Luzhiled's Library

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:heavy_check_mark: Aho Corasick (エイホ–コラシック法) (string/aho-corasick.hpp)

複数文字列に対するパターンマッチングオートマトンを構築します。

Trie のそれぞれのノードがオートマトンのある状態に相当します。

コンストラクタ

AhoCorasick< char_size, margin >()

空の Trie を作ります。

文字の種類数 char_size で、全ての文字に対して margin を減算します。

build

void build(bool heavy = true)

現在の Trie をもとにオートマトンを構築します。

計算量

match

unordered_map<int, int> match(const string &str, int now = 0)

現状態が now で, 文字列 str が現れた時に、新たに各パターン文字列にマッチした回数を返します。

計算量

move

(1) pair<int64_t, int> move(const char &c, int now = 0)
(2) pair<int64_t, int> move(const string &str, int now = 0)

(1) 現状態が now で、文字 c が現れたときに、新たにパターン文字列にマッチした個数と、次状態を返します。

(2) 現状態が now で、文字列 str が現れたときに、新たにパターン文字列にマッチした個数と、次状態を返します。

計算量

Depends on

Verified with

Code

#include "../structure/trie/trie.hpp"

template <int char_size, int margin>
struct AhoCorasick : Trie<char_size + 1, margin> {
  using Trie<char_size + 1, margin>::Trie;

  const int FAIL = char_size;
  vector<int> correct;

  void build(bool heavy = true) {
    correct.resize(this->size());
    for (int i = 0; i < this->size(); i++) {
      correct[i] = (int)this->nodes[i].accept.size();
    }
    queue<int> que;
    for (int i = 0; i <= char_size; i++) {
      if (~this->nodes[0].nxt[i]) {
        this->nodes[this->nodes[0].nxt[i]].nxt[FAIL] = 0;
        que.emplace(this->nodes[0].nxt[i]);
      } else {
        this->nodes[0].nxt[i] = 0;
      }
    }
    while (!que.empty()) {
      auto &now = this->nodes[que.front()];
      int fail = now.nxt[FAIL];
      correct[que.front()] += correct[fail];
      que.pop();
      for (int i = 0; i < char_size; i++) {
        if (~now.nxt[i]) {
          this->nodes[now.nxt[i]].nxt[FAIL] = this->nodes[fail].nxt[i];
          if (heavy) {
            auto &u = this->nodes[now.nxt[i]].accept;
            auto &v = this->nodes[this->nodes[fail].nxt[i]].accept;
            vector<int> accept;
            set_union(begin(u), end(u), begin(v), end(v),
                      back_inserter(accept));
            u = accept;
          }
          que.emplace(now.nxt[i]);
        } else {
          now.nxt[i] = this->nodes[fail].nxt[i];
        }
      }
    }
  }

  unordered_map<int, int> match(const string &str, int now = 0) {
    unordered_map<int, int> result, visit_cnt;
    for (auto &c : str) {
      now = this->nodes[now].nxt[c - margin];
      visit_cnt[now]++;
    }
    for (auto &[now, cnt] : visit_cnt) {
      for (auto &v : this->nodes[now].accept) result[v] += cnt;
    }
    return result;
  }

  pair<int64_t, int> move(const char &c, int now = 0) {
    now = this->nodes[now].nxt[c - margin];
    return {correct[now], now};
  }

  pair<int64_t, int> move(const string &str, int now = 0) {
    int64_t sum = 0;
    for (auto &c : str) {
      auto nxt = move(c, now);
      sum += nxt.first;
      now = nxt.second;
    }
    return {sum, now};
  }
};

#line 1 "structure/trie/trie.hpp"
template <int char_size>
struct TrieNode {
  int nxt[char_size];

  int exist;
  vector<int> accept;

  TrieNode() : exist(0) { memset(nxt, -1, sizeof(nxt)); }
};

template <int char_size, int margin>
struct Trie {
  using Node = TrieNode<char_size>;

  vector<Node> nodes;
  int root;

