How to convert an Iterative Function to a Recursive one in python

Question

I have written an iterative function to solve a very simplified version of the knapsack problem and it is given below.

Iterative Code

def so_rich(self, money):
        """ Find the minimum amount left from the given 'money' after buying s series of products """

        # suppose you haven't seen any product yet
        # the only possible amount of money left is "money"
        # this is a set to record the possible money left
        left = set([money])
        # get products
        lst = list(self.warehouse.inventory.values())
        for product in lst:
            
            # a temporary set to save the updates of "left"
            # you don't want to modify the set you're iterating through
            tmp_left = set()
            # update tmp_left
            for m in left:
                
                if type(product) != Limited_Product:
                    new_left = m
                    while new_left >= product.price:
                        new_left = new_left - product.price
                        tmp_left.add(new_left)
                else:
                    # handle limited product
                    new_left = m
                    product_count = product.amount
                    while new_left >= product.price and product_count > 0:
                        new_left = new_left - product.price
                        tmp_left.add(new_left)
                        product_count -= 1
                        
            left.update(tmp_left)
        return min(left)

And Now I need to write the same function in the recursive format as well and I don't have much of a clue how to do that. I have written the following code but it does not give the correct answer for me. Can anyone help me correct the code?

Recursive Code

def so_rich_recursive(self, money):
        """ recursively find the minimum amount left from the given 'money' after buying s series of products """
        # YOUR CODE GOES HERE #

        # get products
        lst = list(self.warehouse.inventory.values())
        
        def helper(lst, money):
            # base case
            if not lst:
                return money

            cur_min = money
            product = lst[0]
            print(product)
            print(cur_min)
            if type(product) != Limited_Product:
                tmp = money
                while tmp >= product.price:
                    print(product.name, tmp)
                    tmp = tmp - product.price
            else:
                tmp = money
                product_count = product.amount
                while tmp >= product.price and product_count > 0:
                    print(product.name, tmp)
                    tmp = tmp - product.price
                    product_count -= 1
            cur_min = tmp
            lst.pop(0)
            return helper(lst, min(money, cur_min))
            
        
        return helper(lst, money)

Answer 1

One way to think about it is to start with the idea you will use recursion to replace your for product in lst: loop. To do that can use pop() to take the next product off the list and then pass the remaining list to the next call of the function. An empty product_list is the trigger that ends the recursion. Note: since you need the accumulated value of left for each product you would forward it as a parameter as well. Initially, left should be None which can be accomplished by using its default.

Note: I made a standalone function for simplicity, but it can also be implemented as a class method.

Example:

def so_rich_recursive(product_list, money, left=None):

    if not product_list:
        return min(left)

    product = product_list.pop()
    if not left:
        left = set([money])
        
    tmp_left = set()
    # update tmp_left
    for m in left:
                
        if type(product) != Limited_Product:
            new_left = m
            while new_left >= product.price:
                new_left = new_left - product.price
                tmp_left.add(new_left)
        else:
            # handle limited product
            new_left = m
            product_count = product.amount
            while new_left >= product.price and product_count > 0:
                new_left = new_left - product.price
                tmp_left.add(new_left)
                product_count -= 1

    left.update(tmp_left)
    return so_rich_recursive(product_list, money, left)