#580121 (C++14) No.1288 yuki collection

• 問題: No.1288 yuki collection
• ユーザー: どらら
• 提出日時: 2020-11-14 13:37:08
• 言語: C++14 (gcc 15.2.0 + boost 1.89.0)
• 結果: TLE
• 実行時間: -
• コード長: 6,887 bytes
• コンパイル時間: 2,278 ms
• コンパイル使用メモリ: 191,184 KB
• 実行使用メモリ: 74,496 KB
• 最終ジャッジ日時: 2024-07-22 22:52:02
• 合計ジャッジ時間: 30,049 ms
• ジャッジサーバーID （参考情報）: judge4 / judge3

ファイルパターン	結果
sample	AC * 3
other	AC * 18 TLE * 1 -- * 21

ソースコード

#include <bits/stdc++.h>
using namespace std;
#define REP(i,a,n) for(int i=(a); i<(int)(n); i++)
#define rep(i,n) REP(i,0,n)
#define FOR(it,c) for(__typeof((c).begin()) it=(c).begin(); it!=(c).end(); ++it)
#define ALLOF(c) (c).begin(), (c).end()
typedef long long ll;
typedef unsigned long long ull;

class Dinic {
  int MAX_V;
  int INF;
  struct edge {
    int to, cap, rev, icap, flow;
  };

  vector<vector<edge>> G;
  vector<int> level;  // sからの距離
  vector<int> iter;   //どこまで調べたか

  void max_flow_bfs(int s) {
    fill(level.begin(), level.end(), -1);
    queue<int> que;
    level[s] = 0;
    que.push(s);
    while (!que.empty()) {
      int v = que.front();
      que.pop();
      for (int i = 0; i < G[v].size(); i++) {
        edge& e = G[v][i];
        if (e.cap > 0 && level[e.to] < 0) {
          level[e.to] = level[v] + 1;
          que.push(e.to);
        }
      }
    }
  }
  int max_flow_dfs(int v, int t, int f) {
    if (v == t) return f;
    for (int& i = iter[v]; i < G[v].size(); i++) {
      edge& e = G[v][i];
      if (e.cap > 0 && level[v] < level[e.to]) {
        int d = max_flow_dfs(e.to, t, min(f, e.cap));
        if (d > 0) {
          e.cap -= d;
          G[e.to][e.rev].cap += d;
          e.flow += d;
          return d;
        }
      }
    }
    return 0;
  }

 public:
  Dinic(int N) : MAX_V(N), G(N), level(N), iter(N) { INF = 99999999; }

  void add_edge(int from, int to, int cap) {
    G[from].push_back((edge){to, cap, (int)G[to].size(), cap, 0});
    G[to].push_back((edge){from, 0, (int)G[from].size() - 1, 0, 0});
  }

  int get_flow(int from, int to) {  // untried
    rep(i, G[from].size()) {
      if (G[from][i].to == to) {
        return G[from][i].flow;
      }
    }
    return -1;
  }

  int max_flow(int s, int t) {
    int flow = 0;
    while (true) {
      max_flow_bfs(s);
      if (level[t] < 0) return flow;
      fill(iter.begin(), iter.end(), 0);
      int f;
      while ((f = max_flow_dfs(s, t, INF)) > 0) {
        flow += f;
      }
    }
  }

  int min_cut(int s, int t, vector<int>& S, vector<int>& T) {
    S.clear();
    T.clear();

    int maxf = max_flow(s, t);
    for (int i = 0; i < level.size(); i++) {
      if (level[i] >= 0)
        S.push_back(i);
      else
        T.push_back(i);
    }

    return maxf;
  }
};

class CostScalingMinCostFlow {
  static constexpr double alpha = 2;

 public:
  struct Node {
    int b;
    double p;
    int in_f, out_f;
    Node() : b(0), p(0), in_f(0), out_f(0) {}
    Node(int b, double p) : b(b), p(p), in_f(0), out_f(0) {}
  };

  struct Edge {
    int from, to;
    int cap, cost;
    int rev;
    int f;
    bool isrev;
    Edge() : from(-1), to(-1), cap(0), cost(0), rev(-1), f(0), isrev(false) {}
    Edge(int from, int to, int cap, int cost, int rev, int f, bool isrev)
        : from(from),
          to(to),
          cap(cap),
          cost(cost),
          rev(rev),
          f(f),
          isrev(isrev) {}
  };

 private:
  std::vector<Node> nodes;
  std::vector<std::vector<Edge>> G;
  double epsilon;
  std::queue<int> active_nodes;

  int residual_cap(const Edge& e) const {
    if (!e.isrev)
      return e.cap - e.f;
    else
      return G[e.to][e.rev].f;
  }

