_638.java

package com.fishercoder.solutions;

import java.util.ArrayList;
import java.util.List;

/**
 * 638. Shopping Offers
 *
 * In LeetCode Store, there are some kinds of items to sell. Each item has a price.
 * However, there are some special offers, and a special offer consists of one or more different kinds of items with a sale price.
 * You are given the each item's price, a set of special offers,
 * and the number we need to buy for each item.
 * The job is to output the lowest price you have to pay for exactly certain items as given,
 * where you could make optimal use of the special offers.
 * Each special offer is represented in the form of an array,
 * the last number represents the price you need to pay for this special offer,
 * other numbers represents how many specific items you could get if you buy this offer.
 * You could use any of special offers as many times as you want.

 Example 1:
 Input: [2,5], [[3,0,5],[1,2,10]], [3,2]
 Output: 14
 Explanation:
 There are two kinds of items, A and B. Their prices are $2 and $5 respectively.
 In special offer 1, you can pay $5 for 3A and 0B
 In special offer 2, you can pay $10 for 1A and 2B.
 You need to buy 3A and 2B, so you may pay $10 for 1A and 2B (special offer #2), and $4 for 2A.

 Example 2:
 Input: [2,3,4], [[1,1,0,4],[2,2,1,9]], [1,2,1]
 Output: 11
 Explanation:
 The price of A is $2, and $3 for B, $4 for C.
 You may pay $4 for 1A and 1B, and $9 for 2A ,2B and 1C.
 You need to buy 1A ,2B and 1C, so you may pay $4 for 1A and 1B (special offer #1), and $3 for 1B, $4 for 1C.
 You cannot add more items, though only $9 for 2A ,2B and 1C.

 Note:
 There are at most 6 kinds of items, 100 special offers.
 For each item, you need to buy at most 6 of them.
 You are not allowed to buy more items than you want, even if that would lower the overall price.
 */
public class _638 {
    public static class Solution1 {
        /**
         * reference: https://leetcode.com/articles/shopping-offers/#approach-1-using-recursion-accepted
         */
        public int shoppingOffers(List<Integer> price, List<List<Integer>> special, List<Integer> needs) {
            return shopping(price, special, needs, 0);
        }

        public int shopping(List<Integer> price, List<List<Integer>> special, List<Integer> needs, int i) {
            if (i == special.size()) {
                return dot(needs, price);
            }
            ArrayList<Integer> clone = new ArrayList(needs);
            int j = 0;
            for (j = 0; j < special.get(i).size() - 1; j++) {
                int diff = clone.get(j) - special.get(i).get(j);
                if (diff < 0) {
                    break;
                }
                clone.set(j, diff);
            }
            if (j == special.get(i).size() - 1) {
                return Math.min(special.get(i).get(j) + shopping(price, special, clone, i), shopping(price, special, needs, i + 1));
            } else {
                return shopping(price, special, needs, i + 1);
            }
        }

        public int dot(List<Integer> a, List<Integer> b) {
            int sum = 0;
            for (int i = 0; i < a.size(); i++) {
                sum += a.get(i) * b.get(i);
            }
            return sum;
        }
    }
}