Detect Cycle in Linked List Floyd's Algorithm in DSA C++ - Build from Scratch

Detect Cycle in Linked List using Floyd's Algorithm

📖 Scenario: Imagine you have a chain of connected train cars. Sometimes, the chain might loop back on itself, creating a cycle. We want to check if such a loop exists in our chain.

🎯 Goal: Build a simple linked list and use Floyd's cycle detection algorithm to find if there is a cycle in the list.

📋 What You'll Learn

Create a linked list with nodes containing integer values

Add a pointer to create a cycle in the linked list

Implement Floyd's cycle detection algorithm using two pointers

Print Cycle detected if a cycle exists, otherwise print No cycle

💡 Why This Matters

🌍 Real World

Cycle detection is important in network routing, detecting infinite loops in software, and verifying data structures.

💼 Career

Understanding cycle detection helps in debugging linked list problems and is a common interview question for software engineering roles.

1

Create a linked list with 5 nodes

Create a struct called Node with an int data and a Node* next. Then create 5 nodes named node1 to node5 with data values 10, 20, 30, 40, and 50 respectively. Link them in order so that node1.next = &node2, node2.next = &node3, and so on, ending with node5.next = nullptr.

DSA C++

// Define struct Node
// Create nodes node1 to node5 with data 10, 20, 30, 40, 50
// Link nodes in order
// Your code here

Hint

Remember to define the struct first, then create each node with the given data, and finally link them by setting the next pointers.

2

Create a cycle by linking node5 back to node3

Add a cycle by setting node5.next = &node3 to create a loop in the linked list.

DSA C++

struct Node {
    int data;
    Node* next;
};

Node node1 = {10, nullptr};
Node node2 = {20, nullptr};
Node node3 = {30, nullptr};
Node node4 = {40, nullptr};
Node node5 = {50, nullptr};

node1.next = &node2;
node2.next = &node3;
node3.next = &node4;
node4.next = &node5;
// Create a cycle by linking node5.next to node3
// Your code here

Hint

To create a cycle, point the last node's next to an earlier node in the list.

3

Implement Floyd's cycle detection algorithm

Create two pointers slow and fast starting at &node1. Use a while loop to move slow by one step (slow = slow->next) and fast by two steps (fast = fast->next->next) until fast or fast->next is nullptr or slow == fast. If slow == fast, set a boolean variable hasCycle to true, otherwise false.

DSA C++

struct Node {
    int data;
    Node* next;
};

Node node1 = {10, nullptr};
Node node2 = {20, nullptr};
Node node3 = {30, nullptr};
Node node4 = {40, nullptr};
Node node5 = {50, nullptr};

node1.next = &node2;
node2.next = &node3;
node3.next = &node4;
node4.next = &node5;
node5.next = &node3;

// Implement Floyd's cycle detection algorithm
// Your code here

Hint

Use two pointers moving at different speeds. If they meet, a cycle exists.

4

Print if cycle is detected or not

Use an if statement to print Cycle detected if hasCycle is true, otherwise print No cycle.

DSA C++

struct Node {
    int data;
    Node* next;
};

Node node1 = {10, nullptr};
Node node2 = {20, nullptr};
Node node3 = {30, nullptr};
Node node4 = {40, nullptr};
Node node5 = {50, nullptr};

node1.next = &node2;
node2.next = &node3;
node3.next = &node4;
node4.next = &node5;
node5.next = &node3;

Node* slow = &node1;
Node* fast = &node1;
bool hasCycle = false;

while (fast != nullptr && fast->next != nullptr) {
    slow = slow->next;
    fast = fast->next->next;
    if (slow == fast) {
        hasCycle = true;
        break;
    }
}

// Print the result
// Your code here

Hint

Use std::cout to print the message based on the hasCycle boolean.

Practice

1. What is the main purpose of Floyd's Cycle Detection Algorithm in a linked list?

easy

A. To find the middle element of the linked list

B. To sort the linked list in ascending order

C. To reverse the linked list

D. To detect if there is a cycle (loop) in the linked list

Solution

1. Step 1: Understand Floyd's Algorithm goal

   Floyd's Cycle Detection Algorithm is designed to check if a linked list contains a cycle, meaning a node points back to a previous node.

2. Step 2: Compare with other linked list operations

   Sorting, reversing, or finding the middle element are different operations and not the purpose of this algorithm.

