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 are working with a train track system represented as a linked list of stations. Sometimes, the track loops back creating a cycle. Your task is to detect if such a cycle exists in the track.

🎯 Goal: Build a linked list and use Floyd's Cycle Detection Algorithm to find out if there is a cycle in the list.

📋 What You'll Learn

Create a linked list with given nodes

Add a pointer to create a cycle at a specified position

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

Detecting cycles in linked lists is important in systems like train track management, network routing, and memory management to avoid infinite loops or repeated processing.

💼 Career

Understanding cycle detection is useful for software engineers working with linked data structures, debugging memory leaks, or designing efficient algorithms.

1

Create the linked list nodes

Create a struct called Node with an integer data and a pointer next. Then create 5 nodes with data values 10, 20, 30, 40, and 50 linked in order.

DSA C

// Define struct Node and create 5 linked nodes with data 10, 20, 30, 40, 50
// Your code here

Hint

Remember to link each node's next pointer to the next node.

2

Create a cycle in the linked list

Add code to make the next pointer of the last node point to the third node to create a cycle.

DSA C

#include 
#include 

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

int main() {
    Node* head = (Node*)malloc(sizeof(Node));
    Node* second = (Node*)malloc(sizeof(Node));
    Node* third = (Node*)malloc(sizeof(Node));
    Node* fourth = (Node*)malloc(sizeof(Node));
    Node* fifth = (Node*)malloc(sizeof(Node));

    head->data = 10;
    head->next = second;

    second->data = 20;
    second->next = third;

    third->data = 30;
    third->next = fourth;

    fourth->data = 40;
    fourth->next = fifth;

    fifth->data = 50;
    fifth->next = NULL;

    // Make the last node point to the third node to create a cycle
    // Your code here

    return 0;
}

Hint

Set fifth->next equal to third to create the cycle.

3

Implement Floyd's Cycle Detection Algorithm

Create two pointers slow and fast starting at head. Move slow by one step and fast by two steps in a loop. If they meet, a cycle exists. If fast or fast->next becomes NULL, no cycle exists.

DSA C

#include 
#include 

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

int main() {
    Node* head = (Node*)malloc(sizeof(Node));
    Node* second = (Node*)malloc(sizeof(Node));
    Node* third = (Node*)malloc(sizeof(Node));
    Node* fourth = (Node*)malloc(sizeof(Node));
    Node* fifth = (Node*)malloc(sizeof(Node));

    head->data = 10;
    head->next = second;

    second->data = 20;
    second->next = third;

    third->data = 30;
    third->next = fourth;

    fourth->data = 40;
    fourth->next = fifth;

    fifth->data = 50;
    fifth->next = third; // cycle created here

    Node* slow = head;
    Node* fast = head;

    // Your code here

    return 0;
}

Hint

Use a while loop to move slow by one and fast by two steps. Check if they meet.

4

Print the result of cycle detection

Print Cycle detected if cycle_found is 1, otherwise print No cycle.

DSA C

#include 
#include 

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

int main() {
    Node* head = (Node*)malloc(sizeof(Node));
    Node* second = (Node*)malloc(sizeof(Node));
    Node* third = (Node*)malloc(sizeof(Node));
    Node* fourth = (Node*)malloc(sizeof(Node));
    Node* fifth = (Node*)malloc(sizeof(Node));

    head->data = 10;
    head->next = second;

    second->data = 20;
    second->next = third;

    third->data = 30;
    third->next = fourth;

    fourth->data = 40;
    fourth->next = fifth;

    fifth->data = 50;
    fifth->next = third; // cycle created here

    Node* slow = head;
    Node* fast = head;

    int cycle_found = 0;
    while (fast != NULL && fast->next != NULL) {
        slow = slow->next;
        fast = fast->next->next;
        if (slow == fast) {
            cycle_found = 1;
            break;
        }
    }

    // Print the result
    // Your code here

    return 0;
}

Hint

Use printf to print the message based on cycle_found.

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

C. To reverse the linked list

D. To sort the linked list in ascending order

Solution

1. Step 1: Understand Floyd's Algorithm goal

   Floyd's Cycle Detection Algorithm is designed to find if a linked list has a cycle or loop.

2. Step 2: Compare with other linked list operations

   Sorting, reversing, or finding the middle element are different operations and not related to cycle detection.

