Checkout Price Calculator with Best Promotion

Assume you are implementing a checkout price calculator for an online shopping cart.

Input Data

You will be provided with:

• A list of items in the cart: Each item has a price, represented as a non-negative decimal number.
• A shipping_fee: A non-negative decimal number representing the shipping cost for the entire order.
• A list of promotions: Each promotion is one of two types:
  1. Percentage discount: Represented by a percentage value p (e.g., 10 for 10%). This discount applies only to the sum of item prices, not to the shipping fee.
  2. Fixed-amount discount: Represented by a non-negative decimal d. This discount is subtracted from the total amount including shipping.

Rules and Assumptions

• Let items_sum be the sum of all item prices.
• Before any discount, the total amount is items_sum + shipping_fee.
• For a percentage discount p (e.g., 10 for 10%):
  • discounted_items = items_sum * (1 - p/100)
  • total = discounted_items + shipping_fee
• For a fixed-amount discount d:
  • total = max(0, items_sum + shipping_fee - d)
• Percentage values p are assumed to be between 0 and 100.
• Fixed-amount discounts d are assumed to be non-negative.
• The final payable total should never be negative; it must be clamped to 0 if a discount would result in a negative value.
• You must apply at most one promotion to the cart. Some carts may have no promotions.

Task

Given the list of item prices, the shipping fee, and a list of promotions of the two types described above, write a function that performs the following:

1. Computes the final payable amount for each available promotion.
2. Identifies the promotion that yields the lowest payable amount (i.e., provides the maximum savings). This includes the option of applying no promotion if that results in the lowest total.
3. Returns:
   • The minimum payable amount after applying the best promotion (or no promotion).
   • An indication of which promotion was chosen. You may assume each promotion has a unique identifier (e.g., an ID or index) and should define a reasonable representation for it.

Edge Cases to Handle

Your solution should robustly handle relevant edge cases, including but not limited to:

• An empty cart (no items).
• No promotions available.
• Zero or extremely small item prices or shipping fees.
• Promotions that do not improve the price (e.g., a 0% discount or a fixed discount of 0).
• Promotions that would otherwise drive the total below zero (ensuring the total is clamped to 0).

Specify the input and output formats for your function, including how you represent items and promotions, and then implement the function.