Closest Dessert Cost

Problem Description

You would like to make dessert and are preparing to buy the ingredients. You have n ice cream base flavors and m types of toppings to choose from. You must follow these rules when making your dessert:

• There must be exactly one ice cream base.
• You can add one or more types of topping or have no toppings at all.
• There are at most two of each type of topping.

You are given three inputs:

• baseCosts, an integer array of length n, where each baseCosts[i] represents the price of the ith ice cream base flavor.
• toppingCosts, an integer array of length m, where each toppingCosts[i] is the price of one of the ith topping.
• target, an integer representing your target price for dessert.

You want to make a dessert with a total cost as close to target as possible.

Return the closest possible cost of the dessert to target. If there are multiple, return the lower one.

Key Insights

• The dessert cost is calculated as the sum of the chosen ice cream base and any combination of toppings.
• Each topping can be included 0, 1, or 2 times, leading to a combinatorial problem.
• A brute-force approach can be used given the small constraints (n, m ≤ 10).
• The solution should minimize the absolute difference from the target while favoring lower costs if there are ties.

Space and Time Complexity

Time Complexity: O(n * 3^m)
Space Complexity: O(1) (not counting the input space)

Solution

The approach to solve the problem involves iterating over all possible base costs and calculating the potential dessert costs using a backtracking approach for toppings. For each topping, we can choose to either not include it, include it once, or include it twice. We maintain a variable to track the closest dessert cost to the target.

1. Loop through each base cost and calculate the total cost by considering different combinations of toppings.
2. For each topping, use a recursive function to explore the possible inclusion (0, 1, or 2 times) of that topping.
3. Keep track of the closest cost to the target, ensuring to select the lower cost in case of ties.

Code Solutions