JAVA DP:

　　public final int shoppingOffers(List<Integer> price, List<List<Integer>> special, List<Integer> needs) {
        Map<String, Integer> cache = new HashMap<String, Integer>();
        return search(price, special, needs, cache);
    }

    private final int search(List<Integer> prices, List<List<Integer>> specials, List<Integer> needs,
                       Map<String, Integer> cache) {
        int res = 0;
        String key = "";
        for (int i = 0; i < needs.size(); i++) key += "," + needs.get(i);
        if (cache.containsKey(key)) return cache.get(key);
        for (int i = 0; i < needs.size(); i++) res += prices.get(i) * needs.get(i);
        if (res == 0) return 0;
        for (int i = 0; i < specials.size(); i++) {
            List<Integer> special = specials.get(i), clone = new ArrayList<Integer>(needs);
            boolean canBuy = true;
            for (int j = 0; j < needs.size(); j++) {
                int diff = clone.get(j) - special.get(j);
                if (diff < 0) {
                    canBuy = false;
                    break;
                }
                clone.set(j, diff);
            }
            if (canBuy) res = Math.min(res, search(prices, specials, clone, cache) + special.get(special.size()-1));
        }
        cache.put(key, res);
        return res;
    }

　　JS DP:

/**
 * @param {number[]} price
 * @param {number[][]} special
 * @param {number[]} needs
 * @return {number}
 */
var shoppingOffers = function (price, specials, needs) {
    return dfs(price, specials, needs, new Map());
}

var dfs = function (price, specials, needs, cache) {
    let re = 0, key = 0;
    for (let i = 0; i < needs.length; i++) {
        re += needs[i] * price[i];
        key += "," + needs[i];
    }
    if (re == 0) return 0;
    if (cache.has(key)) return cache.get(key);
    for (let i = 0; i < specials.length; i++) {
        let special = specials[i], clone = needs.slice(), canBuy = true;
        for (let j = 0; j < clone.length; j++) {
            let diff = clone[j] - special[j];
            if (diff < 0) {
                canBuy = false;
                break;
            }
            clone[j] = diff;
        }
        if (canBuy) re = Math.min(re, dfs(price, specials, clone, cache) + special[special.length - 1]);
    }
    cache.set(key, re);
    return re;
};