feat(strings): add suffix automaton implementation

Author: Shrithu10

strings/suffix_automaton.py

@@ -0,0 +1,129 @@
+"""
+Suffix Automaton
+----------------
+A suffix automaton (SAM) is a minimal deterministic finite automaton (DFA)
+that recognizes all substrings of a given string.
+
+It can be built in O(n) time and space, where n is the length of the string.
+Suffix automatons are useful for:
+    - counting distinct substrings
+    - checking substring existence
+    - finding longest common substrings between strings
+
+Reference:
+https://cp-algorithms.com/string/suffix-automaton.html
+
+Example:
+>>> sa = build_suffix_automaton("ababa")
+>>> is_substring(sa, "aba")
+True
+>>> is_substring(sa, "abc")
+False
+>>> count_distinct_substrings(sa)
+9
+"""
+
+from typing import TypedDict
+
+
+class State(TypedDict):
+    length: int
+    link: int
+    next: dict[str, int]
+
+
+def build_suffix_automaton(s: str) -> list[State]:
+    """
+    Build the suffix automaton for the given string.
+
+    Each state is represented as a dictionary with:
+        'length'  -> length of the longest substring for this state
+        'link'    -> suffix link (integer)
+        'next'    -> transitions (dict: char -> state index)
+
+    >>> sa = build_suffix_automaton("ababa")
+    >>> isinstance(sa, list)
+    True
+    >>> all(isinstance(state, dict) for state in sa)
+    True
+    """
+    sa: list[State] = [{"length": 0, "link": -1, "next": {}}]
+    last = 0
+
+    for ch in s:
+        cur = len(sa)
+        sa.append({"length": sa[last]["length"] + 1, "link": 0, "next": {}})
+        p = last
+        while p >= 0 and ch not in sa[p]["next"]:
+            sa[p]["next"][ch] = cur
+            p = sa[p]["link"]
+
+        if p == -1:
+            sa[cur]["link"] = 0
+        else:
+            q = sa[p]["next"][ch]
+            if sa[p]["length"] + 1 == sa[q]["length"]:
+                sa[cur]["link"] = q
+            else:
+                clone = len(sa)
+                sa.append(
+                    {
+                        "length": sa[p]["length"] + 1,
+                        "link": sa[q]["link"],
+                        "next": sa[q]["next"].copy(),
+                    }
+                )
+                while p >= 0 and sa[p]["next"].get(ch) == q:
+                    sa[p]["next"][ch] = clone
+                    p = sa[p]["link"]
+                sa[q]["link"] = sa[cur]["link"] = clone
+        last = cur
+    return sa
+
+
+def is_substring(sa: list[State], substring: str) -> bool:
+    """
+    Checks whether the given substring exists in the automaton.
+
+    >>> sa = build_suffix_automaton("ababa")
+    >>> is_substring(sa, "aba")
+    True
+    >>> is_substring(sa, "bab")
+    True
+    >>> is_substring(sa, "abc")
+    False
+    """
+    state = 0
+    for ch in substring:
+        if ch not in sa[state]["next"]:
+            return False
+        state = sa[state]["next"][ch]
+    return True
+
+
+def count_distinct_substrings(sa: list[State]) -> int:
+    """
+    Returns the number of distinct substrings in the original string
+    represented by the suffix automaton.
+
+    The number of distinct substrings is:
+        sum(len[v] - len[link[v]]) for all states v != 0
+
+    >>> sa = build_suffix_automaton("ababa")
+    >>> count_distinct_substrings(sa)
+    9
+    >>> count_distinct_substrings(build_suffix_automaton("aaaa"))
+    4
+    >>> count_distinct_substrings(build_suffix_automaton("abc"))
+    6
+    """
+    total = 0
+    for v in range(1, len(sa)):
+        total += sa[v]["length"] - sa[sa[v]["link"]]["length"]
+    return total
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()