Optimized Recursive Knapsack with Memoization

knapsack/recursive_approach_knapsack.py

@@ -1,47 +1,48 @@
-# 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
+Example:
+    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.
+    max_weight > 0
+    profit[i] >= 0
+    weight[i] >= 0
+
+Calculate the maximum profit the shopkeeper can make given the maximum 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
+    Function description is as follows:
+    :param weights: List of item weights
+    :param values: List of item profits corresponding to the weights
+    :param number_of_items: Number of available items
+    :param max_weight: Maximum weight that can be carried
+    :param index: The item index currently being checked
     :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)
+    >>> 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)
+    ans2 = 0
     if weights[index] <= max_weight:
         ans2 = values[index] + knapsack(
             weights, values, number_of_items, max_weight - weights[index], index + 1
         )
+
     return max(ans1, ans2)