Clearing the Path

Edit PagePage History

TIP102 Unit 6 Session 2 Standard (Click for link to problem statements)

Problem Highlights

• 💡 Difficulty: Medium
• ⏰ Time to complete: 25-35 mins
• 🛠️ Topics: Linked Lists, Cycle Detection, Cycle Removal

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?

• What does the problem ask for?
  • The problem asks to remove any cycles in a linked list and return the head of the cleared list.
• What should be returned?
  • The function should return the head of the linked list after removing any cycles.

HAPPY CASE
Input: marker1 = Node("Trailhead")
       marker2 = Node("Trail Fork")
       marker3 = Node("The Falls")
       marker4 = Node("Peak")
       marker1.next = marker2
       marker2.next = marker3
       marker3.next = marker4
       marker4.next = marker2  # Cycle here
Output: Trailhead -> Trail Fork -> The Falls -> Peak
Explanation: The cycle is removed, resulting in a straightforward linked list.

EDGE CASE
Input: marker1 = Node("Trailhead")
       marker1.next = marker1  # Self-loop
Output: Trailhead
Explanation: The self-loop is removed, leaving a single node.

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.

For Linked List problems involving Cycle Detection and Removal, we want to consider the following approaches:

• Floyd's Cycle Detection Algorithm: Use this algorithm to detect if there is a cycle and to find the start of the cycle.
• Pointer Manipulation: After identifying the start of the cycle, use pointer manipulation to break the cycle.

3: P-lan

Plan the solution with appropriate visualizations and pseudocode.

General Idea: We will first use Floyd's Cycle Detection Algorithm to detect the cycle in the linked list. If a cycle is detected, we will find the start of the cycle and remove it by making the last node in the cycle point to None.

1) Use Floyd's Cycle Detection Algorithm:
    a) Initialize two pointers, `slow` and `fast`, both pointing to the head of the list.
    b) Move `slow` by one step and `fast` by two steps.
    c) If `slow` meets `fast`, a cycle is detected.
2) If a cycle is detected, find the starting node of the cycle:
    a) Reset `slow` to the head of the list.
    b) Move both `slow` and `fast` one step at a time until they meet. The meeting point is the start of the cycle.
3) Traverse the cycle to find the node that points back to the start of the cycle and set its next pointer to `None`.
4) Return the head of the list.

⚠️ Common Mistakes

• Failing to correctly identify the node that needs to have its next pointer set to None.
• Incorrectly handling cases where the list is empty or contains no cycle.

4: I-mplement

Implement the code to solve the algorithm.

class Node:
    def __init__(self, value, next=None):
        self.value = value
        self.next = next

# Function to remove a cycle in the linked list
def clear_trail(trailhead):
    if not trailhead:
        return None

    slow = trailhead
    fast = trailhead

    # Step 1: Detect cycle using Floyd's Cycle Detection Algorithm
    while fast and fast.next:
        slow = slow.next
        fast = fast.next.next
        if slow == fast:
            break
    else:
        # No cycle detected
        return trailhead

    # Step 2: Find the start of the cycle
    slow = trailhead
    while slow != fast:
        slow = slow.next
        fast = fast.next

    # Step 3: Remove the cycle
    while fast.next != slow:
        fast = fast.next
    fast.next = None

    return trailhead

5: R-eview

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

• Example: Use the provided marker1, marker2, marker3, and marker4 linked list with a cycle to verify that the function correctly removes the cycle.

6: E-valuate

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

Assume N represents the number of nodes in the linked list.

• Time Complexity: O(N) because each node is visited exactly once during cycle detection and removal.
• Space Complexity: O(1) because the algorithm uses a constant amount of extra space for pointers.