Detect if a Linked List is Circular in DSA Rust - Time & Space Complexity

Time Complexity: Detect if a Linked List is Circular

O(n)

Understanding Time Complexity

We want to understand how long it takes to check if a linked list loops back on itself.

How does the time needed grow as the list gets longer?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

fn is_circular(head: &Option>) -> bool {
    let mut slow = head.as_ref();
    let mut fast = head.as_ref();
    while let (Some(s), Some(f)) = (slow, fast) {
        fast = f.next.as_ref().and_then(|n| n.next.as_ref());
        slow = s.next.as_ref();
        if slow == fast {
            return true;
        }
    }
    false
}
    

This code uses two pointers moving at different speeds to detect a loop in the linked list.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Moving two pointers through the list nodes.
• How many times: Each pointer moves forward step by step until they meet or reach the end.

How Execution Grows With Input

As the list grows, the pointers move through more nodes, but the fast pointer moves twice as fast.

Input Size (n)	Approx. Operations
10	About 10 to 20 pointer moves
100	About 100 to 200 pointer moves
1000	About 1000 to 2000 pointer moves

Pattern observation: The number of steps grows roughly in a straight line with the list size.

Final Time Complexity

Time Complexity: O(n)

This means the time to detect a loop grows linearly with the number of nodes in the list.

Common Mistake

[X] Wrong: "The fast pointer makes this algorithm run twice as fast, so the time complexity is O(n/2)."

[OK] Correct: We drop constants in time complexity, so O(n/2) is the same as O(n). The fast pointer helps find the loop sooner but does not change the overall growth rate.

Interview Connect

Understanding this technique shows you can handle linked list problems efficiently, a common skill interviewers look for.

Self-Check

"What if we used only one pointer moving one step at a time? How would the time complexity change?"

Practice

1. What does it mean if a linked list is circular?

easy

A. The linked list has no nodes

B. The linked list contains only one node

C. The linked list nodes are sorted in ascending order

D. The last node points back to one of the previous nodes, forming a loop

Solution

1. Step 1: Understand linked list structure

   A linked list is a chain of nodes where each node points to the next node.

2. Step 2: Define circular linked list

   If the last node points back to any previous node, it creates a loop, making the list circular.

3. Final Answer:

   The last node points back to one of the previous nodes, forming a loop -> Option D

4. Quick Check:

   Circular linked list = last node points back [OK]

Hint: Circular means last node links back to earlier node [OK]

Common Mistakes:

• Thinking circular means sorted
• Confusing empty list with circular
• Assuming single node list is always circular

2. Which Rust code snippet correctly defines a singly linked list node struct?

easy

A. struct Node { value: i32, next: Option }

B. struct Node { value: i32, next: Node }

C. struct Node { value: i32, next: &Node }

D. struct Node { value: i32, next: Box<Node> }

Solution

1. Step 1: Understand Rust ownership for linked lists

   Rust requires using Option for next to allow nullable and heap allocation.

2. Step 2: Check each option

   struct Node { value: i32, next: Option } uses Option, which is correct. Others either lack Option or use references incorrectly.

3. Final Answer:

   struct Node { value: i32, next: Option } -> Option A

4. Quick Check:

   Use Option for next pointer in Rust [OK]

Hint: Use Option for next pointer in Rust [OK]

Common Mistakes:

• Using raw Node type for next causes infinite size error
• Using references without lifetimes
• Omitting Option for nullable next

3. Given the following Rust code to detect a circular linked list, what will be printed?

fn is_circular(head: &Option) -> bool {
    let mut slow = head.as_ref();
    let mut fast = head.as_ref();
    while let (Some(s), Some(f)) = (slow, fast) {
        fast = f.next.as_ref().and_then(|n| n.next.as_ref());
        slow = s.next.as_ref();
        if slow == fast {
            return true;
        }
    }
    false
}

// List: 1 -> 2 -> 3 -> 2 (loop back to node with value 2)
// Calling is_circular returns what?

medium

A. false

B. true

C. Compilation error

D. Infinite loop

Solution

1. Step 1: Understand Floyd's cycle detection

   Two pointers move at different speeds; if they meet, list is circular.

2. Step 2: Analyze given list and code

   List loops back from node 3 to node 2, so slow and fast pointers will meet, returning true.

3. Final Answer:

   true -> Option B

4. Quick Check:

   Floyd's algorithm detects loop = true [OK]

Hint: Floyd's cycle detection returns true if pointers meet [OK]

Common Mistakes:

• Confusing pointer movement speeds
• Not checking both pointers for null
• Assuming no loop when pointers meet

4. Identify the bug in this Rust function that tries to detect a circular linked list:

fn has_cycle(head: &Option) -> bool {
    let mut slow = head.as_ref();
    let mut fast = head.as_ref();
    while fast.is_some() && fast.unwrap().next.is_some() {
        slow = slow.unwrap().next.as_ref();
        fast = fast.unwrap().next.as_ref().unwrap().next.as_ref();
        if slow == fast {
            return true;
        }
    }
    false
}

medium

A. Function always returns false due to wrong loop condition

B. Pointers move at the same speed, so no cycle detection

C. Using unwrap() without checking can cause panic if null

D. Missing return type causes compilation error

Solution

1. Step 1: Check unwrap usage safety

   Using unwrap() without confirming Some can panic if null is encountered.

2. Step 2: Identify risk in loop

   fast.unwrap().next.as_ref().unwrap() assumes next exists, which may not be true at list end.

3. Final Answer:

   Using unwrap() without checking can cause panic if null -> Option C

4. Quick Check:

   Unsafe unwrap causes panic [OK]

Hint: Avoid unwrap without checking Option first [OK]

Common Mistakes:

• Ignoring unwrap panic risk
• Assuming pointers move same speed
• Not checking loop exit conditions

5. You have a linked list where the last node's next pointer is mistakenly set to itself, creating a single-node loop. How should you modify the Rust cycle detection function to correctly detect this case?

hard

A. Use a hash set to store visited nodes and detect repeats

B. Ignore cases where next points to itself, treat as non-circular

C. Only check if fast pointer reaches null to decide no cycle

D. Check if slow and fast pointers meet even if they start at the same node

Solution

1. Step 1: Understand single-node loop problem

   If a node points to itself, Floyd's algorithm may detect cycle, but edge cases can be tricky.

2. Step 2: Use hash set for robust detection

   Storing visited nodes in a hash set helps detect any repeated node, including self-loop cases.

3. Final Answer:

   Use a hash set to store visited nodes and detect repeats -> Option A

4. Quick Check:

   Hash set detects all cycles including self-loops [OK]

Hint: Use hash set to catch all loops including self-pointing nodes [OK]

Common Mistakes:

• Assuming Floyd's algorithm covers all edge cases
• Ignoring self-loop as cycle
• Not handling single-node circular lists