#698759 (C++17) No.1288 yuki collection

提出ソース

結果

問題	No.1288 yuki collection
ユーザー	👑 hitonanode
提出日時	2021-09-11 01:10:34
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	303 ms / 5,000 ms
コード長	16,355 bytes
コンパイル時間	2,279 ms
コンパイル使用メモリ	103,816 KB
実行使用メモリ	5,532 KB
最終ジャッジ日時	2023-09-03 16:20:47
合計ジャッジ時間	9,246 ms
ジャッジサーバーID （参考情報）	judge13 / judge12

このコードへのチャレンジ
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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	1 ms 4,384 KB
testcase_01	AC	1 ms 4,384 KB
testcase_02	AC	1 ms 4,384 KB
testcase_03	AC	2 ms 4,380 KB
testcase_04	AC	1 ms 4,384 KB
testcase_05	AC	2 ms 4,384 KB
testcase_06	AC	2 ms 4,380 KB
testcase_07	AC	2 ms 4,384 KB
testcase_08	AC	2 ms 4,384 KB
testcase_09	AC	1 ms 4,384 KB
testcase_10	AC	2 ms 4,384 KB
testcase_11	AC	2 ms 4,384 KB
testcase_12	AC	2 ms 4,388 KB
testcase_13	AC	178 ms 5,412 KB
testcase_14	AC	157 ms 5,440 KB
testcase_15	AC	116 ms 5,064 KB
testcase_16	AC	170 ms 5,064 KB
testcase_17	AC	149 ms 5,288 KB
testcase_18	AC	173 ms 5,408 KB
testcase_19	AC	153 ms 5,496 KB
testcase_20	AC	163 ms 5,332 KB
testcase_21	AC	86 ms 5,488 KB
testcase_22	AC	97 ms 5,276 KB
testcase_23	AC	100 ms 5,332 KB
testcase_24	AC	152 ms 5,432 KB
testcase_25	AC	153 ms 5,432 KB
testcase_26	AC	177 ms 5,292 KB
testcase_27	AC	178 ms 5,328 KB
testcase_28	AC	234 ms 5,444 KB
testcase_29	AC	236 ms 5,404 KB
testcase_30	AC	283 ms 5,288 KB
testcase_31	AC	275 ms 5,408 KB
testcase_32	AC	287 ms 5,440 KB
testcase_33	AC	84 ms 5,532 KB
testcase_34	AC	145 ms 5,344 KB
testcase_35	AC	170 ms 5,292 KB
testcase_36	AC	80 ms 5,380 KB
testcase_37	AC	111 ms 5,404 KB
testcase_38	AC	84 ms 5,336 KB
testcase_39	AC	84 ms 5,336 KB
testcase_40	AC	303 ms 5,404 KB
testcase_41	AC	1 ms 4,384 KB
testcase_42	AC	2 ms 4,380 KB

権限があれば一括ダウンロードができます

ソースコード

raw source code

#line 1 "combinatorial_opt/test/mincostflow.yuki1288.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1288"
#line 2 "combinatorial_opt/mincostflow_nonegativeloop.hpp"
#include <cassert>
#include <limits>
#include <queue>
#include <vector>
/*
// CUT begin
// Minimum cost flow WITH NO NEGATIVE CYCLE (just negative cost edge is allowed)
// Verified:
// - SRM 770 Div1 Medium https://community.topcoder.com/stat?c=problem_statement&pm=15702
// - CodeChef LTIME98 Ancient Magic https://www.codechef.com/problems/ANCT
template <class Cap = long long, class Cost = long long, Cost INF_COST = std::numeric_limits<Cost>::max() / 2>
struct MinCostFlow {
    struct _edge {
        int to, rev;
        Cap cap;
        Cost cost;
        template <class Ostream> friend Ostream &operator<<(Ostream &os, const _edge &e) {
            return os << '(' << e.to << ',' << e.rev << ',' << e.cap << ',' << e.cost << ')';
        }
    };
    bool _is_dual_infeasible;
    int V;
    std::vector<std::vector<_edge>> g;
    std::vector<Cost> dist;
    std::vector<int> prevv, preve;
    std::vector<Cost> dual; // dual[V]: potential
    std::vector<std::pair<int, int>> pos;

