Create recursive_approach_knapsack.py (#7587)

* Create recursive_approach_knapsack.py

Added a new naïve recursive approach to solve the knapsack problem.

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* Update recursive_approach_knapsack.py

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* Update recursive_approach_knapsack.py

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knapsack/recursive_approach_knapsack.py

@@ -0,0 +1,52 @@
+# To get an insight into naive recursive way to solve the Knapsack problem
+
+
+"""
+A shopkeeper has bags of wheat that each have different weights and different profits.
+eg.
+no_of_items 4
+profit 5 4 8 6
+weight 1 2 4 5
+max_weight 5
+Constraints:
+max_weight > 0
+profit[i] >= 0
+weight[i] >= 0
+Calculate the maximum profit that the shopkeeper can make given maxmum weight that can
+be carried.
+"""
+
+
+def knapsack(
+    weights: list, values: list, number_of_items: int, max_weight: int, index: int
+) -> int:
+    """
+    Function description is as follows-
+    :param weights: Take a list of weights
+    :param values: Take a list of profits corresponding to the weights
+    :param number_of_items: number of items available to pick from
+    :param max_weight: Maximum weight that could be carried
+    :param index: the element we are looking at
+    :return: Maximum expected gain
+    >>> knapsack([1, 2, 4, 5], [5, 4, 8, 6], 4, 5, 0)
+    13
+    >>> knapsack([3 ,4 , 5], [10, 9 , 8], 3, 25, 0)
+    27
+    """
+    if index == number_of_items:
+        return 0
+    ans1 = 0
+    ans2 = 0
+    ans1 = knapsack(weights, values, number_of_items, max_weight, index + 1)
+    if weights[index] <= max_weight:
+        ans2 = values[index] + knapsack(
+            weights, values, number_of_items, max_weight - weights[index], index + 1
+        )
+    return max(ans1, ans2)
+
+
+if __name__ == "__main__":
+
+    import doctest
+
+    doctest.testmod()