#698392 (C++23) No.1678 Coin Trade (Multiple)

提出ソース
結果

問題	No.1678 Coin Trade (Multiple)
ユーザー	hitonanode
提出日時	2021-09-10 22:43:53
言語	C++23 (gcc 12.3.0 + boost 1.83.0)
結果	TLE
実行時間	-
コード長	14,743 bytes
コンパイル時間	2,114 ms
コンパイル使用メモリ	185,872 KB
実行使用メモリ	78,024 KB
最終ジャッジ日時	2024-06-12 02:07:09
合計ジャッジ時間	9,015 ms
ジャッジサーバーID （参考情報）	judge1 / judge2
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	2 ms 5,248 KB
testcase_01	AC	2 ms 5,376 KB
testcase_02	AC	2 ms 5,376 KB
testcase_03	TLE	-
testcase_04	--	-
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testcase_17	--	-
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testcase_19	--	-
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testcase_25	--	-
testcase_26	--	-
testcase_27	--	-
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testcase_29	--	-
testcase_30	--	-
testcase_31	--	-
testcase_32	--	-
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testcase_35	--	-
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testcase_42	--	-
testcase_43	--	-
testcase_44	--	-
testcase_45	--	-
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testcase_48	--	-
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testcase_50	--	-
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testcase_52	--	-
testcase_53	--	-
testcase_54	--	-
testcase_55	--	-
testcase_56	--	-
testcase_57	--	-
testcase_58	--	-
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
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define REP(i, n) FOR(i,0,n)

template <class Uint> class radix_heap_array {
    int sz;
    Uint last;
    std::array<std::vector<std::pair<Uint, int>>, std::numeric_limits<Uint>::digits + 1> v;

    struct smallpii {
        unsigned b : 7;
        int j : 25;
    };
    std::vector<smallpii> i2bj;

    template <class U, typename std::enable_if<sizeof(U) == 4>::type* = nullptr>
    static inline unsigned bucket(U x) noexcept {
        return x ? 32 - __builtin_clz(x) : 0;
    }
    template <class U, typename std::enable_if<sizeof(U) == 8>::type* = nullptr>
    static inline unsigned bucket(U x) noexcept {
        return x ? 64 - __builtin_clzll(x) : 0;
    }

    void pull() {
        if (!v[0].empty()) return;
        int b = 1;
        while (v[b].empty()) ++b;
        last = v[b].back().first;
        for (int j = 0; j < int(v[b].size()); j++) last = std::min(last, v[b][j].first);
        for (int j = 0; j < int(v[b].size()); j++) {
            int i = v[b][j].second;
            auto bnxt = bucket(v[b][j].first ^ last);
            i2bj[i] = {bnxt, int(v[bnxt].size())}, v[bnxt].emplace_back(std::move(v[b][j]));
        }
        v[b].clear();
    }

public:
    radix_heap_array() : sz(0), last(0) {}
    bool empty() const noexcept { return sz == 0; }
    int argmin_pop() {
        pull(), --sz;
        int i = v[0].back().second;
        i2bj[i].j = -1;
        v[0].pop_back();
        return i;
    }
    void chmin(Uint vnew, int i) {
        if (i >= int(i2bj.size())) i2bj.resize(i + 1, {0, -1});
        if (i2bj[i].j < 0) {
            auto b = bucket(vnew ^ last);
            ++sz, i2bj[i] = {b, int(v[b].size())}, v[b].emplace_back(vnew, i);
        } else if (v[i2bj[i].b][i2bj[i].j].first > vnew) {
            auto bold = i2bj[i].b, bnew = bucket(vnew ^ last);
            if (bnew < bold) {
                int ilast = v[bold].back().second, j = i2bj[i].j;
                std::swap(v[bold][j], v[bold].back());
                i2bj[ilast].j = j, i2bj[i] = {bnew, int(v[bnew].size())};
                v[bnew].emplace_back(vnew, i), v[bold].pop_back();
            } else {
                v[bold][i2bj[i].j].first = vnew;
            }
        }
    }

    void pop() { argmin_pop(); }
    std::pair<Uint, int> top() { return pull(), v[0].back(); }
    [[deprecated("NOT usual emplace() opeation!")]] void emplace(Uint vnew, int i) { chmin(vnew, i); }

    void clear() noexcept { sz = 0, last = 0, i2bj.assign(i2bj.size(), {0, -1}); }
};


// 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();
    }

    radix_heap_array<unsigned long long> q;
    void _dijkstra(int s) { // O(ElogV)
        prevv.assign(V, -1);
        preve.assign(V, -1);
        dist.assign(V, INF_COST);
        dist[s] = 0;
        q.clear();
        q.chmin(0, s);
        while (!q.empty()) {
            int v = q.argmin_pop();
            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.chmin(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.
    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(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;
    }
};

