greedy_methods.fractional_cover_problem
=======================================

.. py:module:: greedy_methods.fractional_cover_problem


Classes
-------

.. autoapisummary::

   greedy_methods.fractional_cover_problem.Item


Functions
---------

.. autoapisummary::

   greedy_methods.fractional_cover_problem.fractional_cover


Module Contents
---------------

.. py:class:: Item

   .. py:property:: ratio
      :type: 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



   .. py:attribute:: value
      :type:  int


   .. py:attribute:: weight
      :type:  int


.. py:function:: 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