3. Final Answer:

   To detect if there is a cycle (loop) in the linked list -> Option D

4. Quick Check:

   Cycle detection = Detect cycle [OK]

Hint: Floyd's algorithm finds loops, not sorting or reversing [OK]

Common Mistakes:

• Confusing cycle detection with sorting
• Thinking it finds the middle node
• Assuming it reverses the list

2. Which of the following correctly initializes the two pointers used in Floyd's Cycle Detection Algorithm in C++?

easy

A. ListNode* slow = head; ListNode* fast = head;

B. ListNode* slow = head->next; ListNode* fast = head;

C. ListNode* slow = nullptr; ListNode* fast = head;

D. ListNode* slow = head; ListNode* fast = head->next;

Solution

1. Step 1: Understand pointer initialization in Floyd's algorithm

   Both slow and fast pointers start at the head node to begin traversal.

2. Step 2: Check each option

   ListNode* slow = head; ListNode* fast = head; initializes both pointers at head, which is the standard approach. Other options start pointers differently, which can cause errors or miss cycles.

3. Final Answer:

   ListNode* slow = head; ListNode* fast = head; -> Option A

4. Quick Check:

   Both pointers start at head [OK]

Hint: Start both pointers at head for Floyd's algorithm [OK]

Common Mistakes:

• Starting fast pointer at head->next causes skipping
• Initializing slow as nullptr causes null errors
• Swapping slow and fast initialization

3. What will be the output of the following code snippet detecting a cycle in a linked list?

#include <iostream>

struct Node {
  int data;
  Node* next;
};

bool hasCycle(Node* head) {
  Node* slow = head;
  Node* fast = head;
  while (fast && fast->next) {
    slow = slow->next;
    fast = fast->next->next;
    if (slow == fast) return true;
  }
  return false;
}

int main() {
  Node a{1, nullptr};
  Node b{2, nullptr};
  Node c{3, nullptr};
  a.next = &b;
  b.next = &c;
  c.next = &b; // cycle here
  bool result = hasCycle(&a);
  std::cout << (result ? "Cycle detected" : "No cycle") << std::endl;
  return 0;
}

medium

A. No cycle

B. Cycle detected

C. Compilation error

D. Runtime error

Solution

1. Step 1: Analyze linked list structure

   Nodes a, b, c are linked as a->b->c, and c points back to b, creating a cycle.

2. Step 2: Trace Floyd's algorithm behavior

   Slow and fast pointers will eventually meet inside the cycle, so hasCycle returns true.

3. Final Answer:

   Cycle detected -> Option B

4. Quick Check:

   Cycle exists, so output is "Cycle detected" [OK]

Hint: If a node points back, Floyd detects cycle [OK]

Common Mistakes:

• Ignoring the cycle created by c.next = &b
• Assuming no cycle because list looks linear
• Confusing output with compilation or runtime errors

4. Identify the bug in this Floyd's Cycle Detection code snippet:

bool detectCycle(Node* head) {
  Node* slow = head;
  Node* fast = head;
  while (fast->next && fast->next->next) {
    slow = slow->next;
    fast = fast->next->next;
    if (slow == fast) return true;
  }
  return false;
}

medium

A. The return type should be void, not bool

B. Pointers slow and fast should start at different nodes

C. The while condition should check if fast is not nullptr before fast->next

D. The comparison if (slow == fast) should be outside the loop

Solution

1. Step 1: Check while loop condition safety

   The code checks fast->next and fast->next->next but does not check if fast itself is nullptr, risking null pointer access.

2. Step 2: Correct condition order

   Proper check is to ensure fast is not nullptr before accessing fast->next to avoid runtime errors.

3. Final Answer:

   The while condition should check if fast is not nullptr before fast->next -> Option C

4. Quick Check:

   Check fast != nullptr before fast->next [OK]

Hint: Always check pointer not null before accessing members [OK]

Common Mistakes:

• Skipping null check on fast pointer
• Starting pointers at different nodes unnecessarily
• Moving comparison outside loop causing infinite loop

5. Given a linked list where a cycle exists, how can Floyd's algorithm be extended to find the exact node where the cycle begins?

hard

A. After detecting the cycle, reset one pointer to head and move both pointers one step at a time until they meet at the cycle start.

B. Count the number of nodes in the list and divide by two to find the cycle start.

C. Use a hash set to store visited nodes and find the first repeated node.

D. Reverse the linked list and check where the reversal breaks to find the cycle start.

Solution

1. Step 1: Detect cycle using Floyd's algorithm

   First, detect the cycle by moving slow and fast pointers until they meet inside the cycle.

2. Step 2: Find cycle start node

   Reset one pointer to head, then move both pointers one step at a time; their meeting point is the cycle start node.

3. Final Answer:

   After detecting the cycle, reset one pointer to head and move both pointers one step at a time until they meet at the cycle start. -> Option A

4. Quick Check:

   Reset pointer + move stepwise = cycle start [OK]

Hint: Reset pointer to head after detection, move both stepwise [OK]

Common Mistakes:

• Trying to find cycle start by counting nodes
• Using extra memory like hash sets (not Floyd's method)
• Reversing list which breaks structure