    bool _initialize_dual_dag() {
        std::vector<int> deg_in(V);
        for (int i = 0; i < V; i++) {
            for (const auto &e : g[i]) deg_in[e.to] += (e.cap > 0);
        }
        std::vector<int> st;
        st.reserve(V);
        for (int i = 0; i < V; i++) {
            if (!deg_in[i]) st.push_back(i);
        }
        for (int n = 0; n < V; n++) {
            if (int(st.size()) == n) return false; // Not DAG
            int now = st[n];
            for (const auto &e : g[now]) {
                if (!e.cap) continue;
                deg_in[e.to]--;
                if (deg_in[e.to] == 0) st.push_back(e.to);
                if (dual[e.to] >= dual[now] + e.cost) dual[e.to] = dual[now] + e.cost;
            }
        }
        return true;
    }

    bool _initialize_dual_spfa() { // Find feasible dual's when negative cost edges exist
        dual.assign(V, 0);
        std::queue<int> q;
        std::vector<int> in_queue(V);
        std::vector<int> nvis(V);
        for (int i = 0; i < V; i++) q.push(i), in_queue[i] = true;
        while (q.size()) {
            int now = q.front();
            q.pop(), in_queue[now] = false;
            if (nvis[now] > V) return false; // Negative cycle exists
            nvis[now]++;
            for (const auto &e : g[now]) {
                if (!e.cap) continue;
                if (dual[e.to] > dual[now] + e.cost) {
                    dual[e.to] = dual[now] + e.cost;
                    if (!in_queue[e.to]) in_queue[e.to] = true, q.push(e.to);
                }
            }
        }
        return true;
    }

    bool initialize_dual() {
        return !_is_dual_infeasible or _initialize_dual_dag() or _initialize_dual_spfa();
    }

    template <class heap> void _dijkstra(int s) { // O(ElogV)
        prevv.assign(V, -1);
        preve.assign(V, -1);
        dist.assign(V, INF_COST);
        dist[s] = 0;
        heap q;
        q.emplace(0, s);
        while (!q.empty()) {
            auto p = q.top();
            q.pop();
            int v = p.second;
            if (dist[v] < Cost(p.first)) continue;
            for (int i = 0; i < (int)g[v].size(); i++) {
                _edge &e = g[v][i];
                auto c = dist[v] + e.cost + dual[v] - dual[e.to];
                if (e.cap > 0 and dist[e.to] > c) {
                    dist[e.to] = c, prevv[e.to] = v, preve[e.to] = i;
                    q.emplace(dist[e.to], e.to);
                }
            }
        }
    }

    MinCostFlow(int V = 0) : _is_dual_infeasible(false), V(V), g(V), dual(V, 0) {
        static_assert(INF_COST > 0, "INF_COST must be positive");
    }

    int add_edge(int from, int to, Cap cap, Cost cost) {
        assert(0 <= from and from < V);
        assert(0 <= to and to < V);
        assert(cap >= 0);
        if (cost < 0) _is_dual_infeasible = true;
        pos.emplace_back(from, g[from].size());
        g[from].push_back({to, (int)g[to].size() + (from == to), cap, cost});
        g[to].push_back({from, (int)g[from].size() - 1, (Cap)0, -cost});
        return int(pos.size()) - 1;
    }

