Detect Cycle in Linked List Floyd's Algorithm in DSA Go - 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 job is to detect if such a cycle exists.

🎯 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 nodes containing integer values

Add a cycle by linking the last node to one of the previous nodes

Implement Floyd's Cycle Detection Algorithm using two pointers

Print true if a cycle is detected, otherwise false

💡 Why This Matters

🌍 Real World

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

💼 Career

Understanding cycle detection algorithms is essential for software engineers working with linked data, debugging, and optimizing code.

1

Create a linked list with nodes

Create a linked list with nodes containing values 3, 2, 0, and -4 in that order. Define a struct called ListNode with fields Val int and Next *ListNode. Create variables head, second, third, and fourth for the nodes and link them sequentially.

DSA Go

// Define ListNode struct and create linked list nodes
// Your code here

Hint

Define the node structure first. Then create each node and link them using the Next pointer.

2

Create a cycle in the linked list

Create a cycle by setting the Next pointer of the fourth node to point back to the second node.

DSA Go

package main

import "fmt"

type ListNode struct {
    Val  int
    Next *ListNode
}

func main() {
    head := &ListNode{Val: 3}
    second := &ListNode{Val: 2}
    third := &ListNode{Val: 0}
    fourth := &ListNode{Val: -4}

    head.Next = second
    second.Next = third
    third.Next = fourth
    fourth.Next = nil

    // Create a cycle by linking fourth node to second node
    // Your code here
}

Hint

Set the Next of the last node to the second node to form a loop.

3

Implement Floyd's Cycle Detection Algorithm

Implement Floyd's Cycle Detection Algorithm using two pointers named slow and fast. Initialize both to head. Move slow by one step and fast by two steps in a loop. If fast or fast.Next becomes nil, break and conclude no cycle. If slow equals fast at any point, break and conclude cycle detected. Store the result in a boolean variable called hasCycle.

DSA Go

    slow := head
    fast := head
    hasCycle := false
    for fast != nil && fast.Next != nil {
        slow = slow.Next
        fast = fast.Next.Next
        if slow == fast {
            hasCycle = true
            break
        }
    }

Hint

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

4

Print the result of cycle detection

Print the value of the boolean variable hasCycle to display true if a cycle is detected or false if not.

DSA Go

package main

import "fmt"

type ListNode struct {
    Val  int
    Next *ListNode
}

func main() {
    head := &ListNode{Val: 3}
    second := &ListNode{Val: 2}
    third := &ListNode{Val: 0}
    fourth := &ListNode{Val: -4}

    head.Next = second
    second.Next = third
    third.Next = fourth
    fourth.Next = second

    slow := head
    fast := head
    hasCycle := false

    for fast != nil && fast.Next != nil {
        slow = slow.Next
        fast = fast.Next.Next
        if slow == fast {
            hasCycle = true
            break
        }
    }

    // Print the result
    // Your code here
}

Hint

Use fmt.Println(hasCycle) to print the result.

Practice

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

easy

A. Reverse the linked list and check if it matches the original

B. Count the number of nodes and check if it exceeds a limit

C. Use two pointers moving at different speeds to detect a cycle

D. Use a hash map to store visited nodes

Solution

1. Step 1: Understand Floyd's Algorithm concept

   It uses two pointers, one moving one step at a time (slow), and another moving two steps at a time (fast).

2. Step 2: Detect cycle by pointer meeting

   If the fast pointer meets the slow pointer, it means there is a cycle in the linked list.

3. Final Answer:

   Use two pointers moving at different speeds to detect a cycle -> Option C

4. Quick Check:

   Two pointers at different speeds = cycle detection [OK]

Hint: Two pointers at different speeds detect cycle fast [OK]

Common Mistakes:

• Thinking counting nodes detects cycle
• Assuming reversing list helps detect cycle
• Using extra memory like hash map is not Floyd's method

2. Which of the following Go code snippets correctly initializes the two pointers for Floyd's cycle detection in a linked list named head?

easy

A. slow, fast := head, head

B. slow, fast := head.next, head.next.next

C. slow, fast := head, head.next

D. slow, fast := nil, head

Solution

1. Step 1: Initialize both pointers at head

   Floyd's algorithm starts both slow and fast pointers at the head node.

