Create fractional_cover_problem.py

greedy_methods/fractional_cover_problem.py

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+# Explanation:- https://en.wikipedia.org/wiki/Set_cover_problem
+
+from dataclasses import dataclass
+
+
+@dataclass
+class Item:
+    weight: int
+    value: int
+
+    def __eq__(self, other):
+        return self.weight == other.weight and self.value == other.value
+
+
+def fractional_cover(items: list[Item], capacity: int) -> float:
+    """
+    Solve the Fractional Cover Problem.
+
+    Args:
+        items (List[Item]): A list of items, where each item is represented as an
+            Item object with weight and value attributes.
+        capacity (int): The maximum weight capacity of the knapsack.
+
+    Returns:
+        float: The maximum value that can be obtained by selecting fractions of items to
+        cover the knapsack's capacity.
+
+    Examples:
+    >>> items = [Item(10, 60), Item(20, 100), Item(30, 120)]
+    >>> fractional_cover(items, 50)
+    240.0
+
+    >>> items = [Item(20, 100), Item(30, 120), Item(10, 60)]
+    >>> fractional_cover(items, 25)
+    135.0
+
+    >>> items = [Item(10, 60), Item(20, 100), Item(30, 120)]
+    >>> fractional_cover(items, 60)
+    280.0
+
+    >>> items = [Item(5, 30), Item(10, 60), Item(15, 90)]
+    >>> fractional_cover(items, 30)
+    180.0
+
+    >>> items = []
+    >>> fractional_cover(items, 50)
+    0.0
+
+    >>> items = [Item(10, 60)]
+    >>> fractional_cover(items, 5)
+    30.0
+
+    >>> items = [Item(10, 60)]
+    >>> fractional_cover(items, 1)
+    6.0
+
+    >>> items = [Item(1, 1)]
+    >>> fractional_cover(items, 0)
+    0.0
+
+    >>> items = [Item(1, 1)]
+    >>> fractional_cover(items, 1)
+    1.0
+
+    >>> items = [Item(1, 1)]
+    >>> fractional_cover(items, 2)
+    1.0
+
+    >>> items = [Item(1, 1)]
+    >>> fractional_cover(items, 0)
+    0.0
+    """
+    # Calculate the value-to-weight ratios for each item
+    ratios = [(item.value / item.weight, item) for item in items]
+
+    # Sort the items by their value-to-weight ratio in descending order
+    ratios.sort(key=lambda x: x[0], reverse=True)
+
+    total_value = 0.0
+    remaining_capacity = capacity
+
+    for ratio, item in ratios:
+        if remaining_capacity == 0:
+            break
+
+        weight_taken = min(item.weight, remaining_capacity)
+        total_value += weight_taken * ratio
+        remaining_capacity -= weight_taken
+
+    return total_value
+
+
+if __name__ == "__main__":
+    import doctest
+
+    result = doctest.testmod().failed
+    if result == 0:
+        print("All tests passed")
+    else:
+        print(f"{result} test(s) failed")