#1168218 (C++23) No.2713 Just Solitaire

• 問題: No.2713 Just Solitaire
• ユーザー: drken1215
• 提出日時: 2026-06-04 08:51:39
• 言語: C++23 (gcc 15.2.0 + boost 1.89.0)
• 結果: AC
• 実行時間: 4 ms / 2,000 ms
• コード長: 19,099 bytes
• コンパイル時間: 5,838 ms
• コンパイル使用メモリ: 380,652 KB
• 実行使用メモリ: 6,400 KB
• 最終ジャッジ日時: 2026-06-04 08:51:47
• 合計ジャッジ時間: 6,020 ms
• ジャッジサーバーID （参考情報）: judge2_0 / judge3_0

ファイルパターン	結果
sample	AC * 2
other	AC * 32

ソースコード

// code template is in https://github.com/drken1215/algorithm/blob/master/template_minimum.cpp
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")

#include <bits/stdc++.h>
using namespace std;


//------------------------------//
// Utility
//------------------------------//

using ll = long long;
using i128 = __int128_t;
using u128 = __uint128_t;
using pint = pair<int, int>;
using pll = pair<long long, long long>;
using tll = array<long long, 3>;
using fll = array<long long, 4>;
using vint = vector<int>;
using vll = vector<long long>;
using dint = deque<int>;
using dll = deque<long long>;
using vvint = vector<vector<int>>;
using vvll = vector<vector<long long>>;
using vpll = vector<pair<long long, long long>>;
template<class T> using min_priority_queue = priority_queue<T, vector<T>, greater<T>>;

template<class S, class T> inline bool chmax(S &a, T b) { return (a < b ? a = b, 1 : 0); }
template<class S, class T> inline bool chmin(S &a, T b) { return (a > b ? a = b, 1 : 0); }
template<class S, class T> inline auto maxll(S a, T b) { return max(ll(a), ll(b)); }
template<class S, class T> inline auto minll(S a, T b) { return min(ll(a), ll(b)); }
template<class T> auto max(const T &a) { return *max_element(a.begin(), a.end()); }
template<class T> auto min(const T &a) { return *min_element(a.begin(), a.end()); }
template<class T> auto argmax(const T &a) { return max_element(a.begin(), a.end()) - a.begin(); }
template<class T> auto argmin(const T &a) { return min_element(a.begin(), a.end()) - a.begin(); }
template<class T> auto accum(const vector<T> &a) { return accumulate(a.begin(), a.end(), T()); }
template<class T> auto accum(const deque<T> &a) { return accumulate(a.begin(), a.end(), T()); }

#define REP(i, a) for (long long i = 0; i < (long long)(a); i++)
#define REP2(i, a, b) for (long long i = a; i < (long long)(b); i++)
#define RREP(i, a) for (long long i = (a)-1; i >= (long long)(0); --i)
#define RREP2(i, a, b) for (long long i = (b)-1; i >= (long long)(a); --i)
#define EB emplace_back
#define PF push_front
#define PB push_back
#define MP make_pair
#define FI first
#define SE second
#define ALL(x) x.begin(), x.end()
#define COUT(x) cout << #x << " = " << (x) << " (L" << __LINE__ << ")" << endl

// input
template<class T> istream& operator >> (istream &is, vector<T> &P)
{ for (int i = 0; i < (int)P.size(); ++i) cin >> P[i]; return is; }
template<class T> istream& operator >> (istream &is, deque<T> &P)
{ for (int i = 0; i < (int)P.size(); ++i) cin >> P[i]; return is; }
template<class T> istream& operator >> (istream &is, vector<vector<T>> &P)
{ for (int i = 0; i < (int)P.size(); ++i) cin >> P[i]; return is; }

