1774

1774. Closest Dessert Cost (Medium)

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.

 

Example 1:

Input: baseCosts = [1,7], toppingCosts = [3,4], target = 10
Output: 10
Explanation: Consider the following combination (all 0-indexed):
- Choose base 1: cost 7
- Take 1 of topping 0: cost 1 x 3 = 3
- Take 0 of topping 1: cost 0 x 4 = 0
Total: 7 + 3 + 0 = 10.

Example 2:

Input: baseCosts = [2,3], toppingCosts = [4,5,100], target = 18
Output: 17
Explanation: Consider the following combination (all 0-indexed):
- Choose base 1: cost 3
- Take 1 of topping 0: cost 1 x 4 = 4
- Take 2 of topping 1: cost 2 x 5 = 10
- Take 0 of topping 2: cost 0 x 100 = 0
Total: 3 + 4 + 10 + 0 = 17. You cannot make a dessert with a total cost of 18.

Example 3:

Input: baseCosts = [3,10], toppingCosts = [2,5], target = 9
Output: 8
Explanation: It is possible to make desserts with cost 8 and 10. Return 8 as it is the lower cost.

Example 4:

Input: baseCosts = [10], toppingCosts = [1], target = 1
Output: 10
Explanation: Notice that you don't have to have any toppings, but you must have exactly one base.

 

Constraints:

• n == baseCosts.length
• m == toppingCosts.length
• 1 <= n, m <= 10
• 1 <= baseCosts[i], toppingCosts[i] <= 104
• 1 <= target <= 104

Related Topics:
Greedy

Solution 1. DFS

// OJ: https://leetcode.com/problems/closest-dessert-cost/
// Author: github.com/lzl124631x
// Time: O(B * 3^T)
// Space: O(T)
class Solution {
    int ans, diff;
    void dfs(vector<int> &T, int i, int sum, int target) {
        int d = abs(sum - target);
        if (d > diff && sum > ans) return;
        if (d < diff || (d == diff && sum < ans)) {
            ans = sum;
            diff = d;
        }
        if (i == T.size()) return;
        for (int j = 0; j <= 2; ++j) dfs(T, i + 1, sum + j * T[i], target);
    }
public:
    int closestCost(vector<int>& B, vector<int>& T, int target) {
        ans = B[0];
        diff = abs(target - ans);
        for (int b : B) dfs(T, 0, b, target);
        return ans;
    }
};