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Enhancement of the knapsack algorithm with memorization and generalisation #9295

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Enhancement of the knapsack algorithm with memorization and generalisation #9295

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@Jiang15 Jiang15 commented Oct 1, 2023

Describe your change:

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

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 Enchancement of Knapsack algorithm: "Fixes Enhancement of the knapsack algorithm #9266".

@algorithms-keeper algorithms-keeper bot added documentation This PR modified documentation files awaiting reviews This PR is ready to be reviewed labels Oct 1, 2023
@algorithms-keeper algorithms-keeper bot added the tests are failing Do not merge until tests pass label Oct 1, 2023
@algorithms-keeper algorithms-keeper bot removed the tests are failing Do not merge until tests pass label Oct 1, 2023
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Jiang15 commented Oct 5, 2023

I forgot to add the description of the PR:)

  • In knapsack/knapsack.py, I added a flag - allow_repetition. It can be set to true to allow picking the same item multiple times, and vice versa, only once if it is false.
  • I refactored the naive recursion function to be more readable and added @lru_cache to optimize the time complexity.
  • And simple documentation changes in knapsack/README.MD from 0-1 to 0-N knapsack problem.

I added test cases with allow_repetition = true/false in tests and tests are all passed.

jeffreyyancey
jeffreyyancey suggested changes Oct 8, 2024
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A few suggestions, however only two things are blocking an approval from me.

  1. cap and c need to be full names as per the guidelines.
  2. Add a test case that demonstrates that repetition is working.

knapsack/knapsack.py
without_new_value = knapsack(capacity, weights, values, counter - 1)
return max(new_value_included, without_new_value)
@lru_cache
def knapsack_recur(cap: int, c: int) -> int:
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Using the lru_cache is a nice improvement. I might be worth exploring adding allow_repitition as a parameter, since lru_cache uses these parameters as a part of its memorization key.

knapsack/knapsack.py
without_new_value = knapsack(capacity, weights, values, counter - 1)
return max(new_value_included, without_new_value)
@lru_cache
def knapsack_recur(cap: int, c: int) -> int:
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cap and c should be given full descriptive names.

knapsack/knapsack.py
300

Given the repetition is allowed,
the result is 300 cause the values of 60*5 (pick 5 times)
which is the limit of the capacity.
"""

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You might want to consider a few things before getting into the algorithm:

  1. Handle any input constraints. Ensure the inputs make sense and raise an exception for the user if they don't
  • non-positive numbers
  • a capacity lower than the weight of any single object
  • etc
  1. Before getting into the main algorithm, you can go ahead and remove any items that have a weight above the capacity of the knapsack.

knapsack/knapsack.py
300

Given the repetition is allowed,
the result is 300 cause the values of 60*5 (pick 5 times)
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The algorithm has been updated to allow repetition. An example/testcase where repetition is used would be appropriate.

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Enhancement of the knapsack algorithm
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