  Trie() : root(0) { nodes.push_back(Node()); }

  void update_direct(int node, int id) { nodes[node].accept.push_back(id); }

  void update_child(int node, int child, int id) { ++nodes[node].exist; }

  void add(const string &str, int str_index, int node_index, int id) {
    if (str_index == str.size()) {
      update_direct(node_index, id);
    } else {
      const int c = str[str_index] - margin;
      if (nodes[node_index].nxt[c] == -1) {
        nodes[node_index].nxt[c] = (int)nodes.size();
        nodes.push_back(Node());
      }
      add(str, str_index + 1, nodes[node_index].nxt[c], id);
      update_child(node_index, nodes[node_index].nxt[c], id);
    }
  }

  void add(const string &str, int id) { add(str, 0, 0, id); }

  void add(const string &str) { add(str, nodes[0].exist); }

  void query(const string &str, const function<void(int)> &f, int str_index,
             int node_index) {
    for (auto &idx : nodes[node_index].accept) f(idx);
    if (str_index == str.size()) {
      return;
    } else {
      const int c = str[str_index] - margin;
      if (nodes[node_index].nxt[c] == -1) return;
      query(str, f, str_index + 1, nodes[node_index].nxt[c]);
    }
  }

  void query(const string &str, const function<void(int)> &f) {
    query(str, f, 0, 0);
  }

  int count() const { return (nodes[0].exist); }

  int size() const { return ((int)nodes.size()); }
};
#line 2 "string/aho-corasick.hpp"

template <int char_size, int margin>
struct AhoCorasick : Trie<char_size + 1, margin> {
  using Trie<char_size + 1, margin>::Trie;

  const int FAIL = char_size;
  vector<int> correct;

  void build(bool heavy = true) {
    correct.resize(this->size());
    for (int i = 0; i < this->size(); i++) {
      correct[i] = (int)this->nodes[i].accept.size();
    }
    queue<int> que;
    for (int i = 0; i <= char_size; i++) {
      if (~this->nodes[0].nxt[i]) {
        this->nodes[this->nodes[0].nxt[i]].nxt[FAIL] = 0;
        que.emplace(this->nodes[0].nxt[i]);
      } else {
        this->nodes[0].nxt[i] = 0;
      }
    }
    while (!que.empty()) {
      auto &now = this->nodes[que.front()];
      int fail = now.nxt[FAIL];
      correct[que.front()] += correct[fail];
      que.pop();
      for (int i = 0; i < char_size; i++) {
        if (~now.nxt[i]) {
          this->nodes[now.nxt[i]].nxt[FAIL] = this->nodes[fail].nxt[i];
          if (heavy) {
            auto &u = this->nodes[now.nxt[i]].accept;
            auto &v = this->nodes[this->nodes[fail].nxt[i]].accept;
            vector<int> accept;
            set_union(begin(u), end(u), begin(v), end(v),
                      back_inserter(accept));
            u = accept;
          }
          que.emplace(now.nxt[i]);
        } else {
          now.nxt[i] = this->nodes[fail].nxt[i];
        }
      }
    }
  }

  unordered_map<int, int> match(const string &str, int now = 0) {
    unordered_map<int, int> result, visit_cnt;
    for (auto &c : str) {
      now = this->nodes[now].nxt[c - margin];
      visit_cnt[now]++;
    }
    for (auto &[now, cnt] : visit_cnt) {
      for (auto &v : this->nodes[now].accept) result[v] += cnt;
    }
    return result;
  }

  pair<int64_t, int> move(const char &c, int now = 0) {
    now = this->nodes[now].nxt[c - margin];
    return {correct[now], now};
  }

  pair<int64_t, int> move(const string &str, int now = 0) {
    int64_t sum = 0;
    for (auto &c : str) {
      auto nxt = move(c, now);
      sum += nxt.first;
      now = nxt.second;
    }
    return {sum, now};
  }
};
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