Can someone please help me with this whole thing?

B$-$Trees:

Implement the search method for a B$-$Tree.

The method should return the node containing the key if it exists, otherwise, it should

return null.

Implement the insert and delete methods for a B$-$Tree.

Ensure that the tree remains balanced after each operation.

Write unit tests to verify the correctness of both operations.

Dynamic Programming:

Implement the rod cutting problem using dynamic programming.

Write a function that receives a rod length and a list of prices and returns the maximum

revenue achievable.

Implement the Longest Common Subsequence $($LCS$)$ problem using dynamic

programming.

Write a function that receives two strings and returns their LCS$.$

Greedy Algorithms:

Implement a greedy algorithm for a suitable problem of your choice $($e$.$g$.,$ coin change,

scheduling$).$

Justify the choice of the greedy strategy for this problem.

Write unit tests to verify the correctness of your algorithm.

Huffman Codes:

Implement Huffman coding for text compression.

Write a function that takes a string as input and outputs the encoded string along with

the Huffman tree.

Write a decoding function that takes the encoded string and the Huffman tree and

returns the original string.

Write unit tests to ensure your Huffman coding and decoding work correctly.

Graphs $-$ BFS and DFS:

Implement both Breadth$-$First Search $($BFS$)$ and Depth$-$First Search $($DFS$)$ for graphs

represented using adjacency lists.

Write functions that perform BFS and DFS starting from a given node and explore all

connected components.

Write unit tests to verify the correctness of both BFS and DFS implementations.

Submission Requirements:

Your code should be well$-$documented with comments explaining the functionality of

each component.

Ensure that all unit tests pass and provide coverage for edge cases in your

implementations.

Submit a report detailing your approach, challenges faced, and the complexity analysis

of each algorithm implemented$($just code running times with some comments are

enough$).$