Aho-Corasick multiple string matching algorithm (#8)

* Add implementation of Aho-Corasick Automaton
* Add tests
* Add tex+pdf

exact_multiple_string_matching/aho_corasick.py

@@ -0,0 +1,122 @@
+from queue import Queue
+
+
+def create_aho_corasick_automaton(keywords, alphabet='ab'):
+  return AhoCorasickAutomaton(keywords, alphabet)
+
+
+def find_occurrences(text, n, ac_automaton):
+  return ac_automaton.find_occurrences(text, n)
+
+
+# pylint: disable=too-few-public-methods
+class AhoCorasickAutomaton:
+  def __init__(self, keywords, alphabet):
+    self._root = AhoCorasickAutomaton.Node()
+    self._construct_goto(keywords, alphabet)
+    self._construct_fail(alphabet)
+    self._construct_nxt(alphabet)
+
+  def _construct_goto(self, keywords, alphabet):
+    for k, k_len in keywords:
+      self._enter(k, k_len)
+
+    for a in alphabet:
+      if self._root.goto(a) is None:
+        self._root.update_goto(a, self._root)
+
+  def _enter(self, keyword, keyword_len):
+    current_state = self._root
+    j = 1
+
+    while j < keyword_len and current_state.goto(keyword[j]) is not None:
+      current_state = current_state.goto(keyword[j])
+      j += 1
+
+    for a in keyword[j:keyword_len + 1]:
+      next_state = AhoCorasickAutomaton.Node()
+      current_state.update_goto(a, next_state)
+      current_state = next_state
+
+    current_state.append_outputs([keyword_len])
+
+  def _construct_fail(self, alphabet):
+    q = Queue()
+    for s in (self._root.goto(a) for a in alphabet):
+      if s != self._root:
+        q.put(s)
+        s.update_fail(self._root)
+
+    while not q.empty():
+      current = q.get()
+      for a, child in ((a, current.goto(a)) for a in alphabet):
+        if child is not None:
+          q.put(child)
+
+          fallback = current.fail()
+          while fallback.goto(a) is None:
+            fallback = fallback.fail()
+
+          child_fallback = fallback.goto(a)
+          child.update_fail(child_fallback)
+          child.append_outputs(child_fallback.output())
+
+  def _construct_nxt(self, alphabet):
+    q = Queue()
+    for a in alphabet:
+      a_child = self._root.goto(a)
+      self._root.update_nxt(a, a_child)
+      if a_child != self._root:
+        q.put(a_child)
+    self._root.use_only_nxt()
+
+    while not q.empty():
+      current = q.get()
+      for a, child in ((a, current.goto(a)) for a in alphabet):
+        if child is not None:
+          q.put(child)
+          current.update_nxt(a, child)
+        else:
+          fallback = current.fail()
+          current.update_nxt(a, fallback.nxt(a))
+      current.use_only_nxt()
+
+  def find_occurrences(self, text, n):
+    state = self._root
+    for i in range(1, n + 1):
+      state = state.nxt(text[i])
+      for keyword_len in state.output():
+        start_pos = i - keyword_len + 1
+        yield text[start_pos:i + 1], start_pos
+
+  class Node:
+    def __init__(self):
+      self._goto, self._fail, self._output, self._nxt = {}, None, [], {}
+
+    def goto(self, a):
+      return self._goto.get(a, None)
+
+    def update_goto(self, a, target_node):
+      self._goto[a] = target_node
+
+    def output(self):
+      return self._output
+
+    def append_outputs(self, outputs):
+      self._output += outputs
+
+    def fail(self):
+      return self._fail
+
+    def update_fail(self, target_node):
+      self._fail = target_node
+
+    def nxt(self, a):
+      return self._nxt[a]
+
+    def update_nxt(self, a, target_node):
+      self._nxt[a] = target_node
+
+    def use_only_nxt(self):
+      del self._goto
+      del self._fail

test/test_aho_corasick.py

@@ -0,0 +1,65 @@
+import unittest
+from random import randint
+
+from exact_multiple_string_matching.aho_corasick import \
+  create_aho_corasick_automaton, find_occurrences
+from exact_string_matching.forward import brute_force
+from generator.rand import random_word
+
+
+class TestAhoCorasick(unittest.TestCase):
+  def test_single_keyword(self):
+    text, n = '#aabccabcab', 10
+    automaton = self._create_from(['abc'])
+
+    found = list(find_occurrences(text, n, automaton))
+    self.assertListEqual(found, [('abc', 2), ('abc', 6)])
+
+  def test_non_overlapping(self):
+    text, n = '#aabccabcab', 10
+    automaton = self._create_from(['aa', 'bcc', 'bcab'])
+
+    found = list(find_occurrences(text, n, automaton))
+    self.assertListEqual(found, [('aa', 1), ('bcc', 3), ('bcab', 7)])
+
+  def test_overlapping(self):
+    text, n = '#eshers', 6
+    automaton = self._create_from(['he', 'she', 'his', 'her', 'hers'])
+
+    found = set(find_occurrences(text, n, automaton))
+    self.assertSetEqual(found, {('she', 2), ('he', 3), ('hers', 3), ('her', 3)})
+
+  def test_pessimistic(self):
+    text, n = '#' + 'a' * 20, 20
+    automaton = self._create_from([i * 'a' for i in range(1, 6)])
+
+    found = set(find_occurrences(text, n, automaton))
+    self.assertEqual(len(found), 20 + 19 + 18 + 17 + 16)
+
+  def test_no_match(self):
+    text, n = '#abababab', 8
+    automaton = self._create_from(['bb', 'abba'])
+
+    self.assertFalse(list(find_occurrences(text, n, automaton)))
+
+  def test_random(self):
+    n, m, A = 500, 30, ['a', 'b', 'c']
+    for _ in range(100):
+      t = random_word(n, A)
+      patterns = {random_word(randint(2, 10), A) for _ in range(m)}
+      automaton = self._create_from(patterns)
+
+      expected = set()
+      for p in patterns:
+        starts = brute_force(t, f'#{p}', n, len(p) + 1)
+        expected.union({(p, i) for i in starts})
+
+      found = set(find_occurrences(t, n, automaton))
+
+      self.assertSetEqual(expected, found)
+
+  @staticmethod
+  def _create_from(patterns):
+    keywords = ((f'#{p}', len(p)) for p in patterns)
+    alphabet = {a for p in patterns for a in p}
+    return create_aho_corasick_automaton(keywords, alphabet)