Add knapsack variant to count optimal-value subsets#14536
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nickzerjeski wants to merge 3 commits intoTheAlgorithms:masterfrom
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Add knapsack variant to count optimal-value subsets#14536nickzerjeski wants to merge 3 commits intoTheAlgorithms:masterfrom
nickzerjeski wants to merge 3 commits intoTheAlgorithms:masterfrom
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Pull request overview
Adds a new knapsack API that returns both the optimal (max) achievable value and the number of distinct optimal selections, extending the existing memoized recursive approach in knapsack/knapsack.py.
Changes:
- Added
knapsack_with_count(...)-> tuple[int, int]that tracks(max_value, count)and aggregates counts on ties. - Added doctests for
knapsack_with_countinknapsack/knapsack.py. - Added unit tests for baseline and tie-counting behavior (0-1 and unbounded variants).
Reviewed changes
Copilot reviewed 2 out of 2 changed files in this pull request and generated 3 comments.
| File | Description |
|---|---|
| knapsack/knapsack.py | Introduces knapsack_with_count and adds typing for allow_repetition in knapsack() |
| knapsack/tests/test_knapsack.py | Adds tests validating returned (max_value, count) for standard and tie scenarios |
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| """ | ||
| Return both the maximum knapsack value and the number of optimal subsets. | ||
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| The return value is ``(max_value, number_of_optimal_subsets)``. | ||
| If multiple choices produce the same maximum value, their counts are added. | ||
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knapsack/knapsack.py
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| @lru_cache | ||
| def knapsack_recur(remaining_capacity: int, item_count: int) -> tuple[int, int]: |
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| def test_knapsack_with_count(self): | ||
| """ | ||
| test for maximum value and number of optimal subsets | ||
| """ | ||
| cap = 50 | ||
| val = [60, 100, 120] | ||
| w = [10, 20, 30] | ||
| c = len(val) | ||
| assert k.knapsack_with_count(cap, w, val, c) == (220, 1) | ||
| assert k.knapsack_with_count(cap, w, val, c, True) == (300, 1) |
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Summary
This PR adds a new knapsack variation that returns both:
It implements issue #14463 on top of the existing recursive memoized approach in
knapsack/knapsack.py.What Changed
knapsack_with_count(...) -> tuple[int, int]inknapsack/knapsack.py.functools.lru_cache) and extended DP state to track(value, count).0-1knapsack (allow_repetition=False)0-N/ unbounded knapsack (allow_repetition=True)allow_repetitioninknapsack().knapsack_with_count.Issue Discussion Alignment
I reviewed issue comments and incorporated the suggested memoized
(value, count)approach, including aggregation of counts when optimal values tie.Credit: approach inspiration from issue comment by @Mrudul1234.
Validation
python -m doctest -v knapsack/knapsack.py(pass)python -m unittest knapsack.tests.test_knapsack -v(pass)Issue
Closes #14463