Detect Cycle in Linked List Floyd's Algorithm in DSA C - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main idea behind Floyd's Cycle Detection Algorithm in a linked list?

It uses two pointers moving at different speeds (slow and fast). If there is a cycle, the fast pointer will eventually meet the slow pointer inside the loop.

beginner

In Floyd's Algorithm, what speeds do the two pointers move at?

The slow pointer moves one step at a time, while the fast pointer moves two steps at a time.

intermediate

Why does the fast pointer eventually meet the slow pointer if a cycle exists?

Because the fast pointer moves faster inside the cycle, it will lap the slow pointer, causing them to meet at some node within the loop.

beginner

What does it mean if the fast pointer reaches a null pointer in Floyd's Algorithm?

It means the linked list has no cycle because the fast pointer reached the end of the list.

intermediate

How can you find the starting node of the cycle after detecting a cycle using Floyd's Algorithm?

After the slow and fast pointers meet, reset one pointer to the head. Then move both pointers one step at a time. The node where they meet again is the start of the cycle.

In Floyd's Cycle Detection Algorithm, what happens if the fast pointer reaches NULL?

A The linked list has no cycle

B The linked list has a cycle

C The slow pointer moves faster

D The algorithm fails

If the fast pointer reaches NULL, it means the list ends and there is no cycle.

What is the speed of the slow pointer in Floyd's Algorithm?

A Variable speed

B Two steps at a time

C One step at a time

D Three steps at a time

The slow pointer moves one node at a time.

Why does Floyd's Algorithm use two pointers with different speeds?

A To reverse the linked list

B To detect if pointers meet inside a cycle

C To sort the linked list

D To find the length of the list

Different speeds help detect cycles by checking if pointers meet.

After detecting a cycle, how do you find the cycle's starting node?

A Count nodes until the end

B Move fast pointer two steps until it reaches NULL

C Reverse the linked list

D Reset one pointer to head and move both one step until they meet

Resetting one pointer to head and moving both pointers one step finds the cycle start.

What is the time complexity of Floyd's Cycle Detection Algorithm?

A O(n)

B O(n^2)

C O(log n)

D O(1)

The algorithm runs in linear time, O(n), where n is the number of nodes.

Explain step-by-step how Floyd's Cycle Detection Algorithm works to detect a cycle in a linked list.

Think about how the pointers move and what their meeting means.

Describe how to find the starting node of a cycle after detecting it with Floyd's Algorithm.

Focus on pointer movement after detection.

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