3. Final Answer:

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

4. Quick Check:

   Cycle detection = Detect cycle [OK]

Hint: Floyd's algorithm is famous for cycle detection [OK]

Common Mistakes:

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

2. Which of the following is the correct way to initialize the two pointers used in Floyd's Cycle Detection Algorithm in C?

easy

A. Node *slow = head; Node *fast = head->next;

B. Node *slow = NULL; Node *fast = head;

C. Node *slow = head->next; Node *fast = head->next->next;

D. Node *slow = head; Node *fast = head;

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 options for correct initialization

   Node *slow = head; Node *fast = head; initializes both pointers at head, which is the standard approach.

3. Final Answer:

   Node *slow = head; Node *fast = head; -> Option D

4. Quick Check:

   Both pointers start at head [OK]

Hint: Both pointers start at head node in Floyd's algorithm [OK]

Common Mistakes:

• Starting fast pointer ahead of slow incorrectly
• Initializing slow as NULL
• Skipping initialization of one pointer

3. What will be the output of the following C code snippet using Floyd's algorithm on a linked list with a cycle?

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

int detectCycle(Node *head) {
  Node *slow = head, *fast = head;
  while (fast && fast->next) {
    slow = slow->next;
    fast = fast->next->next;
    if (slow == fast) return 1;
  }
  return 0;
}

// Assume linked list has a cycle
printf("%d", detectCycle(head));

medium

A. 1

B. 0

C. Compilation error

D. Infinite loop

Solution

1. Step 1: Analyze the detectCycle function logic

   The function moves slow pointer by one and fast pointer by two nodes. If they meet, it returns 1 indicating a cycle.

2. Step 2: Given the list has a cycle, pointers will meet

   Since the list has a cycle, slow and fast pointers will eventually meet, so function returns 1.

3. Final Answer:

   1 -> Option A

4. Quick Check:

   Cycle present = return 1 [OK]

Hint: Cycle means slow and fast pointers meet, return 1 [OK]

Common Mistakes:

• Assuming function returns 0 for cycle
• Thinking code causes infinite loop
• Confusing return values

4. Identify the bug in this Floyd's cycle detection code snippet:

int detectCycle(Node *head) {
  Node *slow = head, *fast = head;
  while (fast != NULL && fast->next != NULL) {
    slow = slow->next;
    fast = fast->next;
    if (slow == fast) return 1;
    fast = fast->next;
  }
  return 0;
}

medium

A. fast pointer moves two steps but not checked for NULL before second move

B. slow pointer moves two steps instead of one

C. fast pointer moves only one step instead of two

D. slow pointer is not initialized properly

Solution

1. Step 1: Analyze pointer movements in the loop

   Slow moves one step, fast moves one step, then checks if slow == fast, before the second fast move.

2. Step 2: Problem with check timing

   In Floyd's algorithm, fast should move two steps before the cycle check. Here, the check occurs after fast has moved only one step, and the second fast move is done without checking if fast->next is NULL, which can cause a NULL pointer dereference.

3. Final Answer:

   fast pointer moves two steps but not checked for NULL before second move -> Option A

4. Quick Check:

   Second fast move lacks NULL check [OK]

Hint: Fast pointer must complete two steps with NULL checks before cycle check [OK]

Common Mistakes:

• Checking cycle after fast's first step only
• Confusing slow and fast pointer steps
• Not initializing pointers correctly

5. You have a linked list where a cycle exists. After detecting the cycle using Floyd's algorithm, how can you find the starting node of the cycle?

hard

A. Move fast pointer two steps and slow pointer one step until they meet again

B. Count the number of nodes in the list and divide by two

C. Reset slow pointer to head, then move slow and fast one step at a time until they meet

D. Reverse the linked list and check for cycle again

Solution

1. Step 1: Detect cycle and pointers meet inside the loop

   Floyd's algorithm detects cycle when slow and fast pointers meet inside the loop.

2. Step 2: Reset slow to head and move both pointers one step at a time

   Reset slow to head, then move slow and fast one step each until they meet again; this meeting point is the cycle start.

3. Final Answer:

   Reset slow pointer to head, then move slow and fast one step at a time until they meet -> Option C

4. Quick Check:

   Reset slow + move both one step = cycle start [OK]

Hint: Reset slow to head, move both pointers stepwise to find cycle start [OK]

Common Mistakes:

• Moving fast pointer two steps again
• Trying to count nodes to find cycle start
• Reversing list to detect cycle start