Fixes: #3869: Optimize solution #2 for Euler's Problem #74

[tacitvenom]

Describe your change:

Github Issue #3869: Optimize solution #2 for Euler's Problem #74
I have only tweaked the helper functions, primarily for finding the factorial by keeping a cache, since the factorials are only needed for a limited number of numbers

• Add an algorithm?
• Fix a bug or typo in an existing algorithm?
• 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 have a URL in its comments that points to Wikipedia or other similar explanation.
• [ x] If this pull request resolves one or more open issues then the commit message contains Fixes: #{$ISSUE_NO}.

[dhruvmanila]

Thank you for trying but this does not fix the issue. Please time the program first before opening a pull request.

[tacitvenom]

Aah, shoot.
Apologies, I was too sleepy and too eager to open a PR. I have made the changes I had in mind now.