Aho-Corasick String Matching Algorithm (#346)

* add aho-corasick algorithm

* Add a doctest and format with black

strings/aho-corasick.py

@@ -0,0 +1,92 @@
+from collections import deque
+
+
+class Automaton:
+    def __init__(self, keywords):
+        self.adlist = list()
+        self.adlist.append(
+            {"value": "", "next_states": [], "fail_state": 0, "output": []}
+        )
+
+        for keyword in keywords:
+            self.add_keyword(keyword)
+        self.set_fail_transitions()
+
+    def find_next_state(self, current_state, char):
+        for state in self.adlist[current_state]["next_states"]:
+            if char == self.adlist[state]["value"]:
+                return state
+        return None
+
+    def add_keyword(self, keyword):
+        current_state = 0
+        for character in keyword:
+            if self.find_next_state(current_state, character):
+                current_state = self.find_next_state(current_state, character)
+            else:
+                self.adlist.append(
+                    {
+                        "value": character,
+                        "next_states": [],
+                        "fail_state": 0,
+                        "output": [],
+                    }
+                )
+                self.adlist[current_state]["next_states"].append(len(self.adlist) - 1)
+                current_state = len(self.adlist) - 1
+        self.adlist[current_state]["output"].append(keyword)
+
+    def set_fail_transitions(self):
+        q = deque()
+        for node in self.adlist[0]["next_states"]:
+            q.append(node)
+            self.adlist[node]["fail_state"] = 0
+        while q:
+            r = q.popleft()
+            for child in self.adlist[r]["next_states"]:
+                q.append(child)
+                state = self.adlist[r]["fail_state"]
+                while (
+                    self.find_next_state(state, self.adlist[child]["value"]) == None
+                    and state != 0
+                ):
+                    state = self.adlist[state]["fail_state"]
+                self.adlist[child]["fail_state"] = self.find_next_state(
+                    state, self.adlist[child]["value"]
+                )
+                if self.adlist[child]["fail_state"] == None:
+                    self.adlist[child]["fail_state"] = 0
+                self.adlist[child]["output"] = (
+                    self.adlist[child]["output"]
+                    + self.adlist[self.adlist[child]["fail_state"]]["output"]
+                )
+
+    def search_in(self, string):
+        """
+        >>> A = Automaton(["what", "hat", "ver", "er"])
+        >>> A.search_in("whatever, err ... , wherever")
+        {'what': [0], 'hat': [1], 'ver': [5, 25], 'er': [6, 10, 22, 26]}
+        """
+        result = dict()  # returns a dict with keywords and list of its occurences
+        current_state = 0
+        for i in range(len(string)):
+            while (
+                self.find_next_state(current_state, string[i]) == None
+                and current_state != 0
+            ):
+                current_state = self.adlist[current_state]["fail_state"]
+            current_state = self.find_next_state(current_state, string[i])
+            if current_state is None:
+                current_state = 0
+            else:
+                for key in self.adlist[current_state]["output"]:
+                    if not (key in result):
+                        result[key] = []
+                    result[key].append((i - len(key) + 1))
+        return result
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()