ISSUE#4.2- BRIAN - ISSUE DEVELOPMENT

[ba-00001]

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Algorithm Development Template

ISSUE#: [Issue Number]
Title: [Issue Title]
Prepared by: [Developer Name]
Date: [MM/DD/YYYY]

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1. Problem Definition and Clarification

• Objective: Clearly state the problem that the algorithm needs to solve.
• Key Questions:
  • What is the problem to be solved?
  • What are the expected outcomes?
• Sub-tasks: Break down the issue into smaller tasks.

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2. Input/Output Specifications

• Input Data:
  • Define the required input data types, format, and constraints.
• Expected Output:
  • Specify what the algorithm should return or produce after execution.

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3. Constraints and Requirements

• Time Complexity: What is the acceptable time complexity for the solution?
• Space Complexity: Define memory usage constraints.
• Resource Constraints:
  • CPU, memory, and other hardware limitations.
• Ethical Considerations (if applicable):
  • How will the algorithm ensure fairness, privacy, or comply with legal requirements?

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4. Data Structures

• Chosen Data Structures: List the data structures (arrays, trees, hash maps, etc.) that are ideal for solving the problem and why.
• Justification: Explain why these data structures will improve efficiency.

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5. Algorithm Design Approach

• Design Paradigm:
  • Choose one or more design paradigms (e.g., Greedy, Divide and Conquer, Dynamic Programming, etc.).
  • Explain why the paradigm is suitable for this problem.
• Modular Design:
  • Break down the algorithm into reusable functions or components for clarity and maintainability.

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6. Edge Cases and Error Handling

• Edge Cases:
  • Identify possible edge cases (e.g., null values, empty inputs, extreme data).
• Error Handling:
  • Include strategies to handle invalid input or unexpected behavior.

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7. Optimization

• Initial Version: Describe the basic working version of the algorithm.
• Optimization Techniques: List any steps taken to optimize the algorithm for better performance (e.g., memoization, pruning, parallelization).

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8. Testing and Debugging

• Test Cases:
  • Typical input cases.
  • Boundary cases.
  • Edge cases.
• Debugging Tools: Specify the tools or strategies used for debugging.

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9. Documentation and Maintenance

• Documentation:
  • Provide clear explanations of the algorithm, its functions, and how to use it.
• Maintenance Plan:
  • Outline plans for future updates, bug fixes, and ongoing improvements.

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Comments/Notes

[Additional notes or comments regarding the issue development.]

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Version History

Date	Changes Made	Version
MM/DD/YYYY	Initial Draft	1.0
MM/DD/YYYY	[Describe subsequent changes]	X.X

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[ba-00001]

Algorithm Development Template

ISSUE#: TheAlgorithms#5693
Title: Adding Hare and Tortoise Algorithm
Prepared by: BRIAN B.
Date: 10/18/2024

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1. Problem Definition and Clarification

• Objective:
  Implement Floyd’s Cycle Detection algorithm (Hare and Tortoise) to detect cycles in a singly linked list.

• Key Questions:

  • What is the problem to be solved?
    Detect if a cycle exists in a singly linked list.

  • What are the expected outcomes?
    The algorithm should return true if a cycle is found, otherwise false.

• Sub-tasks:

  1. Create the ListNode structure to represent linked list nodes.
  2. Implement the HareAndTortoise class to detect a cycle using two pointers.
  3. Write unit tests in the HareAndTortoiseTest class.

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2. Input/Output Specifications

• Input Data:

  • Input will be the head of a singly linked list.
  • The input linked list can be cyclic or acyclic.

• Expected Output:

  • The algorithm should return a boolean (true or false):
    • true if there is a cycle.
    • false if no cycle is detected.

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3. Constraints and Requirements

• Time Complexity:
  The time complexity should be O(n) where n is the number of nodes in the linked list, as each node is visited at most twice (once by the slow pointer and once by the fast pointer).

• Space Complexity:
  The space complexity should be O(1), as the algorithm only uses a constant amount of extra space (two pointers).

• Resource Constraints:
  There are no special CPU or memory constraints, as the algorithm efficiently operates in linear time and constant space.

• Ethical Considerations:
  No ethical considerations for this algorithm.

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4. Data Structures

• Chosen Data Structures:

  • A singly linked list is the core data structure, represented using ListNode nodes.

• Justification:

  • The algorithm works directly with linked list nodes. No additional data structures like sets or hash maps are needed to detect cycles, which helps keep the space complexity at O(1).

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5. Algorithm Design Approach

• Design Paradigm:

  • Two-pointer approach (Tortoise and Hare):
    This algorithm uses two pointers (slow and fast), where slow moves one step at a time, and fast moves two steps at a time. If there is a cycle, these two pointers will eventually meet inside the cycle.
  • The two-pointer approach is efficient and ensures both time and space complexities are optimal.

• Modular Design:

  • ListNode class: Defines the structure of nodes in the linked list.
  • HareAndTortoise.hasCycle() method: Implements the core cycle detection algorithm.

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6. Edge Cases and Error Handling

• Edge Cases:

  • The linked list is null (empty).
  • The linked list has only one node (which cannot form a cycle).
  • The linked list has two nodes where the second node points back to the first, forming a cycle.

• Error Handling:

  • If the input list is null, the algorithm should return false (no cycle).
  • No exceptions should be thrown, as all cases (including null lists) are properly handled.

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7. Optimization

• Initial Version:

  • The initial version of the algorithm directly implements the two-pointer method (Hare and Tortoise) without optimization.

• Optimization Techniques:

  • No significant optimizations beyond the core two-pointer technique are needed, as this approach already achieves the best time and space complexity for the problem.

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8. Testing and Debugging

• Test Cases:

  • Typical cases:
    1. A linked list with a cycle.
    2. A linked list without a cycle.
  • Boundary cases:
    1. A linked list with only one node (no cycle).
    2. An empty linked list (head is null).
  • Edge cases:
    1. A linked list with two nodes, where the second node points back to the first.

• Debugging Tools:

  • JUnit 5 for automated unit testing.
  • Assertions like assertTrue() and assertFalse() to check the correctness of the algorithm's output.

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9. Documentation and Maintenance

• Documentation:

  • The HareAndTortoise class and hasCycle() method are well-documented with JavaDoc comments explaining their purpose and usage.
  • The test class HareAndTortoiseTest contains clear test cases to ensure correctness.

• Maintenance Plan:

  • Future updates may include additional features like detecting the length of the cycle or finding the start of the cycle. However, the current implementation is sufficient for detecting cycles.
  • Bug fixes and improvements will be documented in future versions as necessary.

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Comments/Notes

• This algorithm is optimal in both time and space, making it suitable for scenarios where memory usage is a concern.
• The two-pointer technique ensures that the algorithm runs efficiently even for very large lists.

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Version History

Date	Changes Made	Version
10/18/2024	Initial Draft	1.0
[MM/DD/YYYY]	[Describe subsequent changes]	X.X