    // Flush flow f from s to t. Graph must not have negative cycle.
    using Pque = std::priority_queue<std::pair<Cost, int>, std::vector<std::pair<Cost, int>>, std::greater<std::pair<Cost, int>>>;
    template <class heap = Pque> std::pair<Cap, Cost> flow(int s, int t, const Cap &flow_limit) {
        // You can also use radix_heap<typename std::make_unsigned<Cost>::type, int> as prique
        if (!initialize_dual()) throw; // Fail to find feasible dual
        Cost cost = 0;
        Cap flow_rem = flow_limit;
        while (flow_rem > 0) {
            _dijkstra<heap>(s);
            if (dist[t] == INF_COST) break;
            for (int v = 0; v < V; v++) dual[v] = std::min(dual[v] + dist[v], INF_COST);
            Cap d = flow_rem;
            for (int v = t; v != s; v = prevv[v]) d = std::min(d, g[prevv[v]][preve[v]].cap);
            flow_rem -= d;
            cost += d * (dual[t] - dual[s]);
            for (int v = t; v != s; v = prevv[v]) {
                _edge &e = g[prevv[v]][preve[v]];
                e.cap -= d;
                g[v][e.rev].cap += d;
            }
        }
        return std::make_pair(flow_limit - flow_rem, cost);
    }

    struct edge {
        int from, to;
        Cap cap, flow;
        Cost cost;
        template <class Ostream> friend Ostream &operator<<(Ostream &os, const edge &e) {
            return os << '(' << e.from << "->" << e.to << ',' << e.flow << '/' << e.cap << ",$" << e.cost << ')';
        }
    };

    edge get_edge(int edge_id) const {
        int m = int(pos.size());
        assert(0 <= edge_id and edge_id < m);
        auto _e = g[pos[edge_id].first][pos[edge_id].second];
        auto _re = g[_e.to][_e.rev];
        return {pos[edge_id].first, _e.to, _e.cap + _re.cap, _re.cap, _e.cost};
    }
    std::vector<edge> edges() const {
        std::vector<edge> ret(pos.size());
        for (int i = 0; i < int(pos.size()); i++) ret[i] = get_edge(i);
        return ret;
    }

    template <class Ostream> friend Ostream &operator<<(Ostream &os, const MinCostFlow &mcf) {
        os << "[MinCostFlow]V=" << mcf.V << ":";
        for (int i = 0; i < mcf.V; i++) {
            for (auto &e : mcf.g[i]) os << "\n" << i << "->" << e.to << ":cap" << e.cap << ",$" << e.cost;
        }
        return os;
    }
};
*/

template <class Cap, class Cost, Cost INF_COST = std::numeric_limits<Cost>::max() / 2> struct MinCostFlow {
    template <class E> struct csr {
        std::vector<int> start;
        std::vector<E> elist;
        explicit csr(int n, const std::vector<std::pair<int, E>> &edges) : start(n + 1), elist(edges.size()) {
            for (auto e : edges) { start[e.first + 1]++; }
            for (int i = 1; i <= n; i++) { start[i] += start[i - 1]; }
            auto counter = start;
            for (auto e : edges) { elist[counter[e.first]++] = e.second; }
        }
    };

public:
    MinCostFlow() {}
    explicit MinCostFlow(int n) : is_dual_infeasible(false), _n(n) {
        static_assert(std::numeric_limits<Cap>::max() > 0, "max() must be greater than 0");
    }

    int add_edge(int from, int to, Cap cap, Cost cost) {
        assert(0 <= from && from < _n);
        assert(0 <= to && to < _n);
        assert(0 <= cap);
        // assert(0 <= cost);
        if (cost < 0) is_dual_infeasible = true;
        int m = int(_edges.size());
        _edges.push_back({from, to, cap, 0, cost});
        return m;
    }

    struct edge {
        int from, to;
        Cap cap, flow;
        Cost cost;
    };

    edge get_edge(int i) {
        int m = int(_edges.size());
        assert(0 <= i && i < m);
        return _edges[i];
    }
    std::vector<edge> edges() { return _edges; }

    std::pair<Cap, Cost> flow(int s, int t) { return flow(s, t, std::numeric_limits<Cap>::max()); }
    std::pair<Cap, Cost> flow(int s, int t, Cap flow_limit) { return slope(s, t, flow_limit).back(); }
    std::vector<std::pair<Cap, Cost>> slope(int s, int t) {
        return slope(s, t, std::numeric_limits<Cap>::max());
    }
    std::vector<std::pair<Cap, Cost>> slope(int s, int t, Cap flow_limit) {
        assert(0 <= s && s < _n);
        assert(0 <= t && t < _n);
        assert(s != t);

