Add a naive recursive implementation of 0-1 Knapsack Problem (#2743)

* Add naive recursive implementation of 0-1 Knapsack problem

* Fix shadowing

* Add doctest

* Fix type hints

* Add link to wiki

* Blacked the file

* Fix isort

* Move knapsack / add readme and more tests

* Add missed main in tests

knapsack/knapsack.py

@@ -0,0 +1,47 @@
+from typing import List
+
+""" A naive recursive implementation of 0-1 Knapsack Problem
+    https://en.wikipedia.org/wiki/Knapsack_problem
+"""
+
+
+def knapsack(capacity: int, weights: List[int], values: List[int], counter: int) -> int:
+    """
+    Returns the maximum value that can be put in a knapsack of a capacity cap,
+    whereby each weight w has a specific value val.
+
+    >>> cap = 50
+    >>> val = [60, 100, 120]
+    >>> w = [10, 20, 30]
+    >>> c = len(val)
+    >>> knapsack(cap, w, val, c)
+    220
+
+    The result is 220 cause the values of 100 and 120 got the weight of 50
+    which is the limit of the capacity.
+    """
+
+    # Base Case
+    if counter == 0 or capacity == 0:
+        return 0
+
+    # If weight of the nth item is more than Knapsack of capacity,
+    #   then this item cannot be included in the optimal solution,
+    # else return the maximum of two cases:
+    #   (1) nth item included
+    #   (2) not included
+    if weights[counter - 1] > capacity:
+        return knapsack(capacity, weights, values, counter - 1)
+    else:
+        left_capacity = capacity - weights[counter - 1]
+        new_value_included = values[counter - 1] + knapsack(
+            left_capacity, weights, values, counter - 1
+        )
+        without_new_value = knapsack(capacity, weights, values, counter - 1)
+        return max(new_value_included, without_new_value)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()