DNA Loop Length

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JCSU Unit 10 Problem Set 2 (Click for link to problem statements)

Problem Highlights

• 💡 Difficulty: Medium
• ⏰ Time to complete: 25-30 mins
• 🛠️ Topics: Linked Lists, Cycle Detection, Floyd's Algorithm

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 is the goal of the problem?
  • Determine the length of a cycle (loop) in a linked list, if it exists. Return 0 if there is no cycle.
• Are there constraints on input?
  • Input linked list may or may not contain a cycle.

HAPPY CASE Input: A linked list: A -> T -> C -> G -> A (loop) Output: 4 Explanation: The loop begins at 'T' and cycles through 4 nodes: 'T -> C -> G -> A'.

EDGE CASE Input: A linked list: C -> G -> A -> T -> None (no loop) Output: 0 Explanation: No loop exists in the DNA sequence.

EDGE CASE Input: A single node pointing to itself: A -> A Output: 1 Explanation: The loop contains only one 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 cycle detection in linked lists, we want to consider the following approaches:

• Floyd's Cycle Detection Algorithm: Use two pointers (slow and fast) to detect and measure the loop.
• Hash Set (Alternative): Use a hash set to track visited nodes (less efficient for space).

3: P-lan

Plan the solution with appropriate visualizations and pseudocode.

General Idea:
Use Floyd's Cycle Detection Algorithm to detect a loop. If a loop is detected, measure its length by traversing the loop until returning to the starting point.

Steps:

1. Initialize two pointers, slow and fast, both pointing to the head of the list.
2. Move slow one step and fast two steps in each iteration.
3. If slow meets fast, a loop is detected. If the end of the list (None) is reached, return 0.
4. To measure the loop length:
   • Start from the meeting point and traverse the loop until returning to the meeting point.
   • Count the number of steps taken.
5. Return the calculated loop length.

4: I-mplement

Implement the code to solve the algorithm.

def detect_dna_loop_length(head):
    # Use Floyd's Cycle Detection algorithm
    slow, fast = head, head

    # Step 1: Detect if a loop exists
    while fast and fast.next:
        slow = slow.next  # Move slow pointer one step
        fast = fast.next.next  # Move fast pointer two steps
        if slow == fast:  # Loop detected
            break
    else:
        # If no loop is detected, return 0
        return 0

    # Step 2: Calculate loop length
    loop_length = 1  # Initialize loop length counter
    current = slow.next
    while current != slow:  # Traverse the loop until returning to the starting point
        loop_length += 1
        current = current.next

    return loop_length  # Return the calculated loop 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 1:

• Input: dna_sequence = A -> T -> C -> G -> A (loop)
• Expected Output: 4
• Observed Output: 4

Example 2:

• Input: dna_sequence = C -> G -> A -> T -> None
• Expected Output: 0
• Observed Output: 0

Example 3:

• Input: dna_sequence = A -> A (single-node loop)
• Expected Output: 1
• Observed Output: 1

6: E-valuate

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

Assume n is the number of nodes in the linked list.

• Time Complexity: O(n) because we traverse the list to detect the loop and then measure the loop length.
• Space Complexity: O(1) because we only use two pointers and no additional data structures.