# 1. Introduction

A common challenge when working with linked lists is cycle detection. A cycle in a linked list means that if you traverse the list indefinitely, you'll find yourself looping through the same set of nodes over and over again. Detecting such cycles is crucial for many algorithms to avoid infinite loops and potential system crashes.

# 2. Program Overview

Our program aims to detect a cycle in a given linked list. We will:

1. Define a Node class that represents each element in the linked list.

2. Create a LinkedList class with methods to:

- append data to the list.

- create_cycle for intentionally introducing a cycle for testing.

- detect_cycle which will identify if the list contains a cycle.

We'll employ Floyd’s cycle-finding algorithm, often termed as the "Tortoise and the Hare" approach. This technique uses two pointers that move through the list at different speeds.

# 3. Code Program

``````class Node:
def __init__(self, data):
"""Initialize node with data and next as None."""
self.data = data
self.next = None

def __init__(self):

def append(self, data):
new_node = Node(data)
return
while temp.next:
temp = temp.next
temp.next = new_node

def create_cycle(self, n):
"""Introduce a cycle in the linked list for testing purposes."""
return
while tail.next:
tail = tail.next
for i in range(n):
if node is None:
return
node = node.next
tail.next = node

def detect_cycle(self):
"""Use Floyd's cycle detection algorithm to identify a cycle."""
while hare and hare.next:
tortoise = tortoise.next
hare = hare.next.next
if tortoise == hare:
return True
return False

# Demonstration
llist.append(1)
llist.append(2)
llist.append(3)
llist.append(4)
llist.append(5)

print(llist.detect_cycle())  # False

llist.create_cycle(2)
print(llist.detect_cycle())  # True
``````

```False
True
```

# 4. Step By Step Explanation

1. The Node class represents individual items in our linked list. Each node has data and a reference to the next node.

2. In the LinkedList class, the append method is for adding data to the list. We traverse the list until we find a node with no next node and then add the new data there.

3. The create_cycle method introduces a cycle in our list intentionally by making the next of the tail nodes point back to some node in the list.

4. Our cycle detection relies on the detect_cycle method using the "Tortoise and the Hare" approach. If there's a cycle, the fast-moving hare will eventually catch up to the slower-moving tortoise, and they will both point to the same node. If they do, it confirms a cycle.