matrix/count_paths.py (#7533)

* added recursive dfs backtracking for count paths with doctests

* fixed doc testing

* added type hints

* redefined r as row, c as col

* fixed naming conventions, ran mypy, only tests that didn't pass were using List[], rathan list()

* added another doctest, as well as a explanation above

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update matrix/count_paths.py

Co-authored-by: Chris O <[email protected]>

* Update matrix/count_paths.py

Co-authored-by: Chris O <[email protected]>

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Apply suggestions from code review

Co-authored-by: Caeden Perelli-Harris <[email protected]>

Co-authored-by: J <[email protected]>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Chris O <[email protected]>
Co-authored-by: Caeden Perelli-Harris <[email protected]>