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The assignment requires implementing a Red-Black Tree as a Map in Java, with specific features for testing and validation. The implementation must be compatible with Eclipse, follow a 200-level data structures course standard, include comprehensive test cases with comments, and adhere to the specified interface and additional methods for validation.

The main tasks include creating a class named RBMap that implements the Map interface, supporting insertions, deletions, and traversal functionalities. You must add three public methods: redViolationExists(), blackHeight(), and toString() for testing the red-black properties and tree structure. The implementation should correctly maintain the red-black tree properties, handle all insertion and deletion cases, and provide thorough tests covering each condition.

Paper For Above instruction

The implementation of a Red-Black Tree (RBT) as a Map data structure in Java presents a vital task for understanding self-balancing binary search trees. The objective of this assignment is to develop an RBMap class that not only functions effectively as a Map but also adheres to red-black balancing rules. This involves implementing insertion, deletion, traversal, and validation methods to ensure the integrity and correctness of the tree structure. The assignment emphasizes detailed testing, including specific methods to verify red node violations and black height consistency, which are critical indicators of a balanced red-black tree.

Red-black trees are a type of self-balancing binary search tree that maintains specific properties to guarantee logarithmic time complexity for search, insert, and delete operations. The key properties of red-black trees include: every node being either red or black, the root being black, red nodes having black children, and every path from a node to its leaves containing the same number of black nodes (black height). Ensuring these properties during insertions and deletions requires careful handling of various cases, such as fixing violations after inserting a red node or removing a node.

The RBMap class must implement the Map interface, incorporating methods such as put, get, remove, and other standard methods. Beyond this, three extra methods are mandated for testing purposes: redViolationExists(), which traverses the tree to detect any red node with a red child; blackHeight(), which calculates the black height at the root and verifies consistency across all paths; and toString(), which outputs a preorder traversal of the tree in a specific format for verification.

While implementing the red-black balancing logic, special attention must be given to handling all the cases during insertion and deletion. These include rotations, recoloring, and fixing violations according to the rules exemplified in standard red-black tree algorithms. Proper handling of mirror cases (e.g., left and right rotations) and ensuring the properties are maintained after every modification are crucial.

For testing, extensive test cases should be crafted to validate each scenario, including inserting nodes that cause different types of violations and verifying the tree’s structure after each operation. Each test should be accompanied by clear comments explaining which specific case it covers, how it tests the fix, and how the validation methods ensure the tree’s correctness. Java classes for testing should be included, utilizing sample data and known violations to demonstrate robustness.

In summary, this assignment demands designing a fully functional red-black tree that correctly implements the Map interface, maintains red-black properties, supports detailed validation, and is accompanied by comprehensive test cases for each operation. Success depends on careful case handling, thorough testing, and clean, understandable code aligned with 200-level data structures coursework standards.

References

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