2. Step 2: Move pointers inside loop, not at initialization

   Moving fast or slow pointer ahead at initialization can skip nodes or cause errors.

3. Final Answer:

   slow, fast := head, head -> Option A

4. Quick Check:

   Both pointers start at head [OK]

Hint: Start both pointers at head before loop [OK]

Common Mistakes:

• Starting fast pointer ahead causing nil pointer errors
• Initializing slow pointer ahead skipping first node
• Setting slow pointer to nil initially

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

type Node struct {
  val  int
  next *Node
}

func hasCycle(head *Node) bool {
  slow, fast := head, head
  for fast != nil && fast.next != nil {
    slow = slow.next
    fast = fast.next.next
    if slow == fast {
      return true
    }
  }
  return false
}

// Linked list setup
n1 := &Node{val: 1}
n2 := &Node{val: 2}
n3 := &Node{val: 3}
n4 := &Node{val: 4}
n1.next = n2
n2.next = n3
n3.next = n4
n4.next = n2 // cycle here

fmt.Println(hasCycle(n1))

medium

A. true

B. false

C. runtime error

D. infinite loop

Solution

1. Step 1: Analyze linked list structure

   The list nodes are connected 1->2->3->4, and 4 points back to 2, creating a cycle.

2. Step 2: Trace Floyd's algorithm behavior

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

3. Final Answer:

   true -> Option A

4. Quick Check:

   Cycle exists, so output is true [OK]

Hint: Cycle means pointers meet, so return true [OK]

Common Mistakes:

• Assuming no cycle because list looks linear
• Expecting false without tracing pointers
• Confusing cycle detection with list length

4. Identify the bug in this Go code snippet for detecting a cycle in a linked list:

func hasCycle(head *Node) bool {
  slow, fast := head, head
  for fast != nil {
    slow = slow.next
    fast = fast.next.next
    if slow == fast {
      return true
    }
  }
  return false
}

medium

A. The slow pointer should move two steps instead of one

B. The loop condition should check fast.next != nil to avoid nil pointer dereference

C. The fast pointer should move one step instead of two

D. The function should return false inside the loop when pointers don't meet

Solution

1. Step 1: Check loop condition safety

   The loop only checks fast != nil, but fast.next could be nil causing fast.next.next to panic.

2. Step 2: Correct loop condition

   Loop should check both fast != nil and fast.next != nil to safely move fast pointer two steps.

3. Final Answer:

   The loop condition should check fast.next != nil to avoid nil pointer dereference -> Option B

4. Quick Check:

   Check fast and fast.next != nil before moving fast [OK]

Hint: Always check fast.next != nil before fast.next.next [OK]

Common Mistakes:

• Ignoring fast.next nil check causing runtime panic
• Moving slow pointer two steps incorrectly
• Returning false too early inside loop

5. Given a linked list where the cycle starts at node with value 3, how can Floyd's algorithm be extended to find the exact node where the cycle begins?

hard

A. Count nodes until pointers meet and return the count as cycle start position

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

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

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

Solution

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

   First, detect if a cycle exists by moving slow and fast pointers until they meet.

2. Step 2: Find cycle start node

   Reset one pointer to head, then move both pointers one step at a time; the node where they meet is the cycle start.

3. Final Answer:

   After detecting the cycle, reset one pointer to head and move both one step until they meet at cycle start -> Option D

4. Quick Check:

   Reset pointer + move one step = cycle start [OK]

Hint: Reset pointer to head after cycle detection to find start [OK]

Common Mistakes:

• Trying to count nodes instead of resetting pointer
• Using extra memory instead of pointer method
• Reversing list which breaks structure