[aarav570]

Describe your change

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

Details:

• The Farey sequence of order $n$ is the sequence of completely reduced fractions between 0 and 1 with denominators less than or equal to $n$, arranged in increasing order.
• Generates fractions efficiently using the standard mediant recurrence algorithm in $O(n^2)$ time and $O(1)$ auxiliary space.
• Returns a list of fractions.Fraction objects.
• Fully typed with Python type hints and accompanied by doctests covering valid orders, boundary cases, and exception handling (ValueError and TypeError).
• Reference: https://en.wikipedia.org/wiki/Farey_sequence

Checklist

• I have read CONTRIBUTING.md.
• This pull request is all my own work -- I have not plagiarized.
• I know that pull requests will not be merged if they fail the automated tests.
• This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
• All new Python files are placed inside an existing directory.
• All filenames are in all lowercase characters with no spaces or dashes.
• All functions and variable names follow Python naming conventions.
• All function parameters and return values are annotated with Python type hints.
• All functions have doctests that pass the automated testing.
• All new algorithms include at least one URL that points to Wikipedia or another similar explanation.
• 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".