// output
template<class S, class T> ostream& operator << (ostream &s, const pair<S, T> &P)
{ return s << '<' << P.first << ", " << P.second << '>'; }
template<class T> ostream& operator << (ostream &s, const array<T, 2> &P)
{ return s << '<' << P[0] << "," << P[1] << '>'; }
template<class T> ostream& operator << (ostream &s, const array<T, 3> &P)
{ return s << '<' << P[0] << "," << P[1] << "," << P[2] << '>'; }
template<class T> ostream& operator << (ostream &s, const array<T, 4> &P)
{ return s << '<' << P[0] << "," << P[1] << "," << P[2] << "," << P[3] << '>'; }
template<class T> ostream& operator << (ostream &s, const vector<T> &P)
{ for (int i = 0; i < P.size(); ++i) { if (i > 0) { s << " "; } s << P[i]; } return s; }
template<class T> ostream& operator << (ostream &s, const deque<T> &P)
{ for (int i = 0; i < P.size(); ++i) { if (i > 0) { s << " "; } s << P[i]; } return s; }
template<class T> ostream& operator << (ostream &s, const vector<vector<T>> &P)
{ for (int i = 0; i < P.size(); ++i) { s << endl << P[i]; } return s << endl; }
template<class T> ostream& operator << (ostream &s, const set<T> &P)
{ for (auto it : P) { s << "<" << it << "> "; } return s; }
template<class T> ostream& operator << (ostream &s, const multiset<T> &P)
{ for (auto it : P) { s << "<" << it << "> "; } return s; }
template<class T> ostream& operator << (ostream &s, const unordered_set<T> &P)
{ for (auto it : P) { s << "<" << it << "> "; } return s; }
template<class S, class T> ostream& operator << (ostream &s, const map<S, T> &P)
{ for (auto it : P) { s << "<" << it.first << "->" << it.second << "> "; } return s; }
template<class S, class T> ostream& operator << (ostream &s, const unordered_map<S, T> &P)
{ for (auto it : P) { s << "<" << it.first << "->" << it.second << "> "; } return s; }
void yes(bool a) { cout << (a ? "yes" : "no") << endl; }
void YES(bool a) { cout << (a ? "YES" : "NO") << endl; }
void Yes(bool a) { cout << (a ? "Yes" : "No") << endl; }
const vector<int> DX = {1, 0, -1, 0, 1, -1, 1, -1};
const vector<int> DY = {0, 1, 0, -1, 1, -1, -1, 1};


// 1, 2, 3-variable submodular optimization
template<class COST> struct ThreeVariableSubmodularOpt {
    // constructors
    ThreeVariableSubmodularOpt() : N(2), S(0), T(0), OFFSET(0) {}
    ThreeVariableSubmodularOpt(int n, COST inf = numeric_limits<COST>::max() / 2)
    : N(n), S(n), T(n + 1), OFFSET(0), INF(inf), list(n + 2) {}
    
    // initializer
    void init(int n, COST inf = numeric_limits<COST>::max() / 2) {
        N = n, S = n, T = n + 1;
        OFFSET = 0, INF = inf;
        list.clear();
        list.resize(N + 2);
        pos.clear();
    }

    // add constant cost
    void add_cost(COST cost) {
        OFFSET += cost;
    }

    // add 1-variable submodular function
    void add_single_cost(int xi, COST false_cost, COST true_cost) {
        assert(0 <= xi && xi < N);
        if (false_cost >= true_cost) {
            OFFSET += true_cost;
            add_edge(S, xi, false_cost - true_cost);
        } else {
            OFFSET += false_cost;
            add_edge(xi, T, true_cost - false_cost);
        }
    }
    void add_single_cost_01(int xi, COST false_cost, COST true_cost) {
        add_single_cost(xi, false_cost, true_cost);
    }
    
    // add "project selection" constraint
    // xi = T, xj = F: strictly prohibited
    void add_psp_constraint(int xi, int xj) {
        assert(0 <= xi && xi < N);
        assert(0 <= xj && xj < N);
        add_edge(xi, xj, INF);
    }
    void add_psp_constraint_01(int xi, int xj) {
        add_psp_constraint(xj, xi);
    }
    void add_psp_constraint_10(int xi, int xj) {
        add_psp_constraint(xi, xj);
    }
    
    // add "project selection" penalty
    // xi = T, xj = F: cost C
    void add_psp_penalty(int xi, int xj, COST C) {
        assert(0 <= xi && xi < N);
        assert(0 <= xj && xj < N);
        assert(C >= 0);
        add_edge(xi, xj, C);
    }
    void add_psp_penalty_01(int xi, int xj, COST C) {
        add_psp_penalty(xj, xi, C);
    }
    void add_psp_penalty_10(int xi, int xj, COST C) {
        add_psp_penalty(xi, xj, C);
    }
    
    // add both True profit
    // xi = T, xj = T: profit P (cost -P)
    void add_both_true_profit(int xi, int xj, COST P) {
        assert(0 <= xi && xi < N);
        assert(0 <= xj && xj < N);
        assert(P >= 0);
        OFFSET -= P;
        add_edge(S, xi, P);
        add_edge(xi, xj, P);
    }
    
