#579497 (C++14) No.1288 yuki collection

• 問題: No.1288 yuki collection
• ユーザー: kyort0n
• 提出日時: 2020-11-13 22:05:01
• 言語: C++14 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 290 ms / 5,000 ms
• コード長: 6,594 bytes
• コンパイル時間: 1,900 ms
• コンパイル使用メモリ: 190,260 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-07-22 20:52:30
• 合計ジャッジ時間: 7,945 ms
• ジャッジサーバーID （参考情報）: judge3 / judge4

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	AC	2 ms; 5,376 KB
testcase_04	AC	2 ms; 5,376 KB
testcase_05	AC	2 ms; 5,376 KB
testcase_06	AC	2 ms; 5,376 KB
testcase_07	AC	2 ms; 5,376 KB
testcase_08	AC	2 ms; 5,376 KB
testcase_09	AC	2 ms; 5,376 KB
testcase_10	AC	2 ms; 5,376 KB
testcase_11	AC	2 ms; 5,376 KB
testcase_12	AC	2 ms; 5,376 KB
testcase_13	AC	221 ms; 5,376 KB
testcase_14	AC	234 ms; 5,376 KB
testcase_15	AC	176 ms; 5,376 KB
testcase_16	AC	180 ms; 5,376 KB
testcase_17	AC	232 ms; 5,376 KB
testcase_18	AC	241 ms; 5,376 KB
testcase_19	AC	230 ms; 5,376 KB
testcase_20	AC	249 ms; 5,376 KB
testcase_21	AC	290 ms; 5,376 KB
testcase_22	AC	284 ms; 5,376 KB
testcase_23	AC	282 ms; 5,376 KB
testcase_24	AC	233 ms; 5,376 KB
testcase_25	AC	224 ms; 5,376 KB
testcase_26	AC	235 ms; 5,376 KB
testcase_27	AC	140 ms; 5,376 KB
testcase_28	AC	154 ms; 5,376 KB
testcase_29	AC	112 ms; 5,376 KB
testcase_30	AC	12 ms; 5,376 KB
testcase_31	AC	18 ms; 5,376 KB
testcase_32	AC	19 ms; 5,376 KB
testcase_33	AC	121 ms; 5,376 KB
testcase_34	AC	235 ms; 5,376 KB
testcase_35	AC	223 ms; 5,376 KB
testcase_36	AC	177 ms; 5,376 KB
testcase_37	AC	198 ms; 5,376 KB
testcase_38	AC	201 ms; 5,376 KB
testcase_39	AC	96 ms; 5,376 KB
testcase_40	AC	4 ms; 5,376 KB
testcase_41	AC	1 ms; 5,376 KB
testcase_42	AC	1 ms; 5,376 KB

ソースコード

#include <bits/stdc++.h>

#include <algorithm>
#include <cassert>
#include <limits>
#include <queue>
#include <vector>

namespace atcoder {

template <class Cap, class Cost> struct mcf_graph {
  public:
    mcf_graph() {}
    mcf_graph(int n) : _n(n), g(n) {}

    int add_edge(int from, int to, Cap cap, Cost cost) {
        assert(0 <= from && from < _n);
        assert(0 <= to && to < _n);
        int m = int(pos.size());
        pos.push_back({from, int(g[from].size())});
        g[from].push_back(_edge{to, int(g[to].size()), cap, cost});
        g[to].push_back(_edge{from, int(g[from].size()) - 1, 0, -cost});
        return m;
    }

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

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

    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);
        // 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
        std::vector<Cost> dual(_n, 0), dist(_n);
        std::vector<int> pv(_n), pe(_n);
        std::vector<bool> vis(_n);
        auto dual_ref = [&]() {
            std::fill(dist.begin(), dist.end(),
                      std::numeric_limits<Cost>::max());
            std::fill(pv.begin(), pv.end(), -1);
            std::fill(pe.begin(), pe.end(), -1);
            std::fill(vis.begin(), vis.end(), false);
            struct Q {
                Cost key;
                int to;
                bool operator<(Q r) const { return key > r.key; }
            };
            std::priority_queue<Q> que;
            dist[s] = 0;
            que.push(Q{0, s});
            while (!que.empty()) {
                int v = que.top().to;
                que.pop();
                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
                for (int i = 0; i < int(g[v].size()); i++) {
                    auto e = g[v][i];
                    if (vis[e.to] || !e.cap) continue;
                    // |-dual[e.to] + dual[v]| <= (n-1)C
                    // cost <= C - -(n-1)C + 0 = nC
                    Cost cost = e.cost - dual[e.to] + dual[v];
                    if (dist[e.to] - dist[v] > cost) {
                        dist[e.to] = dist[v] + cost;
                        pv[e.to] = v;
                        pe[e.to] = i;
                        que.push(Q{dist[e.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[v] -= dist[t] - dist[v];
            }
            return true;
        };
        Cap flow = 0;
        Cost cost = 0, prev_cost = -1;
        std::vector<std::pair<Cap, Cost>> result;
        result.push_back({flow, cost});
        while (flow < flow_limit) {
            if (!dual_ref()) break;
            Cap c = flow_limit - flow;
            for (int v = t; v != s; v = pv[v]) {
                c = std::min(c, g[pv[v]][pe[v]].cap);
            }
            for (int v = t; v != s; v = pv[v]) {
                auto& e = g[pv[v]][pe[v]];
                e.cap -= c;
                g[v][e.rev].cap += c;
            }
            Cost d = -dual[s];
            flow += c;
            cost += c * d;
            if (prev_cost == d) {
                result.pop_back();
            }
            result.push_back({flow, cost});
            prev_cost = cost;
        }
        return result;
    }

  private:
    int _n;

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

    std::vector<std::pair<int, int>> pos;
    std::vector<std::vector<_edge>> g;
};

}  // namespace atcoder

#define endl "\n"
using namespace std;
typedef long long ll;
typedef pair<ll, ll> l_l;
typedef pair<int, int> i_i;
template<class T>
inline bool chmax(T &a, T b) {
    if(a < b) {
        a = b;
        return true;
    }
    return false;
}

template<class T>
inline bool chmin(T &a, T b) {
    if(a > b) {
        a = b;
        return true;
    }
    return false;
}

const long long INF = 1e18;
//const ll mod = 1000000007;
ll N;
string S;
vector<ll> V;
ll ans = 0;
vector<ll> s;
string yuki = "yuki";

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cin >> N >> S;
    V.resize(N);
    for(int i = 0; i < N; i++) cin >> V[i];
    ll s = 4 * N;
    ll t = s + 1;
    atcoder::mcf_graph<ll, ll> g(t + 1);
    g.add_edge(s, 0, N, 0);
    for(int i = 0; i + 1 < N; i++) {
        for(int j = 0; j < 4; j++) {
            g.add_edge(4 * i + j, 4 * (i + 1) + j, N, 0);
        }
    }
    for(int i = 0; i < N; i++) {
        for(int j = 0; j < 4; j++) {
            if(S[i] != yuki[j]) continue;
            if(j != 3) {
                g.add_edge(4*i+j, 4*i+j+1, 1, (ll)1e9 - V[i]);
            } else {
                g.add_edge(4*i+j, t, 1, (ll)1e9 - V[i]);
            }
        }
    }
    ll mflow = N / 4;
    g.add_edge(s, t, mflow, 4e9);
    l_l tmp = g.flow(s, t, mflow);
    ll ans = tmp.first * (ll)1e9 * 4 - tmp.second;
    cout << ans << endl;
    return 0;
}