Add advanced algorithms implementation

[TechnoBlogger14o3]

• Add Fast Fourier Transform (FFT) using Cooley-Tukey algorithm

  • Supports forward and inverse FFT
  • Includes magnitude/phase extraction and frequency bin generation
  • Complete with visualization examples

• Add Bloom Filter implementation

  • Space-efficient probabilistic data structure
  • Configurable false positive rate
  • Includes Counting Bloom Filter for deletion support
  • Comprehensive examples and testing

• Add Fenwick Tree (Binary Indexed Tree)

  • Efficient range sum queries and updates
  • 1D and 2D implementations
  • O(log n) time complexity for operations
  • Complete with range query examples

• Add Segment Tree implementation

  • Range queries and updates
  • Lazy propagation for efficient range updates
  • Min/Max segment tree variants
  • Comprehensive examples and testing

• Add Advanced Trie (Prefix Tree)

  • Full-featured trie with autocomplete
  • Pattern matching with wildcards
  • Longest common prefix functionality
  • Compressed trie for memory efficiency
  • Complete with all operations and examples

All implementations include:

• Comprehensive documentation
• Type hints and examples
• Error handling
• Performance analysis
• Test cases and usage examples

Describe your change:

• [ x] Add an algorithm?
• [ x] Fix a bug or typo in an existing algorithm?
• [ x] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request.
• [ x] Documentation change?

Checklist:

• [ x] I have read CONTRIBUTING.md.
• [ x] This pull request is all my own work -- I have not plagiarized.
• [ x] I know that pull requests will not be merged if they fail the automated tests.
• [ x] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
• [ x] All new Python files are placed inside an existing directory.
• [ x] All filenames are in all lowercase characters with no spaces or dashes.
• [ x] All functions and variable names follow Python naming conventions.
• [ x] All function parameters and return values are annotated with Python type hints.
• [ x] All functions have doctests that pass the automated testing.
• [ x] All new algorithms include at least one URL that points to Wikipedia or another similar explanation.
• [ x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a closing keyword: "Fixes #ISSUE-NUMBER".

[algorithms-keeper]

Closing this pull request as invalid

@TechnoBlogger14o3, this pull request is being closed as none of the checkboxes have been marked. It is important that you go through the checklist and mark the ones relevant to this pull request. Please read the Contributing guidelines.

If you're facing any problem on how to mark a checkbox, please read the following instructions:

• Read a point one at a time and think if it is relevant to the pull request or not.
• If it is, then mark it by putting a x between the square bracket like so: [x]

NOTE: Only [x] is supported so if you have put any other letter or symbol between the brackets, that will be marked as invalid. If that is the case then please open a new pull request with the appropriate changes.