Detect Cycle in Linked List Floyd's Algorithm in DSA Go - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Floyd's Cycle Detection on a Linked List with a Cycle

What is the output of the following Go code that uses Floyd's algorithm to detect a cycle in a linked list?

DSA Go

package main
import "fmt"
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
}

func main() {
    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))
}

A runtime error

B true

C false

D compile error

💡 Hint

Remember that Floyd's algorithm uses two pointers moving at different speeds to detect cycles.

The code creates a linked list with a cycle starting at node with value 2. Floyd's algorithm detects this cycle by the slow and fast pointers meeting, so the output is true.

❓ Predict Output

intermediate

Output of Floyd's Algorithm on a Linked List without a Cycle

What will the following Go code print when checking a linked list with no cycle using Floyd's algorithm?

DSA Go

package main
import "fmt"
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
}

func main() {
    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 = nil // no cycle
    fmt.Println(hasCycle(n1))
}

A false

B true

C runtime error

D compile error

💡 Hint

If the fast pointer reaches the end of the list, there is no cycle.

Since the list ends with nil and no cycle is formed, the function returns false.

🔧 Debug

advanced

Identify the Error in Floyd's Cycle Detection Implementation

What error will the following Go code produce when trying to detect a cycle in a linked list?

DSA Go

package main
import "fmt"
type Node struct {
    val  int
    next *Node
}

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

func main() {
    fmt.Println(hasCycle(nil))
}

A compile error

B false

C true

D runtime panic: nil pointer dereference

💡 Hint

Check the order of conditions in the for loop to avoid accessing nil pointers.

The code checks fast.next before ensuring fast is not nil, causing a nil pointer dereference panic.

🧠 Conceptual

advanced

Why Does Floyd's Algorithm Use Two Pointers Moving at Different Speeds?

Why does Floyd's cycle detection algorithm use a slow pointer moving one step and a fast pointer moving two steps?

A To reverse the linked list during traversal

B To reduce the memory usage by storing fewer nodes

C To ensure the fast pointer eventually catches the slow pointer if a cycle exists

D To sort the linked list while detecting the cycle

💡 Hint

Think about how two pointers moving at different speeds behave in a cycle.

The fast pointer moves faster and will eventually meet the slow pointer inside the cycle, confirming its presence.

🚀 Application

expert

Find the Starting Node of the Cycle Using Floyd's Algorithm

Given a linked list with a cycle, which code snippet correctly finds the node where the cycle begins after detecting the cycle using Floyd's algorithm?

DSA Go

func detectCycleStart(head *Node) *Node {
    slow, fast := head, head
    for fast != nil && fast.next != nil {
        slow = slow.next
        fast = fast.next.next
        if slow == fast {
            // Find start of cycle
            slow = head
            for slow != fast {
                slow = slow.next
                fast = fast.next
            }
            return slow
        }
    }
    return nil
}

A The code correctly returns the node where the cycle starts

B The code returns nil even if a cycle exists

C The code causes an infinite loop when a cycle exists

D The code returns the last node before the cycle

💡 Hint

After detecting the cycle, resetting slow to head and moving both pointers one step at a time finds the cycle start.

Resetting slow to head and moving both pointers one step at a time makes them meet at the cycle start node.

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