638. Shopping Offers

Problem refer: https://leetcode.com/problems/shopping-offers/description/

Official solution refer: https://leetcode.com/problems/shopping-offers/solution/

// My solution:
// A good dp problem.
// The solution has refered to the official solution
// because I didn't figure out that how to store the state
// for dynamic plannning until told to use std::map.

// Some optimizations added by myself:
// There is no point in using using special offers in needs,
// so we only care about the unused offers and ignore the ones that be applyed before
// when do the memory search(dynamic planning). 

class Solution {
public:
    // These two varibles will nerver gonna to be changed, so move its out of the function.
    vector<int> g_price;
    vector<vector<int>> g_special;
    
    // Store the state of the dynamic plannning.
    std::map<vector<int>, int> g_ans;
    std::map<vector<int>, int>::iterator it_g_ans;
    
    // The function to do memory search with every state of needs.
    // The special id is used to pruning.
    int shop_calc(vector<int> needs, int special_id) {
        // If the state was already get, return the result directly.
        it_g_ans = g_ans.find(needs);
        if (it_g_ans != g_ans.end())
            return it_g_ans -> second;

        // For every new state, just calc the normal price as the initial value.
        // PS.I also used memory search there at the beginning which leaded to the time limit exceeded.
        // It really don't need to plannning because the special offers are the variables.
        int ans = 0;
        for (int i=0; i<g_price.size(); i++) {
            if (needs[i] <= 0) continue;
            ans += needs[i] * g_price[i];
        }
        
        // To do the memory search with every possible special offers.
        // The offers which be processed before are no need to join the next search.
        for (int i=special_id; i<g_special.size();i++) {
            bool cansp = true;
            vector<int> next = needs;
            for (int j=0; j<g_price.size(); j++) {
                next [j] -= g_special[i][j];
                if (next[j] < 0) {
                    cansp = false;
                    break;
                }
            }
            // To figure out the optimized answer for this state.
            if (cansp) {
                ans = min(ans, shop_calc(next, i) + g_special[i][g_price.size()]);
            }
        }
        g_ans[needs] = ans;
        return ans;
    }
    
    int shoppingOffers(vector<int>& price, vector<vector<int>>& special, vector<int>& needs) {
        
        g_price = price;
        g_special = special;

        return shop_calc(needs, 0);
    }
};