Collect Nodes of a Cycle in a Linked List

Unit 6 Session 2 (Click for link to problem statements)

Problem Highlights

• 💡 Difficulty: Medium
• ⏰ Time to complete: 20 mins
• 🛠️ Topics: Linked Lists, Cycle Detection

1: U-nderstand

Understand what the interviewer is asking for by using test cases and questions about the problem.

• Established a set (2-3) of test cases to verify their own solution later.
• Established a set (1-2) of edge cases to verify their solution handles complexities.
• Have fully understood the problem and have no clarifying questions.
• Have you verified any Time/Space Constraints for this problem?

• Q: What if there is no cycle?
  • A: Return an empty list.

HAPPY CASE
Input: 1 -> 2 -> 3 -> 4 -> 2 (Cycle starting at 2)
Output: [2, 3, 4]
Explanation: The cycle consists of the nodes starting from 2 to 4 and back to 2.

EDGE CASE
Input: 1 -> 2 -> 3 -> 4 -> 5 (No cycle)
Output: []
Explanation: There is no cycle, so the output is an empty list.

2: M-atch

Match what this problem looks like to known categories of problems, e.g. Linked List or Dynamic Programming, and strategies or patterns in those categories.

This is a classic problem of cycle detection in a linked list, specifically identifying the nodes that make up the cycle.

3: P-lan

Plan the solution with appropriate visualizations and pseudocode.

General Idea: Detect a cycle using the two-pointer technique (Floyd's Cycle Detection), then identify and collect the cycle nodes.

1) Start with two pointers, slow and fast, to detect a cycle.
2) If a cycle is detected, find the start of the cycle.
3) Traverse the cycle, collecting node values until the start is reached again.
4) Return the list of cycle nodes.

⚠️ Common Mistakes

• Not handling the case where there is no cycle correctly, leading to an incorrect return value.

4: I-mplement

Implement the code to solve the algorithm.

def collect_cycle_nodes(head):
    if not head or not head.next:
        return []

    slow = fast = head
    has_cycle = False

    while fast and fast.next:
        slow = slow.next
        fast = fast.next.next
        if slow == fast:
            has_cycle = True
            break

    if not has_cycle:
        return []

    slow = head
    while slow != fast:
        slow = slow.next
        fast = fast.next

    cycle_nodes = []
    start_cycle = slow
    current = start_cycle
    while True:
        cycle_nodes.append(current.value)
        current = current.next
        if current == start_cycle:
            break

    return cycle_nodes

5: R-eview

Review the code by running specific example(s) and recording values (watchlist) of your code's variables along the way.

• Trace the code with a cycle to verify that all cycle nodes are collected.
• Check the edge case of no cycle to ensure the empty list is returned.

6: E-valuate

Evaluate the performance of your algorithm and state any strong/weak or future potential work.

• Time Complexity: O(N) because detecting the cycle and collecting nodes both traverse parts of the list.
• Space Complexity: O(k) where k is the number of nodes in the cycle, needed for storing the cycle nodes.