        int m = int(_edges.size());
        std::vector<int> edge_idx(m);

        auto g = [&]() {
            std::vector<int> degree(_n), redge_idx(m);
            std::vector<std::pair<int, _edge>> elist;
            elist.reserve(2 * m);
            for (int i = 0; i < m; i++) {
                auto e = _edges[i];
                edge_idx[i] = degree[e.from]++;
                redge_idx[i] = degree[e.to]++;
                elist.push_back({e.from, {e.to, -1, e.cap - e.flow, e.cost}});
                elist.push_back({e.to, {e.from, -1, e.flow, -e.cost}});
            }
            auto _g = csr<_edge>(_n, elist);
            for (int i = 0; i < m; i++) {
                auto e = _edges[i];
                edge_idx[i] += _g.start[e.from];
                redge_idx[i] += _g.start[e.to];
                _g.elist[edge_idx[i]].rev = redge_idx[i];
                _g.elist[redge_idx[i]].rev = edge_idx[i];
            }
            return _g;
        }();

        auto result = slope(g, s, t, flow_limit);

        for (int i = 0; i < m; i++) {
            auto e = g.elist[edge_idx[i]];
            _edges[i].flow = _edges[i].cap - e.cap;
        }

        return result;
    }

private:
    bool is_dual_infeasible;
    int _n;
    std::vector<edge> _edges;

    // inside edge
    struct _edge {
        int to, rev;
        Cap cap;
        Cost cost;
    };

    std::vector<std::pair<Cap, Cost>> slope(csr<_edge> &g, int s, int t, Cap flow_limit) {
        // variants (C = maxcost):
        // -(n-1)C <= dual[s] <= dual[i] <= dual[t] = 0
        // reduced cost (= e.cost + dual[e.from] - dual[e.to]) >= 0 for all edge

        // dual_dist[i] = (dual[i], dist[i])
        std::vector<std::pair<Cost, Cost>> dual_dist(_n);
        if (is_dual_infeasible) {
            auto check_dag = [&]() {
                std::vector<int> deg_in(_n);
                for (int v = 0; v < _n; v++) {
                    for (int i = g.start[v]; i < g.start[v + 1]; i++) {
                        deg_in[g.elist[i].to] += g.elist[i].cap > 0;
                    }
                }
                std::vector<int> st;
                st.reserve(_n);
                for (int i = 0; i < _n; i++) {
                    if (!deg_in[i]) st.push_back(i);
                }
                for (int n = 0; n < _n; n++) {
                    if (int(st.size()) == n) return false; // Not DAG
                    int now = st[n];
                    for (int i = g.start[now]; i < g.start[now + 1]; i++) {
                        const auto &e = g.elist[i];
                        if (!e.cap) continue;
                        deg_in[e.to]--;
                        if (deg_in[e.to] == 0) st.push_back(e.to);
                        if (dual_dist[e.to].first >= dual_dist[now].first + e.cost)
                            dual_dist[e.to].first = dual_dist[now].first + e.cost;
                    }
                }
                return true;
            }();
            if (!check_dag) throw;
        }
        std::vector<int> prev_e(_n);
        std::vector<bool> vis(_n);
        struct Q {
            Cost key;
            int to;
            bool operator<(Q r) const { return key > r.key; }
        };
        std::vector<int> que_min;
        std::vector<Q> que;
        auto dual_ref = [&]() {
            for (int i = 0; i < _n; i++) { dual_dist[i].second = std::numeric_limits<Cost>::max(); }
            std::fill(vis.begin(), vis.end(), false);
            que_min.clear();
            que.clear();