    // add both False profit
    // xi = F, xj = F: profit P (cost -P)
    void add_both_false_profit(int xi, int xj, COST P) {
        assert(0 <= xi && xi < N);
        assert(0 <= xj && xj < N);
        assert(P >= 0);
        OFFSET -= P;
        add_edge(xj, T, P);
        add_edge(xi, xj, P);
    }
    
    // add general 2-variable submodular function
    // (xi, xj) = (F, F): A, (F, T): B
    // (xi, xj) = (T, F): C, (T, T): D
    void add_submodular_function(int xi, int xj, COST A, COST B, COST C, COST D) {
        assert(0 <= xi && xi < N);
        assert(0 <= xj && xj < N);
        assert(B + C >= A + D);  // assure submodular function
        OFFSET += A;
        add_single_cost(xi, 0, D - B);
        add_single_cost(xj, 0, B - A);
        add_psp_penalty(xi, xj, B + C - A - D);
    }
    
    // add all True profit
    // y = F: not gain profit (= cost is P), T: gain profit (= cost is 0)
    // y: T, xi: F is prohibited
    void add_all_true_profit(const vector<int> &xs, COST P) {
        assert(P >= 0);
        int y = (int)list.size();
        list.resize(y + 1);
        OFFSET -= P;
        add_edge(S, y, P);
        for (auto xi : xs) {
            assert(xi >= 0 && xi < N);
            add_edge(y, xi, INF);
        }
    }
    
    // add all False profit
    // y = F: gain profit (= cost is 0), T: not gain profit (= cost is P)
    // xi = T, y = F is prohibited
    void add_all_false_profit(const vector<int> &xs, COST P) {
        assert(P >= 0);
        int y = (int)list.size();
        list.resize(y + 1);
        OFFSET -= P;
        add_edge(y, T, P);
        for (auto xi : xs) {
            assert(xi >= 0 && xi < N);
            add_edge(xi, y, INF);
        }
    }
    
    // add general 3-variable submodular function
    // (xi, xj, xk) = (F, F, F): cost A
    // (xi, xj, xk) = (F, F, T): cost B
    // (xi, xj, xk) = (F, T, F): cost C
    // (xi, xj, xk) = (F, T, T): cost D
    // (xi, xj, xk) = (T, F, F): cost E
    // (xi, xj, xk) = (T, F, T): cost F
    // (xi, xj, xk) = (T, T, F): cost G
    // (xi, xj, xk) = (T, T, T): cost H
    void add_submodular_function(int xi, int xj, int xk,
                                 COST A, COST B, COST C, COST D,
                                 COST E, COST F, COST G, COST H) {
        assert(0 <= xi && xi < N);
        assert(0 <= xj && xj < N);
        assert(0 <= xk && xk < N);
        COST P = (A + D + F + G) - (B + C + E + H);
        COST P12 = (C + E) - (A + G), P13 = (D + G) - (C + H);
        COST P21 = (D + F) - (B + H), P23 = (B + C) - (A + D);
        COST P31 = (B + E) - (A + F), P32 = (F + G) - (E + H);
        assert(P12 >= 0 && P21 >= 0);
        assert(P23 >= 0 && P32 >= 0);
        assert(P31 >= 0 && P13 >= 0);
        if (P >= 0) {
            OFFSET += A;
            add_single_cost(xi, 0, F - B);
            add_single_cost(xj, 0, G - E);
            add_single_cost(xk, 0, D - C);
            add_psp_penalty(xj, xi, P12);
            add_psp_penalty(xk, xj, P23);
            add_psp_penalty(xi, xk, P31);
            add_all_true_profit({xi, xj, xk}, P);
        } else {
            OFFSET += H;
            add_single_cost(xi, C - G, 0);
            add_single_cost(xj, B - D, 0);
            add_single_cost(xk, E - F, 0);
            add_psp_penalty(xi, xj, P21);
            add_psp_penalty(xj, xk, P32);
            add_psp_penalty(xk, xi, P13);
            add_all_false_profit({xi, xj, xk}, -P);
        }
    }
    
    // solve
    COST solve() {
        return dinic() + OFFSET;
    }
    
    // reconstrcut the optimal assignment
    vector<bool> reconstruct() {
        vector<bool> res(N, false), seen(list.size(), false);
        queue<int> que;
        seen[S] = true;
        que.push(S);
        while (!que.empty()) {
            int v = que.front();
            que.pop();
            for (const auto &e : list[v]) {
                if (e.cap && !seen[e.to]) {
                    if (e.to < N) res[e.to] = true;
                    seen[e.to] = true;
                    que.push(e.to);
                }
            }
        }
        return res;
    }
    
