Measuring Loop Length

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

Problem Highlights

• 💡 Difficulty: Easy
• ⏰ Time to complete: 10-15 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?

• What does the problem ask for?
  • The problem asks to find the length of a loop in a linked list where the last node points back to the first node.
• What should be returned?
  • The function should return the length of the loop, which is the number of nodes in the linked list.

HAPPY CASE
Input: marker1 = Node("Marker 1")
       marker2 = Node("Marker 2")
       marker3 = Node("Marker 3")
       marker1.next = marker2
       marker2.next = marker3
       marker3.next = marker1
Output: 3
Explanation: The linked list has a loop with three markers.

EDGE CASE
Input: marker1 = Node("Marker 1")
       marker1.next = marker1  # Single node loop
Output: 1
Explanation: The linked list has a loop with one marker.

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 Length Calculation, we want to consider the following approaches:

• Cycle Traversal: Traverse the cycle and count the number of nodes to determine the length of the loop.

3: P-lan

Plan the solution with appropriate visualizations and pseudocode.

General Idea: We will traverse the linked list starting from the head and count the nodes until we return to the head, which indicates that we've completed the loop.

1) Initialize a variable `length` to 1 to count the nodes.
2) Initialize a pointer `current` to the head of the list.
3) Traverse the list:
    a) Move the `current` pointer to the next node.
    b) Increment `length` by 1.
    c) If `current` points back to the head, stop the traversal.
4) Return the value of `length`.

⚠️ Common Mistakes

• Forgetting to handle cases where the list is empty.
• Incorrectly managing pointers, leading to incorrect length calculation.

4: I-mplement

Implement the code to solve the algorithm.

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

def trail_length(trailhead):
    if not trailhead:
        return 0

    current = trailhead
    length = 1

    while current.next != trailhead:
        current = current.next
        length += 1

    return length

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, and marker3 linked list to verify that the function correctly calculates the length of the loop.

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 until the loop is detected.
• Space Complexity: O(1) because the algorithm uses a constant amount of extra space for pointers and counters.