如何將迭代 Function 轉換為 python 中的遞歸

Question

我寫了一個迭代的 function 來解決背包問題的一個非常簡化的版本，它在下面給出。

迭代代碼

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)

現在我還需要以遞歸格式編寫相同的 function 並且我不知道如何做到這一點。 我已經編寫了以下代碼，但它沒有給我正確的答案。 誰能幫我更正代碼？

遞歸代碼

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

考慮它的一種方法是從使用遞歸替換for product in lst:的想法開始。 為此，可以使用pop()將下一個產品從列表中刪除，然后將剩余的列表傳遞給 function 的下一個調用。 一個空的product_list是結束遞歸的觸發器。 注意：由於您需要每個產品的left累積值，因此您也可以將其作為參數轉發。 最初，left 應該是None ，這可以通過使用其默認值來完成。

注意：為簡單起見，我制作了一個獨立的 function，但它也可以實現為 class 方法。

例子：

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)