer = fast_pointer.next.next
 
     return slow_pointer
+
+
+def has_cycle(
+    head: Optional[Node], func: Optional[Callable[[Node, Node], Any]] = None
+) -> bool:
+    f"""
+    Checks if a given linked list has a cycle if a head node is provided. A cycle is when a linked list node can be
+    reached again after traversing the entire linked list
+    Args:
+        head(Node): head node of a linked list
+        func(Callable): An optional callable function that if passed in will be executed
+    Returns:
+        bool: True if there is a cycle, False otherwise
+    """
+    if not head or not head.next:
+        return False
+
+    fast_pointer, slow_pointer = head, head
+    while fast_pointer and fast_pointer.next:
+        slow_pointer = slow_pointer.next
+        fast_pointer = fast_pointer.next.next
+
+        if slow_pointer is fast_pointer:
+            # do something after detecting cycle passing in the two nodes
+            if func:
+                func(slow_pointer, fast_pointer)
+            return True
+    return False
+
+
+def cycle_length(head: Optional[Node]) -> int:
+    """
+    Determines the length of the cycle in a linked list if it has one. The length of the cycle is the number
+    of nodes that are 'caught' in the cycle
+    Args:
+        head(Node): head node of linked list
+    Returns:
+        int: length of the cycle or number of nodes in the cycle
+    """
+    if not head:
+        return 0
+    slow_pointer = fast_pointer = head
+
+    while fast_pointer and fast_pointer.next:
+        slow_pointer = slow_pointer.next
+        fast_pointer = fast_pointer.next.next
+
+        # Cycle detected
+        if slow_pointer is fast_pointer:
+            length = 1
+            # Move slow-pointer by one step to start counting
+            slow_pointer = slow_pointer.next
+
+            # Continue moving the slow pointer until it meets the fast pointer again
+            while slow_pointer is not fast_pointer:
+                length += 1
+                slow_pointer = slow_pointer.next
+
+            return length
+    return 0
+
+
+def detect_node_with_cycle(head: Optional[Node]) -> Optional[Node]:
+    """
+    Detects a node with a cycle in a Linked List and returns it. The node with a cycle is the entry point of the loop
+    Args:
+        head(Node): head node of a linked list
+    Returns:
+        Node: node with a cycle if the linked list has a cycle
+    """
+    slow_pointer = fast_pointer = head
+
+    while fast_pointer and slow_pointer and fast_pointer.next:
+        fast_pointer = fast_pointer.next.next
+        slow_pointer = slow_pointer.next
+
+        if slow_pointer == fast_pointer:
+            break
+    else:
+        return None
+
+    current = head
+    while current is not slow_pointer:
+        slow_pointer = slow_pointer.next
+        current = current.next
+    return current
+
+
+def remove_cycle(head: Optional[Node]) -> Optional[Node]:
+    """
+    Removes cycle from a linked list given the head node
+    Args:
+        head(Node): head node of a linked list
+    Returns:
+        Node: head node without the cycle
+    """
+    # This is the entry point of the cycle
+    node_with_cycle = detect_node_with_cycle(head)
+
+    # If there is no node with a cycle, return the head node as is
+    if not node_with_cycle:
+        return head
+
+    # Now, with the node with the cycle, we set a current pointer that will move a node at a time, until its next pointer
+    # points back to the fixed pointer
+    current = node_with_cycle
+    fixed_pointer = node_with_cycle
+
+    # Move the pointer on this current until the next pointer reaches the fixed pointer
+    while current.next is not fixed_pointer:
+        current = current.next
+
+    # Remove the cycle by setting the next to None
+    current.next = None
+
+    return head
+
+def remove_nth_from_end(head: Optional[Node], n: int) -> Optional[Node]:
+    """
+    Removes the nth node from a linked list from the head given the head of the linked list and the position from the
+    end of the linked list to remove.
+    Args:
+        head(Node): head node of linkedlist
+        n(int): the position of the last node from the tail in the linked list to remove
+    Returns:
+        Node: head node of modified linked list
+    """
+    if not head:
+        return head
+
+    # Initialize two pointers, both starting at the head node
+    fast = slow = head
+
+    # Move the fast pointer until it reaches position n in the linked list
+    for _ in range(n):
+        fast = fast.next
+
+    # If there is no node at this pointers position, then we have reached the end of the linked list and we return the
+    # next node from the head. This means, we are removing the head node
+    if not fast:
+        return head.next
+
+    # Move the fast pointer, until it reaches the end of the linked list and until the slow pointer reaches n nodes from
+    # the end of the linked list
+    while fast.next:
+        fast = fast.next
+        slow = slow.next
+
+    # Set the next pointer of the node at the slow pointer's position to the next node's next pointer, removing the node in the middle
+    slow.next = slow.next.next
+
+    # Return the modified head node of the linked list with the node removed
+    return head
+