# 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
class LinkedList:
def __init__(self):
"""Initialize linked list with head as None."""
self.head = None
def append(self, data):
"""Add data to the end of the linked list."""
new_node = Node(data)
if not self.head:
self.head = new_node
return
temp = self.head
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."""
if self.head is None:
return
tail = self.head
while tail.next:
tail = tail.next
node = self.head
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."""
tortoise = self.head
hare = self.head
while hare and hare.next:
tortoise = tortoise.next
hare = hare.next.next
if tortoise == hare:
return True
return False
# Demonstration
llist = LinkedList()
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
```

### Output:

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.

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