Codeforces-solutions/2023-2024 ICPC Central Europe Regional Contest (CERC 23)/C. Cakes.cpp

/* Problem URL: https://codeforces.com/gym/104871/problem/C */

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;

template <class T, class comp = less<>>
using ordered_set = tree<T, null_type , comp , rb_tree_tag , tree_order_statistics_node_update>;

#define V vector

#define rmin(a, b) a = min(a, b)
#define rmax(a, b) a = max(a, b)

#define rep(i, lim) for (int i = 0; i < (lim); i++)
#define nrep(i, s, lim) for (int i = s; i < (lim); i++)

#define repv(i, v) for (auto &i : (v))
#define fillv(v) for (auto &itr_ : (v)) { cin >> itr_; }
#define sortv(v) sort(v.begin(), v.end())
#define all(v) (v).begin(), (v).end()

using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using vvvvi = vector<vvvi>;

using ll = long long;

using vl = vector<ll>;
using vvl = vector<vl>;
using vvvl = vector<vvl>;
using vvvvl = vector<vvvl>;

template<class v>
auto operator<<(ostream &os, const vector<v> &vec)->ostream& {
    os << vec[0];
    for (size_t i = 1; i < vec.size(); i++) {
        os << ' ' << vec[i];
    }
    os << '\n';
    return os;
}

template<class v>
auto operator>>(istream &is, vector<v> &vec)->istream& {
    for (auto &i : vec) {
        is >> i;
    }
    return is;
}

template<class v>
auto operator<<(ostream &os, const vector<vector<v>> &vec)->ostream& {
    for (auto &i : vec) {
        os << i[0];
        for (size_t j = 1; j < i.size(); j++) {
            os << ' ' << i[j];
        }
        os << '\n';
    }
    return os;
}

template<class v>
auto operator>>(istream  &is, vector<vector<v>> &vec)->istream& {
    for (auto &i : vec) {
        for (auto &j : i) {
            is >> j;
        }
    }
    return is;
}

#define int ll
#define INF (INT64_MAX >> 1)
struct dinitz {
	const bool scaling = false; // com scaling -> O(nm log(MAXCAP)),
	int lim;                    // com constante alta
	struct edge {
		int to, cap, rev, flow;
		bool res;
		edge(int to_, int cap_, int rev_, bool res_)
			: to(to_), cap(cap_), rev(rev_), flow(0), res(res_) {}
	};

	vector<vector<edge>> g;
	vector<int> lev, beg;
	ll F;
	dinitz(int n) : g(n), F(0) {}

	void add(int a, int b, int c) {
		g[a].emplace_back(b, c, g[b].size(), false);
		g[b].emplace_back(a, 0, g[a].size()-1, true);
	}
	bool bfs(int s, int t) {
		lev = vector<int>(g.size(), -1); lev[s] = 0;
		beg = vector<int>(g.size(), 0);
		queue<int> q; q.push(s);
		while (q.size()) {
			int u = q.front(); q.pop();
			for (auto& i : g[u]) {
				if (lev[i.to] != -1 or (i.flow == i.cap)) continue;
				if (scaling and i.cap - i.flow < lim) continue;
				lev[i.to] = lev[u] + 1;
				q.push(i.to);
			}
		}
		return lev[t] != -1;
	}
	int dfs(int v, int s, int f = INF) {
		if (!f or v == s) return f;
		for (int& i = beg[v]; i < g[v].size(); i++) {
			auto& e = g[v][i];
			if (lev[e.to] != lev[v] + 1) continue;
			int foi = dfs(e.to, s, min(f, e.cap - e.flow));
			if (!foi) continue;
			e.flow += foi, g[e.to][e.rev].flow -= foi;
			return foi;
		}
		return 0;
	}
	ll max_flow(int s, int t) {
		for (lim = scaling ? (1<<30) : 1; lim; lim /= 2)
			while (bfs(s, t)) while (int ff = dfs(s, t)) F += ff;
		return F;
	}
};

signed main()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int g, c, t;
    cin >> g >> c >> t;

    int size = g + c + t + 2;

    dinitz din(size);
    int s = g + c + t;
    int si = g + c + t + 1;

    ll total = 0;

    rep(i, c) {
        ll c;
        cin >> c;
        din.add(s, i, c);
        total += c;
    }

    vl ccost(g);
    rep(i, g) {
        cin >> ccost[i];
        din.add(i + c, si, INF);
    }

    rep(i, t) {
        ll cost;
        cin >> cost;
        din.add(i + g + c, si, cost);
    }

    rep(i, c) {
        rep(j, g) {
            ll act;
            cin >> act;
            din.add(i, j + c, ccost[j] * act);
        }
    }

    rep(i, c) {
        int n;
        cin >> n;
        while (n--) {
            int j;
            cin >> j;
            j--;

            din.add(i, j + g + c, INF);
        }
    }

    cout << total - din.max_flow(s, si) << '\n';
}