    // debug
    friend ostream& operator << (ostream& s, const ThreeVariableSubmodularOpt &tvs) {
        const auto &edges = tvs.get_edges();
        for (const auto &e : edges) s << e << endl;
        return s;
    }
    
private:
    // edge class
    struct Edge {
        // core members
        int rev, from, to;
        COST cap, icap, flow;
        
        // constructor
        Edge(int r, int f, int t, COST c)
        : rev(r), from(f), to(t), cap(c), icap(c), flow(0) {}
        void reset() { cap = icap, flow = 0; }
        
        // debug
        friend ostream& operator << (ostream& s, const Edge& E) {
            return s << E.from << "->" << E.to << '(' << E.flow << '/' << E.icap << ')';
        }
    };
    
    // inner data
    int N, S, T;
    COST OFFSET, INF;
    vector<vector<Edge>> list;
    vector<pair<int,int>> pos;
    
    // add edge
    Edge &get_rev_edge(const Edge &e) {
        if (e.from != e.to) return list[e.to][e.rev];
        else return list[e.to][e.rev + 1];
    }
    Edge &get_edge(int i) {
        return list[pos[i].first][pos[i].second];
    }
    const Edge &get_edge(int i) const {
        return list[pos[i].first][pos[i].second];
    }
    vector<Edge> get_edges() const {
        vector<Edge> edges;
        for (int i = 0; i < (int)pos.size(); ++i) {
            edges.push_back(get_edge(i));
        }
        return edges;
    }
    void add_edge(int from, int to, COST cap) {
        if (!cap) return;
        pos.emplace_back(from, (int)list[from].size());
        list[from].push_back(Edge((int)list[to].size(), from, to, cap));
        list[to].push_back(Edge((int)list[from].size() - 1, to, from, 0));
    }
    
    // Dinic's algorithm
    COST dinic(COST limit_flow) {
        COST current_flow = 0;
        vector<int> level((int)list.size(), -1), iter((int)list.size(), 0);
        
        // Dinic BFS
        auto bfs = [&]() -> void {
            level.assign((int)list.size(), -1);
            level[S] = 0;
            queue<int> que;
            que.push(S);
            while (!que.empty()) {
                int v = que.front();
                que.pop();
                for (const Edge &e : list[v]) {
                    if (level[e.to] < 0 && e.cap > 0) {
                        level[e.to] = level[v] + 1;
                        if (e.to == T) return;
                        que.push(e.to);
                    }
                }
            }
        };
        
        // Dinic DFS
        auto dfs = [&](auto self, int v, COST up_flow) {
            if (v == T) return up_flow;
            COST res_flow = 0;
            for (int &i = iter[v]; i < (int)list[v].size(); ++i) {
                Edge &e = list[v][i], &re = get_rev_edge(e);
                if (level[v] >= level[e.to] || e.cap == 0) continue;
                COST flow = self(self, e.to, min(up_flow - res_flow, e.cap));
                if (flow <= 0) continue;
                res_flow += flow;
                e.cap -= flow, e.flow += flow;
                re.cap += flow, re.flow -= flow;
                if (res_flow == up_flow) break;
            }
            return res_flow;
        };
        
        // flow
        while (current_flow < limit_flow) {
            bfs();
            if (level[T] < 0) break;
            iter.assign((int)iter.size(), 0);
            while (current_flow < limit_flow) {
                COST flow = dfs(dfs, S, limit_flow - current_flow);
                if (!flow) break;
                current_flow += flow;
            }
        }
        return current_flow;
    };
    COST dinic() {
        return dinic(numeric_limits<COST>::max() / 2);
    }
};

// K-value Two Variable Monge Function Optimization 
/*
    X[i] = 0, 1, ..., K-1 -> (x[i][1], ..., x[i][K-1])

    X[i] < d -> x[i][d] = 1
    X[i] = d -> x[i][1] = 0, ..., x[i][d] = 0, x[i][d+1] = 1, ..., x[i][K] = 1

    X[i] = 0   -> (1, 1, 1, ..., 1, 1)
    X[i] = 1   -> (0, 1, 1, ..., 1, 1)
    X[i] = 2   -> (0, 0, 1, ..., 1, 1)
    ...
    X[i] = K-2 -> (0, 0, 0, ..., 0, 1)
    X[i] = K-1 -> (0, 0, 0, ..., 0, 0)
 */
template<class COST> struct TwoVariableMongeOpt {
    // inner data
    int N, N01;
    COST INF;
    vector<int> ks;  // size of x[i]
    vector<vector<int>> x;  // index of x[i][k] in normal submodular optimization
    ThreeVariableSubmodularOpt<COST> tvs;

