Add dynamic programming solution for Egg Dropping Problem

[thisizaro]

Describe your change:

Add Dynamic Programming Solution for the Egg Dropping Problem

• Add an algorithm?
• Fix a bug or typo in an existing algorithm?
• Add or change doctests?
• Documentation change?

Brief Overview:

This pull request introduces a new algorithm for solving the Egg Dropping Problem using dynamic programming. The implementation determines the minimum number of attempts required to find the critical floor in a building with a given number of eggs and floors. It includes detailed comments and doctests to validate the functionality of the algorithm.

Description

This pull request introduces a dynamic programming solution for the Egg Dropping Problem, a well-known problem in combinatorial optimization. The goal is to determine the minimum number of attempts required to find the highest floor from which an egg can be dropped without breaking.

Changes Made

• Implemented the egg_dropping() function to compute the optimal solution using dynamic programming.
• Added docstrings and doctests to ensure correctness and cover edge cases.
• Integrated input validation to handle invalid inputs gracefully by raising exceptions.

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".