  double reduced_cost(const Edge& e) const {
    return e.cost + nodes[e.from].p - nodes[e.to].p;
  }
  int excess(int i) const {
    return nodes[i].b - nodes[i].out_f + nodes[i].in_f;
  }
  bool is_active(int i) const { return excess(i) > 0; }

  void push(Edge& edge, int delta) {
    if (!edge.isrev) {
      edge.f += delta;
      nodes[edge.from].out_f += delta;
      nodes[edge.to].in_f += delta;
    } else {
      G[edge.to][edge.rev].f -= delta;
      nodes[edge.to].out_f -= delta;
      nodes[edge.from].in_f -= delta;
    }
  }

  void relabel(int v) {
    double mx = std::numeric_limits<double>::lowest();
    for (Edge& edge : G[v]) {
      if (residual_cap(edge) > 0) {
        mx = std::max(mx, nodes[edge.to].p - edge.cost - epsilon);
      }
    }
    nodes[v].p = mx;
  }

  void refine() {
    for (auto& edges : G) {
      for (Edge& edge : edges) {
        // if (edge.isrev) continue;
        if (reduced_cost(edge) >= 0) continue;
        if (residual_cap(edge) <= 0) continue;
        push(edge, residual_cap(edge));
      }
    }

    for (int i = 0; i < nodes.size(); i++) {
      if (is_active(i)) active_nodes.push(i);
    }

    while (!active_nodes.empty()) {
      int v = active_nodes.front();
      active_nodes.pop();
      if (!is_active(v)) continue;

      bool is_pushed = false;
      for (Edge& edge : G[v]) {
        if (reduced_cost(edge) >= 0) continue;
        if (residual_cap(edge) <= 0) continue;

        push(edge, std::min(residual_cap(edge), excess(v)));
        if (is_active(edge.from)) active_nodes.push(edge.from);
        if (is_active(edge.to)) active_nodes.push(edge.to);
        is_pushed = true;
        break;
      }

      if (!is_pushed) {
        relabel(v);
        if (is_active(v)) active_nodes.push(v);
      }
    }
  }

 public:
  CostScalingMinCostFlow(int N) : nodes(N), G(N), epsilon(0) {}

  void add_edge(int from, int to, int cap, int cost) {
    epsilon = std::max(epsilon, (double)abs(cost));
    G[from].emplace_back(from, to, cap, cost, G[to].size(), 0, false);
    G[to].emplace_back(to, from, cap, -cost, G[from].size() - 1, cap, true);
  }

  void set_b(int i, int b) { nodes[i].b = b; }

  long long mincostflow() {
    int N = nodes.size();
    while (epsilon >= 1.0 / N) {
      epsilon /= alpha;
      refine();
    }

    long long ret = 0;
    for (auto& edges : G) {
      for (Edge& edge : edges) {
        if (edge.isrev) continue;
        ret += edge.cost * edge.f;
      }
    }
    return ret;
  }
};

int main(){
  int N;
  cin >> N;
  string S;
  cin >> S;
  vector<ll> v;
  rep(i,N){
    ll a;
    cin >> a;
    v.push_back(a);
  }

  Dinic dinic(2*N+2);
  CostScalingMinCostFlow mcf(2*N+2);
  
  int s = 2*N;
  int t = s+1;
  
  rep(i,N){
    if(S[i] == 'y'){
      mcf.add_edge(s, i, 1, -v[i]);
      dinic.add_edge(s, i, 1);
    }
    mcf.add_edge(i, i+N, 1, 0);
    dinic.add_edge(i, i+N, 1);
    if(S[i] == 'i'){
      mcf.add_edge(i+N, t, 1, 0);
      dinic.add_edge(i+N, t, 1);
    }
    rep(j,N){
      if(S[i] == 'y' && S[j] == 'u'){
        if(i<j){
          mcf.add_edge(i+N, j, 1, -v[j]);
          dinic.add_edge(i+N, j, 1);
        }
      }
      if(S[i] == 'u' && S[j] == 'k'){
        if(i<j){
          mcf.add_edge(i+N, j, 1, -v[j]);
          dinic.add_edge(i+N, j, 1);
        }
      }
      if(S[i] == 'k' && S[j] == 'i'){
        if(i<j){
          mcf.add_edge(i+N, j, 1, -v[j]);
          dinic.add_edge(i+N, j, 1);
        }
      }
    }
  }

  mcf.add_edge(s, t, 10000, 0);

  int f = dinic.max_flow(s, t);
  cerr << f << endl;
  mcf.set_b(s, f);
  mcf.set_b(t, -f);
  cout << -mcf.mincostflow() << endl;
  
  return 0;
}