3928. Minimum Cost to Buy Apples II

You are given an integer n and an integer array prices of length n, where prices[i] is the price of apples at shop i.

You are also given a 2D integer array roads, where roads[i] = [u_i, v_i, cost_i, tax_i] represents a bidirectional road:

• u_i and v_i are the shops connected by the road.
• cost_i is the cost to travel the road without carrying apples.
• tax_i is the multiplier applied to cost_i when traveling with apples.

For each shop i, you can either:

• Buy apples locally at shop i for prices[i].
• Travel empty to any shop j using any number of roads, buy apples for prices[j], and return to shop i while carrying apples, paying cost * tax on each road used for the return trip.

The forward path, where you travel empty, and the return path may be different.

Return an integer array ans of length n, where ans[i] is the minimum total cost to buy apples starting from shop i.

class Solution {
    int helper(int n, vector<int>& prices, vector<vector<array<long long,2>>>& adj, int start) {
        long long res = LLONG_MAX;
        vector<long long> cost(2 * n, INT_MAX);
        priority_queue<pair<long long, long long>, vector<pair<long long, long long>>, greater<>> q;
        auto push = [&](long long idx, long long c) {
            if(cost[idx] > c and c < res) {
                cost[idx] = c;
                q.push({c,idx});
                long long a = idx >= n ? idx - n : idx, b = a + n;
                res = min(res, cost[a] + cost[b] + prices[a]);
            }
        };
        push(start, 0);
        push(start + n, 0);
        while(q.size()) {
            auto [c, u] = q.top(); q.pop();
            if(cost[u] != c) continue;
            for(auto& [v,w] : adj[u]) push(v, c + w);
        }
        return res;
    }
public:
    vector<int> minCost(int n, vector<int>& prices, vector<vector<int>>& roads) {
        vector<vector<array<long long,2>>> adj(2 * n);
        for(auto& r : roads) {
            long long u = r[0], v = r[1], w = r[2], m = r[3];
            adj[u].push_back({v,w});
            adj[u+n].push_back({v+n,w*m});
            adj[v].push_back({u,w});
            adj[v+n].push_back({u+n,w*m});
        }
        vector<int> res;
        for(int i = 0; i < n; i++) res.push_back(helper(n,prices,adj,i));
        return res;
    }
};