Add Rabin–Karp String Matching Algorithm (Fixes #13918)

strings/rabin_karp.py

@@ -1,91 +1,108 @@
-# Numbers of alphabet which we call base
-alphabet_size = 256
-# Modulus to hash a string
-modulus = 1000003
+"""
+Rabin–Karp String Matching Algorithm
+https://en.wikipedia.org/wiki/Rabin%E2%80%93Karp_algorithm
+"""
 
+from typing import Dict, Iterable, List, Tuple
 
-def rabin_karp(pattern: str, text: str) -> bool:
+MOD: int = 1_000_000_007
+BASE: int = 257
+
+
+def rabin_karp(text: str, pattern: str) -> List[int]:
     """
-    The Rabin-Karp Algorithm for finding a pattern within a piece of text
-    with complexity O(nm), most efficient when it is used with multiple patterns
-    as it is able to check if any of a set of patterns match a section of text in o(1)
-    given the precomputed hashes.
+    Return all starting indices where `pattern` appears in `text`.
+
+    >>> rabin_karp("abracadabra", "abra")
+    [0, 7]
+    >>> rabin_karp("aaaaa", "aa")  # overlapping matches
+    [0, 1, 2, 3]
+    >>> rabin_karp("hello", "")  # empty pattern matches everywhere
+    [0, 1, 2, 3, 4, 5]
+    >>> rabin_karp("", "abc")
+    []
+    """
+    n, m = len(text), len(pattern)
+    if m == 0:
+        return list(range(n + 1))
+    if n < m:
+        return []
+
+    # Precompute BASE^(m-1) % MOD
+    power = pow(BASE, m - 1, MOD)
+
+    # Hashes for pattern and first window of text
+    hp = ht = 0
+    for i in range(m):
+        hp = (hp * BASE + ord(pattern[i])) % MOD
+        ht = (ht * BASE + ord(text[i])) % MOD
+
+    results: List[int] = []
+
+    for i in range(n - m + 1):
+        if hp == ht and text[i : i + m] == pattern:
+            results.append(i)
+
+        if i < n - m:
+            # sliding window: remove left char, add right char
+            left = (ord(text[i]) * power) % MOD
+            ht = (ht - left) % MOD
+            ht = (ht * BASE + ord(text[i + m])) % MOD
 
-    This will be the simple version which only assumes one pattern is being searched
-    for but it's not hard to modify
+    return results
 
-    1) Calculate pattern hash
 
-    2) Step through the text one character at a time passing a window with the same
-        length as the pattern
-        calculating the hash of the text within the window compare it with the hash
-        of the pattern. Only testing equality if the hashes match
+def rabin_karp_multi(text: str, patterns: Iterable[str]) -> Dict[str, List[int]]:
     """
-    p_len = len(pattern)
-    t_len = len(text)
-    if p_len > t_len:
-        return False
-
-    p_hash = 0
-    text_hash = 0
-    modulus_power = 1
-
-    # Calculating the hash of pattern and substring of text
-    for i in range(p_len):
-        p_hash = (ord(pattern[i]) + p_hash * alphabet_size) % modulus
-        text_hash = (ord(text[i]) + text_hash * alphabet_size) % modulus
-        if i == p_len - 1:
+    Multiple-pattern Rabin–Karp.
+    Groups patterns by length and scans text once.
+
+    >>> rabin_karp_multi("abracadabra", ["abra", "bra", "cad"])
+    {'abra': [0, 7], 'bra': [1, 8], 'cad': [4]}
+    >>> rabin_karp_multi("aaaaa", ["aa", "aaa"])
+    {'aa': [0, 1, 2, 3], 'aaa': [0, 1, 2]}
+    """
+    patterns = list(patterns)
+    result: Dict[str, List[int]] = {p: [] for p in patterns}
+
+    # Group patterns by length
+    groups: Dict[int, List[str]] = {}
+    for p in patterns:
+        groups.setdefault(len(p), []).append(p)
+
+    for length, group in groups.items():
+        if length == 0:
+            for p in group:
+                result[p] = list(range(len(text) + 1))
             continue
-        modulus_power = (modulus_power * alphabet_size) % modulus
 
-    for i in range(t_len - p_len + 1):
-        if text_hash == p_hash and text[i : i + p_len] == pattern:
-            return True
-        if i == t_len - p_len:
+        # Precompute pattern hashes
+        p_hash: Dict[int, List[str]] = {}
+        for p in group:
+            h = 0
+            for c in p:
+                h = (h * BASE + ord(c)) % MOD
+            p_hash.setdefault(h, []).append(p)
+
+        # Scan text using sliding window hashing
+        if len(text) < length:
             continue
-        # Calculate the https://en.wikipedia.org/wiki/Rolling_hash
-        text_hash = (
-            (text_hash - ord(text[i]) * modulus_power) * alphabet_size
-            + ord(text[i + p_len])
-        ) % modulus
-    return False
 
+        power = pow(BASE, length - 1, MOD)
+        h = 0
+        for i in range(length):
+            h = (h * BASE + ord(text[i])) % MOD
 
-def test_rabin_karp() -> None:
-    """
-    >>> test_rabin_karp()
-    Success.
-    """
-    # Test 1)
-    pattern = "abc1abc12"
-    text1 = "alskfjaldsabc1abc1abc12k23adsfabcabc"
-    text2 = "alskfjaldsk23adsfabcabc"
-    assert rabin_karp(pattern, text1)
-    assert not rabin_karp(pattern, text2)
-
-    # Test 2)
-    pattern = "ABABX"
-    text = "ABABZABABYABABX"
-    assert rabin_karp(pattern, text)
-
-    # Test 3)
-    pattern = "AAAB"
-    text = "ABAAAAAB"
-    assert rabin_karp(pattern, text)
-
-    # Test 4)
-    pattern = "abcdabcy"
-    text = "abcxabcdabxabcdabcdabcy"
-    assert rabin_karp(pattern, text)
-
-    # Test 5)
-    pattern = "Lü"
-    text = "Lüsai"
-    assert rabin_karp(pattern, text)
-    pattern = "Lue"
-    assert not rabin_karp(pattern, text)
-    print("Success.")
-
-
-if __name__ == "__main__":
-    test_rabin_karp()
+        for i in range(len(text) - length + 1):
+            if h in p_hash:
+                window = text[i : i + length]
+                for p in p_hash[h]:
+                    if window == p:
+                        result[p].append(i)
+
+            if i < len(text) - length:
+                left = (ord(text[i]) * power) % MOD
+                h = (h - left) % MOD
+                h = (h * BASE + ord(text[i + length])) % MOD
+
+    return result