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Commit 4961b3a

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Jiang15weijiangpre-commit-ci[bot]MaximSmolskiy
authored
Enhancement of the knapsack algorithm with memorization and generalisation (#9295)
* enhance knapsack problem * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * wei/refactor code * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Update test_knapsack.py * Update knapsack.py * Update test_knapsack.py * Update knapsack.py * Update knapsack.py * Update knapsack.py * Update knapsack.py * Update knapsack.py * Update test_knapsack.py --------- Co-authored-by: weijiang <weijiang@weijiangs-MacBook-Pro.local> Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com> Co-authored-by: Maxim Smolskiy <mithridatus@mail.ru>
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‎knapsack/README.md

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@@ -1,4 +1,4 @@
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# A naive recursive implementation of 0-1 Knapsack Problem
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# A recursive implementation of 0-N Knapsack Problem
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This overview is taken from:
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‎knapsack/knapsack.py

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@@ -1,14 +1,23 @@
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"""A naive recursive implementation of 0-1 Knapsack Problem
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"""A recursive implementation of 0-N Knapsack Problem
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https://en.wikipedia.org/wiki/Knapsack_problem
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"""
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from __future__ import annotations
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from functools import lru_cache
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def knapsack(capacity: int, weights: list[int], values: list[int], counter: int) -> int:
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def knapsack(
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capacity: int,
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weights: list[int],
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values: list[int],
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counter: int,
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allow_repetition=False,
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) -> int:
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"""
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Returns the maximum value that can be put in a knapsack of a capacity cap,
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whereby each weight w has a specific value val.
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whereby each weight w has a specific value val
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with option to allow repetitive selection of items
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>>> cap = 50
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>>> val = [60, 100, 120]
@@ -17,28 +26,40 @@ def knapsack(capacity: int, weights: list[int], values: list[int], counter: int)
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>>> knapsack(cap, w, val, c)
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220
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The result is 220 cause the values of 100 and 120 got the weight of 50
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Given the repetition is NOT allowed,
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the result is 220 cause the values of 100 and 120 got the weight of 50
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which is the limit of the capacity.
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>>> knapsack(cap, w, val, c, True)
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300
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Given the repetition is allowed,
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the result is 300 cause the values of 60*5 (pick 5 times)
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got the weight of 10*5 which is the limit of the capacity.
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"""
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# Base Case
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if counter == 0 or capacity == 0:
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return 0
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# If weight of the nth item is more than Knapsack of capacity,
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# then this item cannot be included in the optimal solution,
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# else return the maximum of two cases:
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# (1) nth item included
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# (2) not included
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if weights[counter - 1] > capacity:
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return knapsack(capacity, weights, values, counter - 1)
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else:
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left_capacity = capacity - weights[counter - 1]
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new_value_included = values[counter - 1] + knapsack(
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left_capacity, weights, values, counter - 1
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)
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without_new_value = knapsack(capacity, weights, values, counter - 1)
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return max(new_value_included, without_new_value)
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@lru_cache
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def knapsack_recur(capacity: int, counter: int) -> int:
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# Base Case
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if counter == 0 or capacity == 0:
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return 0
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# If weight of the nth item is more than Knapsack of capacity,
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# then this item cannot be included in the optimal solution,
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# else return the maximum of two cases:
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# (1) nth item included only once (0-1), if allow_repetition is False
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# nth item included one or more times (0-N), if allow_repetition is True
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# (2) not included
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if weights[counter - 1] > capacity:
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return knapsack_recur(capacity, counter - 1)
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else:
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left_capacity = capacity - weights[counter - 1]
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new_value_included = values[counter - 1] + knapsack_recur(
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left_capacity, counter - 1 if not allow_repetition else counter
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)
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without_new_value = knapsack_recur(capacity, counter - 1)
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return max(new_value_included, without_new_value)
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return knapsack_recur(capacity, counter)
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if __name__ == "__main__":

‎knapsack/tests/test_knapsack.py

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@@ -30,7 +30,7 @@ def test_base_case(self):
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def test_easy_case(self):
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"""
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test for the base case
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test for the easy case
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"""
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cap = 3
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val = [1, 2, 3]
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c = len(val)
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assert k.knapsack(cap, w, val, c) == 220
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def test_knapsack_repetition(self):
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"""
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test for the knapsack repetition
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"""
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cap = 50
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val = [60, 100, 120]
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w = [10, 20, 30]
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c = len(val)
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assert k.knapsack(cap, w, val, c, True) == 300
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if __name__ == "__main__":
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unittest.main()

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