    // constructors
    TwoVariableMongeOpt() {}
    TwoVariableMongeOpt(int N, int K, COST inf = numeric_limits<COST>::max() / 2) {
        vector<int> ks(N, K);
        init(ks, inf);
    }
    TwoVariableMongeOpt(const vector<int> &ks, COST inf = numeric_limits<COST>::max() / 2) {
        init(ks, inf);
    }
    void init(const vector<int> &iks, COST inf = numeric_limits<COST>::max() / 2) {
        N = (int)iks.size(), INF = inf, ks = iks, N01 = 0;
        x.resize(N);
        for (int i = 0; i < N; i++) {
            assert(ks[i] >= 2);
            x[i].assign(ks[i], 0);
            for (int k = 1; k < ks[i]; k++) x[i][k] = N01++;
        }
        tvs.init(N01, INF);
        for (int i = 0; i < N; i++) {
            for (int k = 1; k < ks[i] - 1; k++) {
                tvs.add_psp_constraint(x[i][k], x[i][k + 1]);
            }
        }
    }

    // add constant cost
    void add_cost(COST cost) {
        tvs.add_cost(cost);
    }

    // add 1-variable function
    void add_single_cost(int xi, const vector<COST> &cost) {
        assert(0 <= xi && xi < N);
        assert((int)cost.size() == ks[xi]);
        tvs.add_cost(cost[ks[xi] - 1]);
        for (int k = 1; k < ks[xi]; k++) {
            tvs.add_single_cost(x[xi][k], 0, cost[k-1] - cost[k]);
        }
    }

    // add 2-variable Monge function
    // cost[i][j]+cost[i+1][j+1] <= cost[i+1][j]+cost[i][j+1]
    void add_monge_function(int xi, int xj, vector<vector<COST>> cost) {
        assert(0 <= xi && xi < N);
        assert(0 <= xj && xj < N);
        assert(xi != xj);
        assert(cost.size() == ks[xi]);
        assert(cost[0].size() == ks[xj]);
        vector<COST> icost(ks[xi]), jcost(ks[xj]);
        for (int ki = 0; ki < ks[xi]; ki++) {
            icost[ki] = cost[ki][0];
            for (int kj = 0; kj < ks[xj]; kj++) cost[ki][kj] -= icost[ki];
        }
        for (int kj = 0; kj < ks[xj]; kj++) {
            jcost[kj] = cost[0][kj];
            for (int ki = 0; ki < ks[xi]; ki++) cost[ki][kj] -= jcost[kj];
        }
        add_single_cost(xi, icost), add_single_cost(xj, jcost);
        for (int ki = 1; ki < ks[xi]; ki++) {
            for (int kj = 1; kj < ks[xj]; kj++) {
                COST c = cost[ki][kj] - cost[ki][kj-1] - cost[ki-1][kj] + cost[ki-1][kj-1];
                assert(c <= 0);
                tvs.add_both_false_profit(x[xi][ki], x[xj][kj], -c);
            }
        }
    }

    // solve
    COST solve() {
        return tvs.solve();
    }
    
    // reconstrcut the optimal assignment
    vector<int> reconstruct() {
        vector<int> res(N, 0);
        vector<bool> tres = tvs.reconstruct();
        for (int i = 0; i < N; i++) for (int ki = 1; ki < ks[i]; ki++) {
            res[i] += not tres[x[i][ki]];
        }
        return res;
    }
};


//------------------------------//
// Solver
//------------------------------//

/*
    0: 行くけどツアーに参加しない（-C[i]）
    1: 行かない（0）
    2: 行ってツアーにも参加する（-B[i]）

    (x, y) に対して
    x/y  0   1   2
     0   0   0   0
     1   0   0   0
     2   INF 0   0
*/
int main() {
    ll N, M; cin >> N >> M;
    vll A(N), B(M); cin >> A >> B;
    vvint C(M);
    REP(i, M) {
        ll K; cin >> K;
        C[i].resize(K);
        REP(j, K) cin >> C[i][j], C[i][j]--;
    }

    ThreeVariableSubmodularOpt<ll> opt(N);
    REP(i, N) opt.add_single_cost(i, 0, A[i]);
    REP(i, M) opt.add_all_true_profit(C[i], B[i]);
    auto res = -opt.solve();
    cout << res << endl;
}