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* Create fractional_cover_problem.py * Update fractional_cover_problem.py * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Update fractional_cover_problem.py * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Update fractional_cover_problem.py * Update fractional_cover_problem.py * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Update fractional_cover_problem.py * Update fractional_cover_problem.py * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Update fractional_cover_problem.py * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Lose __eq__() * Update fractional_cover_problem.py * Define Item property ratio --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com> Co-authored-by: Christian Clauss <cclauss@me.com>
103 lines
2.5 KiB
Python
103 lines
2.5 KiB
Python
# https://en.wikipedia.org/wiki/Set_cover_problem
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from dataclasses import dataclass
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from operator import attrgetter
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@dataclass
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class Item:
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weight: int
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value: int
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@property
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def ratio(self) -> float:
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"""
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Return the value-to-weight ratio for the item.
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Returns:
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float: The value-to-weight ratio for the item.
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Examples:
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>>> Item(10, 65).ratio
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6.5
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>>> Item(20, 100).ratio
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5.0
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>>> Item(30, 120).ratio
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4.0
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"""
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return self.value / self.weight
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def fractional_cover(items: list[Item], capacity: int) -> float:
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"""
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Solve the Fractional Cover Problem.
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Args:
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items: A list of items, where each item has weight and value attributes.
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capacity: The maximum weight capacity of the knapsack.
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Returns:
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The maximum value that can be obtained by selecting fractions of items to cover
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the knapsack's capacity.
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Raises:
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ValueError: If capacity is negative.
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Examples:
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>>> fractional_cover((Item(10, 60), Item(20, 100), Item(30, 120)), capacity=50)
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240.0
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>>> fractional_cover([Item(20, 100), Item(30, 120), Item(10, 60)], capacity=25)
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135.0
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>>> fractional_cover([Item(10, 60), Item(20, 100), Item(30, 120)], capacity=60)
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280.0
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>>> fractional_cover(items=[Item(5, 30), Item(10, 60), Item(15, 90)], capacity=30)
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180.0
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>>> fractional_cover(items=[], capacity=50)
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0.0
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>>> fractional_cover(items=[Item(10, 60)], capacity=5)
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30.0
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>>> fractional_cover(items=[Item(10, 60)], capacity=1)
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6.0
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>>> fractional_cover(items=[Item(10, 60)], capacity=0)
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0.0
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>>> fractional_cover(items=[Item(10, 60)], capacity=-1)
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Traceback (most recent call last):
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...
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ValueError: Capacity cannot be negative
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"""
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if capacity < 0:
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raise ValueError("Capacity cannot be negative")
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total_value = 0.0
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remaining_capacity = capacity
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# Sort the items by their value-to-weight ratio in descending order
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for item in sorted(items, key=attrgetter("ratio"), reverse=True):
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if remaining_capacity == 0:
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break
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weight_taken = min(item.weight, remaining_capacity)
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total_value += weight_taken * item.ratio
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remaining_capacity -= weight_taken
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return total_value
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if __name__ == "__main__":
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import doctest
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if result := doctest.testmod().failed:
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print(f"{result} test(s) failed")
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else:
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print("All tests passed")
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