            // que[0..heap_r) was heapified
            unsigned heap_r = 0;

            dual_dist[s].second = 0;
            que_min.push_back(s);
            while (!que_min.empty() || !que.empty()) {
                int v;
                if (!que_min.empty()) {
                    v = que_min.back();
                    que_min.pop_back();
                } else {
                    while (heap_r < que.size()) {
                        heap_r++;
                        std::push_heap(que.begin(), que.begin() + heap_r);
                    }
                    v = que.front().to;
                    std::pop_heap(que.begin(), que.end());
                    que.pop_back();
                    heap_r--;
                }
                if (vis[v]) continue;
                vis[v] = true;
                if (v == t) break;
                // dist[v] = shortest(s, v) + dual[s] - dual[v]
                // dist[v] >= 0 (all reduced cost are positive)
                // dist[v] <= (n-1)C
                Cost dual_v = dual_dist[v].first, dist_v = dual_dist[v].second;
                for (int i = g.start[v]; i < g.start[v + 1]; i++) {
                    auto e = g.elist[i];
                    if (!e.cap) continue;
                    // |-dual[e.to] + dual[v]| <= (n-1)C
                    // cost <= C - -(n-1)C + 0 = nC
                    Cost cost = e.cost - dual_dist[e.to].first + dual_v;
                    if (dual_dist[e.to].second - dist_v > cost) {
                        Cost dist_to = dist_v + cost;
                        dual_dist[e.to].second = dist_to;
                        prev_e[e.to] = e.rev;
                        if (dist_to == dist_v) {
                            que_min.push_back(e.to);
                        } else {
                            que.push_back(Q{dist_to, e.to});
                        }
                    }
                }
            }
            if (!vis[t]) { return false; }

            for (int v = 0; v < _n; v++) {
                if (!vis[v]) continue;
                // dual[v] = dual[v] - dist[t] + dist[v]
                //         = dual[v] - (shortest(s, t) + dual[s] - dual[t]) +
                //         (shortest(s, v) + dual[s] - dual[v]) = - shortest(s,
                //         t) + dual[t] + shortest(s, v) = shortest(s, v) -
                //         shortest(s, t) >= 0 - (n-1)C
                dual_dist[v].first -= dual_dist[t].second - dual_dist[v].second;
            }
            return true;
        };
        Cap flow = 0;
        Cost cost = 0, prev_cost_per_flow = -1;
        std::vector<std::pair<Cap, Cost>> result = {{Cap(0), Cost(0)}};
        while (flow < flow_limit) {
            if (!dual_ref()) break;
            Cap c = flow_limit - flow;
            for (int v = t; v != s; v = g.elist[prev_e[v]].to) {
                c = std::min(c, g.elist[g.elist[prev_e[v]].rev].cap);
            }
            for (int v = t; v != s; v = g.elist[prev_e[v]].to) {
                auto &e = g.elist[prev_e[v]];
                e.cap += c;
                g.elist[e.rev].cap -= c;
            }
            Cost d = -dual_dist[s].first;
            flow += c;
            cost += c * d;
            if (prev_cost_per_flow == d) { result.pop_back(); }
            result.push_back({flow, cost});
            prev_cost_per_flow = d;
        }
        return result;
    }
};
#line 3 "combinatorial_opt/test/mincostflow.yuki1288.test.cpp"
#include <iostream>
#include <numeric>
#include <string>
#line 7 "combinatorial_opt/test/mincostflow.yuki1288.test.cpp"
using namespace std;

int main() {
    int N;
    string S;
    cin >> N >> S;
    vector<long long> V(N);
    for (auto &x : V) cin >> x;

    const int s = N * 5, t = s + 1;
    MinCostFlow<int, long long> graph(t + 1);
    for (int d = 0; d < 5; d++) {
        for (int i = 0; i < N - 1; i++) graph.add_edge(d * N + i, d * N + i + 1, N / 4, 0);
    }
    graph.add_edge(s - 1, 0, N / 4, 0);

    for (int i = 0; i < N; i++) {
        int b = 0;
        if (S[i] == 'u') b = N * 1;
        if (S[i] == 'k') b = N * 2;
        if (S[i] == 'i') b = N * 3;
        int fr = b + i + N, to = b + i;
        graph.add_edge(s, fr, 1, 0);
        graph.add_edge(fr, to, 1, V[i]);
        graph.add_edge(to, t, 1, 0);
    }
    auto cost = graph.flow(s, t, N).second;
    cout << accumulate(V.begin(), V.end(), 0LL) - cost << '\n';
}