Add Aho Corasick

Signed-off-by: Bruno Freitas Tissei <bft15@inf.ufpr.br>

algorithms/string/aho_corasick.cpp

+/// Aho-Corasick
+///
+/// Time:
+///   - build:      O(n)
+///   - preprocess: O(n)
+///   - match:      O(p + n)
+///   - match_all:  O(p + x)
+/// Space: O(n + p)
+///
+/// Caution:
+///   - Match might not find all occurences when repeated strings are given (fix with map)
+
+// *: Use only if "match_all" is necessary
+struct AhoCorasick {
+  struct Node {
+    //*: vector<int> words;
+    map<char,int> next;
+    int idx, fail, cnt, hei;
+
+    Node() : idx(-1), fail(0), cnt(0), hei(0) {}
+    int has(char i) { return next.count(i); }
+    int &operator[](char i) { return next[i]; }
+  };
+  
+  vector<int> top;
+  vector<Node> trie;
+
+  AhoCorasick(const vector<string> &v) {
+    trie.pb(Node());
+    build(v);
+    top = preprocess();
+  }
+
+  int insert(const string &s) {
+    int n = 0;
+    for (int i = 0; i < s.size(); n = trie[n][s[i]], ++i)
+      if (!trie[n].has(s[i])) {
+        trie[n][s[i]] = trie.size();
+        //*: trie[n].hei = i + 1;
+        trie.pb(Node());
+      }
+    return n;
+  }
+
+  void build(const vector<string> &v) {
+    for (int i = 0; i < v.size(); ++i) {
+      int n = insert(v[i]);
+      trie[n].idx = i;
+      //*: trie[n].words.pb(i);
+    }
+    preprocess();
+  }
+
+  inline int suffix(int v, char c) {
+    while (v != 0 && !trie[v].has(c)) v = trie[v].fail;
+    if (trie[v].has(c)) v = trie[v][c];
+    return v;
+  }
+
+  vector<int> preprocess() {
+    vector<int> Q = { 0 };
+    for (int i = 0; i != Q.size(); ++i) {
+      int u = Q[i];
+      for (auto j : trie[u].next) {
+        trie[j.se].fail = u ? suffix(trie[u].fail, j.fi) : trie[u].fail;
+
+        //*: trie[j.se].words.insert(trie[j.se].words.end(), 
+        // all(trie[trie[j.se].fail].words));
+        Q.pb(j.se);
+      }
+    }
+    return Q;
+  }
+
+  // Returns vector with indices of the strings occuring at 
+  // least once in pattern p
+  vector<int> match(const string &p) {
+    int u = 0;
+    for (auto i : p) {
+      u = suffix(u, i);
+      trie[u].cnt++;
+    }
+
+    for (int i = top.size() - 1; i >= 0; --i)
+      trie[trie[top[i]].fail].cnt += trie[top[i]].cnt;
+
+    vector<int> ans;
+    for (auto i : trie)
+      if (i.idx != -1 && i.cnt)
+        ans.pb(i.idx);
+
+    sort(all(ans));
+    return ans;
+  }
+
+  // Returns all occurences of strings in p, where ans[i].fi
+  // is the indice of the string and ans[i].se is where in p
+  // does the string start
+  vector<ii> match_all(const string &p) {
+    int u = 0;
+    vector<ii> ans;
+    for (int i = 0; i < p.size(); ++i) {
+      u = suffix(u, p[i]);
+      for (auto j : trie[u].words)
+        ans.pb({j, i - trie[u].hei + 1});
+    }
+    return ans;
+  }
+};