Add Floyd's Cycle Detection Algorithm (#10833)

* Add Floyd's Cycle Detection Algorithm

* Add tests for add_node function

* Apply suggestions from code review

* Update floyds_cycle_detection.py

---------

Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>

data_structures/linked_list/floyds_cycle_detection.py

@@ -0,0 +1,150 @@
+"""
+Floyd's cycle detection algorithm is a popular algorithm used to detect cycles
+in a linked list. It uses two pointers, a slow pointer and a fast pointer,
+to traverse the linked list. The slow pointer moves one node at a time while the fast
+pointer moves two nodes at a time. If there is a cycle in the linked list,
+the fast pointer will eventually catch up to the slow pointer and they will
+meet at the same node. If there is no cycle, the fast pointer will reach the end of
+the linked list and the algorithm will terminate.
+
+For more information: https://en.wikipedia.org/wiki/Cycle_detection#Floyd's_tortoise_and_hare
+"""
+
+from collections.abc import Iterator
+from dataclasses import dataclass
+from typing import Any, Self
+
+
+@dataclass
+class Node:
+    """
+    A class representing a node in a singly linked list.
+    """
+
+    data: Any
+    next_node: Self | None = None
+
+
+@dataclass
+class LinkedList:
+    """
+    A class representing a singly linked list.
+    """
+
+    head: Node | None = None
+
+    def __iter__(self) -> Iterator:
+        """
+        Iterates through the linked list.
+
+        Returns:
+            Iterator: An iterator over the linked list.
+
+        Examples:
+        >>> linked_list = LinkedList()
+        >>> list(linked_list)
+        []
+        >>> linked_list.add_node(1)
+        >>> tuple(linked_list)
+        (1,)
+        """
+        visited = []
+        node = self.head
+        while node:
+            # Avoid infinite loop in there's a cycle
+            if node in visited:
+                return
+            visited.append(node)
+            yield node.data
+            node = node.next_node
+
+    def add_node(self, data: Any) -> None:
+        """
+        Adds a new node to the end of the linked list.
+
+        Args:
+            data (Any): The data to be stored in the new node.
+
+        Examples:
+        >>> linked_list = LinkedList()
+        >>> linked_list.add_node(1)
+        >>> linked_list.add_node(2)
+        >>> linked_list.add_node(3)
+        >>> linked_list.add_node(4)
+        >>> tuple(linked_list)
+        (1, 2, 3, 4)
+        """
+        new_node = Node(data)
+
+        if self.head is None:
+            self.head = new_node
+            return
+
+        current_node = self.head
+        while current_node.next_node is not None:
+            current_node = current_node.next_node
+
+        current_node.next_node = new_node
+
+    def detect_cycle(self) -> bool:
+        """
+        Detects if there is a cycle in the linked list using
+        Floyd's cycle detection algorithm.
+
+        Returns:
+            bool: True if there is a cycle, False otherwise.
+
+        Examples:
+        >>> linked_list = LinkedList()
+        >>> linked_list.add_node(1)
+        >>> linked_list.add_node(2)
+        >>> linked_list.add_node(3)
+        >>> linked_list.add_node(4)
+
+        >>> linked_list.detect_cycle()
+        False
+
+        # Create a cycle in the linked list
+        >>> linked_list.head.next_node.next_node.next_node = linked_list.head.next_node
+
+        >>> linked_list.detect_cycle()
+        True
+        """
+        if self.head is None:
+            return False
+
+        slow_pointer: Node | None = self.head
+        fast_pointer: Node | None = self.head
+
+        while fast_pointer is not None and fast_pointer.next_node is not None:
+            slow_pointer = slow_pointer.next_node if slow_pointer else None
+            fast_pointer = fast_pointer.next_node.next_node
+            if slow_pointer == fast_pointer:
+                return True
+
+        return False
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
+    linked_list = LinkedList()
+    linked_list.add_node(1)
+    linked_list.add_node(2)
+    linked_list.add_node(3)
+    linked_list.add_node(4)
+
+    # Create a cycle in the linked list
+    # It first checks if the head, next_node, and next_node.next_node attributes of the
+    # linked list are not None to avoid any potential type errors.
+    if (
+        linked_list.head
+        and linked_list.head.next_node
+        and linked_list.head.next_node.next_node
+    ):
+        linked_list.head.next_node.next_node.next_node = linked_list.head.next_node
+
+    has_cycle = linked_list.detect_cycle()
+    print(has_cycle)  # Output: True