Synchronous shopping1.cpp

#include <bits/stdc++.h>
#define N 1025
#define oo 1234567890

using namespace std;
typedef pair<int, int> ii;
typedef pair<int, ii> iii;

vector< pair<int, int> > road[N];
priority_queue<iii, vector<iii>, greater<iii> > Q;

int n, m, k, ans, fish[N], dis[N][N];

void dijkstra()
{
    for(int i = 0; i <= n; ++i)
        for(int j = 0; j < (1<<k); ++j) dis[i][j] = oo;
    Q.push(iii(0, ii(1, fish[1])));
    dis[1][fish[1]] = 0;
    // dis[i][state] : smallest weights to achieve state at node i

    while(Q.size())
    {
        // st : state   nst : new state   u,v : node   du, uv : weight
        int u = Q.top().second.first,
            du = Q.top().first,
            st = Q.top().second.second;
        Q.pop();

        if(du != dis[u][st]) continue;

        for(auto i : road[u]){
            int v = i.second,
                uv = i.first,
                nst = st | fish[v];
            if(dis[v][nst] > uv + du){
                dis[v][nst] = uv + du;
                Q.push(iii(dis[v][nst], ii(v, nst)));
            }
        }
    }
}

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(0); cout.tie(0);

    cin >> n >> m >> k;
    for(int i = 1; i <= n; ++i){
        int t, x; fish[i] = 0;
        cin >> t;
        while(t--){
            cin >> x;
            fish[i] |= (1<<(x-1));
    /*fish[i] : represent types of fish at node i by bitmask technique
                we call this as a state */   
        }
    }
    while(m--){
        int u, v, w; cin >> u >> v >> w;
        road[u].push_back(make_pair(w,v));
        road[v].push_back(make_pair(w,u));
    }

    dijkstra();

    ans = oo;
    for(int i = 0; i < (1<<k); ++i)
        for(int j = i; j < (1<<k); ++j)
            if((i|j) == (1<<k)-1) // means achieve state 11...111(k times) 
                ans = min(ans, max(dis[n][i], dis[n][j]));
    cout << ans;
    return 0;
}