Implementation of the Knapsack Problem Solver #11401

[snigdha510]

Describe your change:

Fixes #11401

• 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?

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".

[imSanko]

How about adding few of these?

"""

>>> capacity = 50
>>> values = [60, 100, 120]
>>> weights = [10, 20, 30]
>>> knapsack_dp(capacity, weights, values)
220

>>> capacity = 0
>>> values = [60, 100, 120]
>>> weights = [10, 20, 30]
>>> knapsack_dp(capacity, weights, values)
0

>>> capacity = 10
>>> values = [10, 10, 10]
>>> weights = [5, 5, 5]
>>> knapsack_dp(capacity, weights, values)
20

>>> capacity = 100
>>> values = [60, 100, 120, 80, 30]
>>> weights = [10, 20, 30, 40, 50]
>>> knapsack_dp(capacity, weights, values)
300

>>> capacity = 7
>>> values = [1, 4, 5, 7]
>>> weights = [1, 3, 4, 5]
>>> knapsack_dp(capacity, weights, values)
9
"""

[imSanko]

Until that looks fine!!

[snigdha510]

sure I'll do that as well

[snigdha510]

Implemented the changes asked as well

[liyahshaikh]

Here the docstring has an incorrect case.
The below should be 360 I believe, which is why the doctest is failing.

>>> capacity = 100
>>> values = [60, 100, 120, 80, 30]
>>> weights = [10, 20, 30, 40, 50]
>>> knapsack_dp(capacity, weights, values)
360

[tianyizheng02]

We already have an implementation of the DP solution to the 0-1 knapsack problem in dynamic_programming/knapsack.py. Please check the repo for existing implementations before you contribute, and please consider improving upon the existing implementation instead of contributing a duplicate.