638. Shopping Offers

Explanation:

To solve this problem, we can use a recursive approach with backtracking. We iterate through each special offer, and for each offer, we check if it is beneficial to use the offer or not. If we use the offer, we update the remaining needs and recursively call the function with the updated needs. If we do not use the offer, we calculate the price without using the offer and compare it with the price using the offer.

At each step, we keep track of the minimum price. We also memoize the results to avoid recalculating the same subproblems.

Algorithm:

Implement a recursive function that takes the current needs array and iterates through each special offer.
For each offer, check if it can be applied, update the needs array, and recursively call the function with the updated needs.
Keep track of the minimum price using the current offer and without using the offer.
Memoize the results to avoid redundant calculations.

Time Complexity:

The time complexity of this approach is O(S^N) where S is the number of special offers and N is the number of items.

Space Complexity:

The space complexity is O(N) for the recursion stack and memoization. :

View Leetcode Problem

class Solution {
    public int shoppingOffers(List<Integer> price, List<List<Integer>> special, List<Integer> needs) {
        Map<List<Integer>, Integer> memo = new HashMap<>();
        return shopping(price, special, needs, memo);
    }

    private int shopping(List<Integer> price, List<List<Integer>> special, List<Integer> needs, Map<List<Integer>, Integer> memo) {
        if (memo.containsKey(needs)) {
            return memo.get(needs);
        }

        int minPrice = dot(needs, price);

        for (List<Integer> offer : special) {
            List<Integer> temp = new ArrayList<>(needs);
            boolean canApply = true;
            for (int i = 0; i < needs.size(); i++) {
                if (needs.get(i) < offer.get(i)) {
                    canApply = false;
                    break;
                }
                temp.set(i, needs.get(i) - offer.get(i));
            }
            if (canApply) {
                minPrice = Math.min(minPrice, offer.get(needs.size()) + shopping(price, special, temp, memo));
            }
        }

        memo.put(needs, minPrice);
        return minPrice;
    }

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

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