結果

問題 No.1288 yuki collection
ユーザー oteraotera
提出日時 2020-11-18 12:48:01
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 115 ms / 5,000 ms
コード長 8,388 bytes
コンパイル時間 2,841 ms
コンパイル使用メモリ 224,904 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-07-23 09:00:35
合計ジャッジ時間 5,739 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge2
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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
6,812 KB
testcase_01 AC 2 ms
6,940 KB
testcase_02 AC 2 ms
6,940 KB
testcase_03 AC 2 ms
6,944 KB
testcase_04 AC 2 ms
6,944 KB
testcase_05 AC 2 ms
6,940 KB
testcase_06 AC 2 ms
6,944 KB
testcase_07 AC 2 ms
6,940 KB
testcase_08 AC 2 ms
6,940 KB
testcase_09 AC 2 ms
6,944 KB
testcase_10 AC 2 ms
6,940 KB
testcase_11 AC 2 ms
6,940 KB
testcase_12 AC 2 ms
6,944 KB
testcase_13 AC 85 ms
6,940 KB
testcase_14 AC 89 ms
6,940 KB
testcase_15 AC 69 ms
6,940 KB
testcase_16 AC 71 ms
6,940 KB
testcase_17 AC 91 ms
6,940 KB
testcase_18 AC 92 ms
6,944 KB
testcase_19 AC 89 ms
6,944 KB
testcase_20 AC 96 ms
6,940 KB
testcase_21 AC 102 ms
6,940 KB
testcase_22 AC 103 ms
6,944 KB
testcase_23 AC 101 ms
6,944 KB
testcase_24 AC 91 ms
6,940 KB
testcase_25 AC 89 ms
6,944 KB
testcase_26 AC 93 ms
6,940 KB
testcase_27 AC 46 ms
6,940 KB
testcase_28 AC 55 ms
6,940 KB
testcase_29 AC 41 ms
6,944 KB
testcase_30 AC 5 ms
6,940 KB
testcase_31 AC 7 ms
6,940 KB
testcase_32 AC 7 ms
6,940 KB
testcase_33 AC 85 ms
6,944 KB
testcase_34 AC 115 ms
6,940 KB
testcase_35 AC 100 ms
6,940 KB
testcase_36 AC 56 ms
6,944 KB
testcase_37 AC 62 ms
6,940 KB
testcase_38 AC 38 ms
6,944 KB
testcase_39 AC 31 ms
6,944 KB
testcase_40 AC 3 ms
6,944 KB
testcase_41 AC 2 ms
6,944 KB
testcase_42 AC 2 ms
6,944 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

diff # 

/**
 *    author:  otera    
**/
#include<bits/stdc++.h>
using namespace std;

// #define int long long
typedef long long ll;
typedef long double ld;
#define rep(i, n) for(int i = 0; i < n; ++ i)
#define per(i,n) for(int i=n-1;i>=0;i--)
typedef pair<int, int> P;
typedef pair<ll, ll> LP;
#define fr first
#define sc second
#define all(c) c.begin(),c.end()
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }

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

using namespace atcoder;

const ll INF = 1LL<<60;

void solve() {
    int n; string s; cin >> n >> s;
    vector<ll> v(n);
    rep(i, n) {
        cin >> v[i];
    }
    mcf_graph<ll, ll> g(n + 2);
    int src = n, t = n + 1;
    const ll BIG = 1LL<<32;
    // int y = -1, u = -1, k = -1, i = -1;
    // rep(j, n) {
    //     if(s[j] == 'y') {
    //         if(y == -1) {
    //             g.add_edge(src, j, INF, 0);
    //         } else {
    //             g.add_edge(y, j, INF, 0);
    //         }
    //         y = j;
    //     } else if(s[j] == 'u') {
    //         if(y != -1 and y < j) {
    //             g.add_edge(y, j, 1, BIG - v[y]);
    //         }
    //         if(u != -1) {
    //             g.add_edge(u, j, INF, 0);
    //         }
    //         u = j;
    //     } else if(s[j] == 'k') {
    //         if(u != -1 and u < j) {
    //             g.add_edge(u, j, 1, BIG - v[u]);
    //         }
    //         if(k != -1) {
    //             g.add_edge(k, j, INF, 0);
    //         }
    //         k = j;
    //     } else if(s[j] == 'i') {
    //         if(k != -1 and k < j) {
    //             g.add_edge(k, j, 1, BIG - v[k]);
    //         }
    //         if(i != -1) {
    //             g.add_edge(i, j, INF, 0);
    //         }
    //         g.add_edge(j, t, 1, BIG - v[j]);
    //         i = j;
    //     }
    // }
    for(int j = 0; j < n; ++ j) {
        if(s[j] == 'y') {
            g.add_edge(src, j, n, 0);
            break;
        }
    }
    rep(i, n) {
        for(int j = i + 1; j < n; ++ j) {
            if(s[i] == s[j]) {
                g.add_edge(i, j, n, 0);
                break;
            }
        }
        if(s[i] == 'y') {
            for(int j = i + 1; j < n; ++ j) {
                if(s[j] == 'u') {
                    g.add_edge(i, j, 1LL, BIG - v[i]);
                    break;
                }
            }
        } else if(s[i] == 'u') {
            for(int j = i + 1; j < n; ++ j) {
                if(s[j] == 'k') {
                    g.add_edge(i, j, 1LL, BIG - v[i]);
                    break;
                }
            }
        } else if(s[i] == 'k') {
            for(int j = i + 1; j < n; ++ j) {
                if(s[j] == 'i') {
                    g.add_edge(i, j, 1LL, BIG - v[i]);
                    break;
                }
            }
        } else if(s[i] == 'i') {
            g.add_edge(i, t, 1, BIG - v[i]);
        }
    }
    auto res = g.slope(src, t);
    ll ans = 0;
    for (auto&[f,cost] : res) {
        chmax(ans, f * BIG * 4LL - cost);
    }
    cout << ans << "\n";
}

signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	//cout << fixed << setprecision(20);
	//int t; cin >> t; rep(i, t)solve();
	solve();
    return 0;
}
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