#### Fractional Cover Problem

p
```# https://en.wikipedia.org/wiki/Set_cover_problem

from dataclasses import dataclass
from operator import attrgetter

@dataclass
class Item:
weight: int
value: int

@property
def ratio(self) -> float:
"""
Return the value-to-weight ratio for the item.

Returns:
float: The value-to-weight ratio for the item.

Examples:
>>> Item(10, 65).ratio
6.5

>>> Item(20, 100).ratio
5.0

>>> Item(30, 120).ratio
4.0
"""
return self.value / self.weight

def fractional_cover(items: list[Item], capacity: int) -> float:
"""
Solve the Fractional Cover Problem.

Args:
items: A list of items, where each item has weight and value attributes.
capacity: The maximum weight capacity of the knapsack.

Returns:
The maximum value that can be obtained by selecting fractions of items to cover
the knapsack's capacity.

Raises:
ValueError: If capacity is negative.

Examples:
>>> fractional_cover((Item(10, 60), Item(20, 100), Item(30, 120)), capacity=50)
240.0

>>> fractional_cover([Item(20, 100), Item(30, 120), Item(10, 60)], capacity=25)
135.0

>>> fractional_cover([Item(10, 60), Item(20, 100), Item(30, 120)], capacity=60)
280.0

>>> fractional_cover(items=[Item(5, 30), Item(10, 60), Item(15, 90)], capacity=30)
180.0

>>> fractional_cover(items=[], capacity=50)
0.0

>>> fractional_cover(items=[Item(10, 60)], capacity=5)
30.0

>>> fractional_cover(items=[Item(10, 60)], capacity=1)
6.0

>>> fractional_cover(items=[Item(10, 60)], capacity=0)
0.0

>>> fractional_cover(items=[Item(10, 60)], capacity=-1)
Traceback (most recent call last):
...
ValueError: Capacity cannot be negative
"""
if capacity < 0:
raise ValueError("Capacity cannot be negative")

total_value = 0.0
remaining_capacity = capacity

# Sort the items by their value-to-weight ratio in descending order
for item in sorted(items, key=attrgetter("ratio"), reverse=True):
if remaining_capacity == 0:
break

weight_taken = min(item.weight, remaining_capacity)
total_value += weight_taken * item.ratio
remaining_capacity -= weight_taken