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47 lines
1.4 KiB
Python
47 lines
1.4 KiB
Python
""" A naive recursive implementation of 0-1 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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def knapsack(capacity: int, weights: list[int], values: list[int], counter: int) -> 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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>>> 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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>>> 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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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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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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