Fractional knapsack (#1524)

* Add files via upload

* Added doctests, type hints, f-strings, URLs

* Rename knapsack.py to fractional_knapsack.py

* Rename graphs/fractional_knapsack.py to dynamic_programming/fractional_knapsack_2.py

dynamic_programming/fractional_knapsack_2.py

@@ -0,0 +1,60 @@
+# https://en.wikipedia.org/wiki/Continuous_knapsack_problem
+# https://www.guru99.com/fractional-knapsack-problem-greedy.html
+# https://medium.com/walkinthecode/greedy-algorithm-fractional-knapsack-problem-9aba1daecc93
+
+from typing import List, Tuple
+
+
+def fractional_knapsack(
+    value: List[int], weight: List[int], capacity: int
+) -> Tuple[int, List[int]]:
+    """
+    >>> value = [1, 3, 5, 7, 9]
+    >>> weight = [0.9, 0.7, 0.5, 0.3, 0.1]
+    >>> fractional_knapsack(value, weight, 5)
+    (25, [1, 1, 1, 1, 1])
+    >>> fractional_knapsack(value, weight, 15)
+    (25, [1, 1, 1, 1, 1])
+    >>> fractional_knapsack(value, weight, 25)
+    (25, [1, 1, 1, 1, 1])
+    >>> fractional_knapsack(value, weight, 26)
+    (25, [1, 1, 1, 1, 1])
+    >>> fractional_knapsack(value, weight, -1)
+    (-90.0, [0, 0, 0, 0, -10.0])
+    >>> fractional_knapsack([1, 3, 5, 7], weight, 30)
+    (16, [1, 1, 1, 1])
+    >>> fractional_knapsack(value, [0.9, 0.7, 0.5, 0.3, 0.1], 30)
+    (25, [1, 1, 1, 1, 1])
+    >>> fractional_knapsack([], [], 30)
+    (0, [])
+    """
+    index = list(range(len(value)))
+    ratio = [v / w for v, w in zip(value, weight)]
+    index.sort(key=lambda i: ratio[i], reverse=True)
+
+    max_value = 0
+    fractions = [0] * len(value)
+    for i in index:
+        if weight[i] <= capacity:
+            fractions[i] = 1
+            max_value += value[i]
+            capacity -= weight[i]
+        else:
+            fractions[i] = capacity / weight[i]
+            max_value += value[i] * capacity / weight[i]
+            break
+
+    return max_value, fractions
+
+
+if __name__ == "__main__":
+    n = int(input("Enter number of items: "))
+    value = input(f"Enter the values of the {n} item(s) in order: ").split()
+    value = [int(v) for v in value]
+    weight = input(f"Enter the positive weights of the {n} item(s) in order: ".split())
+    weight = [int(w) for w in weight]
+    capacity = int(input("Enter maximum weight: "))
+
+    max_value, fractions = fractional_knapsack(value, weight, capacity)
+    print("The maximum value of items that can be carried:", max_value)
+    print("The fractions in which the items should be taken:", fractions)