From b632e4c72d06c75d872df8ff0f6540b7f395fae4 Mon Sep 17 00:00:00 2001
From: Yan Victor <yn.guimaraes@gmail.com>
Date: Wed, 20 Dec 2023 01:43:33 -0300
Subject: [PATCH] add suffix automaton algo

---
 strings/suffix_automaton.py | 150 ++++++++++++++++++++++++++++++++++++
 1 file changed, 150 insertions(+)
 create mode 100644 strings/suffix_automaton.py

diff --git a/strings/suffix_automaton.py b/strings/suffix_automaton.py
new file mode 100644
index 000000000..c92121f26
--- /dev/null
+++ b/strings/suffix_automaton.py
@@ -0,0 +1,150 @@
+from __future__ import annotations
+
+
+class SuffixAutomaton:
+    """
+    Suffix Automaton data structure for efficient substring counting and searching.
+
+    Usage:
+    sa = SuffixAutomaton()
+    sa.extend('abc')
+    terminal_states = sa.terminal()
+    is_found = sa.find('ab')
+
+    :param alpha: Number of characters in the alphabet
+    (default is 26 for lowercase English letters)
+    :param first: ASCII value of the first character in the alphabet (default is 'a')
+    """
+
+    def __init__(self, alpha: int = 26, first: int = ord("a")):
+        self.alpha = alpha
+        self.first = first
+        self.substrings = 0
+        self.last = 0
+        self.st = [self.Node(0, -1, [0] * self.alpha)]
+
+    class Node:
+        def __init__(self, length: int, link: int, next_states: list[int]):
+            self.len = length
+            self.link = link
+            self.next = next_states
+
+    def extend(self, c: str) -> None:
+        """
+        Extend the suffix automaton with a new character.
+
+        :param c: The character to extend with.
+
+        >>> sa = SuffixAutomaton()
+        >>> sa.add('aabaaab')
+        >>> terminal_states = [7, 3, 0]
+        >>> sa.terminal() == terminal_states
+        True
+        >>> sa.find('a')
+        True
+        >>> sa.find('b')
+        True
+        >>> sa.find('c')
+        False
+        >>> sa.find('aa')
+        True
+        >>> sa.find('ab')
+        True
+        >>> sa.find('aaaab')
+        False
+        >>> sa.find('bab')
+        False
+        >>> sa.find('baaaab')
+        False
+        >>> sa.find('baaaaab')
+        False
+        >>> sa.extend('xy')  # doctest: +IGNORE_EXCEPTION_DETAIL
+        Traceback (most recent call last):
+            ...
+        ValueError: Invalid input to extend method. Only single characters are allowed.
+        """
+        if len(c) != 1:
+            raise ValueError("The character to extend with must be a single character.")
+
+        char_value = ord(c) - self.first
+        cur = len(self.st)
+        p, q = self.last, 0
+
+        self.st.append(self.Node(self.st[p].len + 1, -1, [0] * self.alpha))
+
+        while p != -1 and not self.st[p].next[char_value]:
+            self.st[p].next[char_value] = cur
+            p = self.st[p].link
+
+        if p == -1:
+            self.st[cur].link = 0
+            self.substrings += self.st[cur].len
+        else:
+            q = self.st[p].next[char_value]
+
+            if self.st[p].len + 1 == self.st[q].len:
+                self.st[cur].link = q
+                self.substrings += self.st[cur].len - self.st[q].len
+            else:
+                clone = len(self.st)
+                self.st.append(
+                    self.Node(self.st[p].len + 1, self.st[q].link, self.st[q].next[:])
+                )
+                self.substrings += self.st[clone].len - self.st[self.st[clone].link].len
+
+                while p != -1 and self.st[p].next[char_value] == q:
+                    self.st[p].next[char_value] = clone
+                    p = self.st[p].link
+
+                self.substrings -= self.st[q].len - self.st[self.st[q].link].len
+                self.st[q].link = self.st[cur].link = clone
+                self.substrings += (
+                    self.st[q].len
+                    - self.st[self.st[q].link].len
+                    + self.st[cur].len
+                    - self.st[self.st[cur].link].len
+                )
+
+        self.last = cur
+
+    def add(self, s: str) -> None:
+        """
+        Add a string to the suffix automaton.
+
+        :param s: The string to add.
+        """
+        for i in range(len(s)):
+            self.extend(s[i])
+
+    def terminal(self) -> list[int]:
+        """
+        Get the terminal states of the suffix automaton.
+
+        :return: List of terminal states.
+        """
+        p = self.last
+        terminal_states = []
+        while p >= 0:
+            terminal_states.append(p)
+            p = self.st[p].link
+        return terminal_states
+
+    def find(self, s: str) -> bool:
+        """
+        Check if a string is present in the suffix automaton.
+
+        :param s: The string to search for.
+        :return: True if the string is found, False otherwise.
+        """
+        p = 0
+        for j in range(len(s)):
+            if not self.st[p].next[ord(s[j]) - self.first]:
+                return False
+            p = self.st[p].next[ord(s[j]) - self.first]
+        return True
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()