#579796 (C++14) No.1288 yuki collection

• 問題: No.1288 yuki collection
• ユーザー: auaua
• 提出日時: 2020-11-13 23:08:09
• 言語: C++14 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 4,663 ms / 5,000 ms
• コード長: 7,062 bytes
• コンパイル時間: 2,277 ms
• コンパイル使用メモリ: 191,332 KB
• 実行使用メモリ: 71,164 KB
• 最終ジャッジ日時: 2024-07-22 22:02:40
• 合計ジャッジ時間: 55,931 ms
• ジャッジサーバーID （参考情報）: judge3 / judge2

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	3 ms; 5,376 KB
testcase_09	AC	3 ms; 5,376 KB
testcase_10	AC	3 ms; 5,376 KB
testcase_11	AC	3 ms; 5,376 KB
testcase_12	AC	3 ms; 5,376 KB
testcase_13	AC	1,777 ms; 42,108 KB
testcase_14	AC	1,874 ms; 42,072 KB
testcase_15	AC	1,232 ms; 34,904 KB
testcase_16	AC	1,272 ms; 35,056 KB
testcase_17	AC	1,895 ms; 41,432 KB
testcase_18	AC	1,910 ms; 41,652 KB
testcase_19	AC	1,780 ms; 41,880 KB
testcase_20	AC	2,072 ms; 43,160 KB
testcase_21	AC	4,362 ms; 61,244 KB
testcase_22	AC	3,993 ms; 59,652 KB
testcase_23	AC	3,979 ms; 59,384 KB
testcase_24	AC	1,915 ms; 42,564 KB
testcase_25	AC	1,829 ms; 42,896 KB
testcase_26	AC	1,934 ms; 42,372 KB
testcase_27	AC	603 ms; 24,044 KB
testcase_28	AC	972 ms; 34,144 KB
testcase_29	AC	796 ms; 37,612 KB
testcase_30	AC	113 ms; 39,640 KB
testcase_31	AC	159 ms; 41,064 KB
testcase_32	AC	162 ms; 39,548 KB
testcase_33	AC	4,410 ms; 69,688 KB
testcase_34	AC	2,486 ms; 44,032 KB
testcase_35	AC	2,179 ms; 41,940 KB
testcase_36	AC	1,167 ms; 43,812 KB
testcase_37	AC	1,283 ms; 43,464 KB
testcase_38	AC	4,663 ms; 71,164 KB
testcase_39	AC	829 ms; 69,308 KB
testcase_40	AC	57 ms; 38,452 KB
testcase_41	AC	2 ms; 5,376 KB
testcase_42	AC	2 ms; 5,376 KB

ソースコード

#include<bits/stdc++.h>
using namespace std;
//#define int long long
#define REP(i,m,n) for(int i=(m);i<(n);i++)
#define rep(i,n) REP(i,0,n)
#define pb push_back
#define all(a) a.begin(),a.end()
#define rall(c) (c).rbegin(),(c).rend()
#define mp make_pair
#define endl '\n'
#define vec vector<ll>
#define mat vector<vector<ll> >
#define fi first
#define se second
typedef long long ll;
typedef unsigned long long ull;
typedef pair<ll,ll> pll;
typedef long double ld;
typedef complex<double> comp;
const ll INF=1e9+7;
const ll inf=INF*INF;
const ll MOD=1e9+7;
const ll mod=MOD;
const ll MAX=3e12;
const double PI=acos(-1.0);

//min_cost_flow
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())});
        int from_id = int(g[from].size());
        int to_id = int(g[to].size());
        if (from == to) to_id++;
        g[from].push_back(_edge{to, to_id, cap, cost});
        g[to].push_back(_edge{from, from_id, 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_per_flow = -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_per_flow == d) {
                result.pop_back();
            }
            result.push_back({flow, cost});
            prev_cost_per_flow = d;
        }
        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;
};


signed main(){
    ll n;cin>>n;
    string st;cin>>st;
    vector<ll>v(n);
    rep(i,n)cin>>v[i];
    ll s=n*2,t=n*2+1;
    mcf_graph<ll,ll>g(n*2+2);
    rep(i,n){
        if(st[i]=='y'){
            g.add_edge(i,i+n,1,0);
            g.add_edge(s,i,1,0);
            REP(j,i+1,n){
                if(st[j]=='u'){
                    g.add_edge(i+n,j,1,MAX-v[i]);
                }
            }
        }
        if(st[i]=='u'){
            g.add_edge(i,i+n,1,0);
            REP(j,i+1,n){
                if(st[j]=='k'){
                    g.add_edge(i+n,j,1,MAX-v[i]);
                }
            }
        }
        if(st[i]=='k'){
            g.add_edge(i,i+n,1,0);
            REP(j,i+1,n){
                if(st[j]=='i'){
                    g.add_edge(i+n,j,1,MAX-v[i]);
                }
            }
        }
        if(st[i]=='i'){
            g.add_edge(i,t,1,MAX-v[i]);
        }
    }
    
    
    vector<pll> sl=g.slope(s,t);vector<mcf_graph<ll,ll>::edge> e=g.edges();
    /*
    for(auto edge :e){
        cout<<edge.from<<' '<<edge.to<<' '<<edge.flow<<endl;
    }
    */
    ll ans=0;
    rep(i,sl.size()){
        ans=max(ans,MAX*4LL*sl[i].fi-sl[i].se);
        //cout<<sl[i].fi<<' '<<MAX*4LL*sl[i].fi-sl[i].se<<endl;
    }
    cout<<ans<<endl;
}