// Cost scaling
// https://people.orie.cornell.edu/dpw/orie633/
template <class Cap, class Cost, int SCALING = 1, int REFINEMENT_ITER = 20> struct mcf_costscaling {
    mcf_costscaling() = default;
    mcf_costscaling(int n) : _n(n), to(n), b(n), p(n) {}

    int _n;
    std::vector<Cap> cap;
    std::vector<Cost> cost;
    std::vector<int> opposite;
    std::vector<std::vector<int>> to;
    std::vector<Cap> b;
    std::vector<Cost> p;

    int add_edge(int from_, int to_, Cap cap_, Cost cost_) {
        assert(0 <= from_ and from_ < _n);
        assert(0 <= to_ and to_ < _n);
        assert(0 <= cap_);
        cost_ *= (_n + 1);
        const int e = int(cap.size());
        to[from_].push_back(e);
        cap.push_back(cap_);
        cost.push_back(cost_);
        opposite.push_back(to_);

        to[to_].push_back(e + 1);
        cap.push_back(0);
        cost.push_back(-cost_);
        opposite.push_back(from_);
        return e / 2;
    }
    void add_supply(int v, Cap supply) { b[v] += supply; }
    void add_demand(int v, Cap demand) { add_supply(v, -demand); }

    template <typename RetCost = Cost> RetCost solve() {
        Cost eps = 1;
        std::vector<int> que;
        for (const auto c : cost) {
            while (eps <= -c) eps <<= SCALING;
        }
        for (; eps >>= SCALING;) {
            auto no_admissible_cycle = [&]() -> bool {
                for (int i = 0; i < _n; i++) {
                    if (b[i]) return false;
                }
                std::vector<Cost> pp = p;
                for (int iter = 0; iter < REFINEMENT_ITER; iter++) {
                    bool flg = false;
                    for (int e = 0; e < int(cap.size()); e++) {
                        if (!cap[e]) continue;
                        int i = opposite[e ^ 1], j = opposite[e];
                        if (pp[j] > pp[i] + cost[e] + eps) pp[j] = pp[i] + cost[e] + eps, flg = true;
                    }
                    if (!flg) return p = pp, true;
                }
                return false;
            };
            if (no_admissible_cycle()) continue; // Refine

            for (int e = 0; e < int(cap.size()); e++) {
                const int i = opposite[e ^ 1], j = opposite[e];
                const Cost cp_ij = cost[e] + p[i] - p[j];
                if (cap[e] and cp_ij < 0) b[i] -= cap[e], b[j] += cap[e], cap[e ^ 1] += cap[e], cap[e] = 0;
            }
            que.clear();
            int qh = 0;
            for (int i = 0; i < _n; i++) {
                if (b[i] > 0) que.push_back(i);
            }
            std::vector<int> iters(_n);
            while (qh < int(que.size())) {
                const int i = que[qh++];
                for (; iters[i] < int(to[i].size()) and b[i]; ++iters[i]) { // Push
                    int e = to[i][iters[i]];
                    if (!cap[e]) continue;
                    int j = opposite[e];
                    Cost cp_ij = cost[e] + p[i] - p[j];
                    if (cp_ij >= 0) continue;
                    Cap f = b[i] > cap[e] ? cap[e] : b[i];
                    if (b[j] <= 0 and b[j] + f > 0) que.push_back(j);
                    b[i] -= f, b[j] += f, cap[e] -= f, cap[e ^ 1] += f;
                }

                if (b[i] > 0) { // Relabel
                    bool flg = false;
                    for (int e : to[i]) {
                        if (!cap[e]) continue;
                        Cost x = p[opposite[e]] - cost[e] - eps;
                        if (!flg or x > p[i]) flg = true, p[i] = x;
                    }
                    que.push_back(i), iters[i] = 0;
                }
            }
        }
        RetCost ret = 0;
        for (int e = 0; e < int(cap.size()); e += 2) ret += RetCost(cost[e]) * cap[e ^ 1];
        return ret / (_n + 1);
    }
    std::vector<Cost> potential() const {
        std::vector<Cost> ret = p, c0 = cost;
        for (auto &x : ret) x /= (_n + 1);
        for (auto &x : c0) x /= (_n + 1);
        while (true) {
            bool flg = false;
            for (int i = 0; i < _n; i++) {
                for (const auto e : to[i]) {
                    if (!cap[e]) continue;
                    int j = opposite[e];
                    auto y = ret[i] + c0[e];
                    if (ret[j] > y) ret[j] = y, flg = true;
                }
            }
            if (!flg) break;
        }
        return ret;
    }
    struct edge {
        int from, to;
        Cap cap, flow;
        Cost cost;
    };
    edge get_edge(int e) const {
        int m = cap.size() / 2;
        assert(e >= 0 and e < m);
        return {opposite[e * 2 + 1], opposite[e * 2], cap[e * 2] + cap[e * 2 + 1], cap[e * 2 + 1], cost[e * 2] / (_n + 1)};
    }
    std::vector<edge> edges() const {
        int m = cap.size() / 2;
        std::vector<edge> result(m);
        for (int i = 0; i < m; i++) result[i] = get_edge(i);
        return result;
    }
};



int main() {
    cin.tie(nullptr), ios::sync_with_stdio(false);
    int N, K;
    cin >> N >> K;
    constexpr lint INF = 1LL << 60;
    // MinCostFlow<int, lint> mcf(N + 2);
    mcf_costscaling<int, lint> mcf(N + 1);
    REP(i, N) mcf.add_edge(i, i + 1, K, 0);
    vector<int> A(N + 1);
    FOR(i, 1, N + 1) {
        int m;
        cin >> A[i] >> m;
        while (m--) {
            int b;
            cin >> b;
            mcf.add_edge(b, i, 1, -A[i] + A[b]);
        }
    }
    mcf.add_supply(0, K);
    mcf.add_demand(N, K);
    // cout << -mcf.flow(0, N, K).second << '\n';
    cout << -mcf.solve<lint>() << '\n';
}
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結果

テストケース

ソースコード
