From 414062d3ff6802eb00811bea2bbea3643511f49e Mon Sep 17 00:00:00 2001 From: Hamid Gasmi Date: Wed, 21 Sep 2022 03:33:23 -0700 Subject: [PATCH] #44: add rabin karp algorithm --- .../string_pattern_matching_algorithms.py | 0 .../string_pattern_matching_rabin_karp.py | 71 +++++++++++++++++++ 2 files changed, 71 insertions(+) delete mode 100644 10-algo-ds-implementations/string_pattern_matching_algorithms.py create mode 100644 10-algo-ds-implementations/string_pattern_matching_rabin_karp.py diff --git a/10-algo-ds-implementations/string_pattern_matching_algorithms.py b/10-algo-ds-implementations/string_pattern_matching_algorithms.py deleted file mode 100644 index e69de29..0000000 diff --git a/10-algo-ds-implementations/string_pattern_matching_rabin_karp.py b/10-algo-ds-implementations/string_pattern_matching_rabin_karp.py new file mode 100644 index 0000000..350420f --- /dev/null +++ b/10-algo-ds-implementations/string_pattern_matching_rabin_karp.py @@ -0,0 +1,71 @@ +''' +Problem: Exact pattern matching + - Input: a text (T), a pattern (P) + - Output: 1 or all occurences of P in T + +Algorithm: + - Hashing function: H(S: str, n: int, m: int) = Sum(S[i] * x^i-n % p) for n <= i < m + - Compute H(P, 0, |P|) + - Compute H(T, 0, |P|) + - H(S, n + 1, m + 1) = (H(S, n, m) - S[n]) / x + S[m] * x^m-n-1 % p + - Loop through T: + - Compute H(T, i + 1, i + 1 + |P|) by using H(T, i, i + |P|) in O(1) time complexity + - Compare it with H(P) + +Questions: + - How to choose the multiplier and the prime numbers? + - How to make the trade-off between collision numbers and performance of recurrence calculation for H[i]? + - More the prime is bigger, less false positive we gets. This is supposed to make our code faster. + - In the other hand, more the prime is bigger, the related division and multiplication operations get slower. + +''' + +class Rabin_Karp: + def __init__(self): + self.__multiplier = 31 + self._prime = 1000000007 + + self.__multiplier_power_prime = self.__multiplier ** self._prime % self._prime + + def __abs_hash__(self, s: str, length: int) -> int: + assert(length < len(s)) + + hash, power_x = 0, 1 + for idx in range(length): + hash += ord(s[idx]) * power_x + hash %= self.__prime + + power_x *= self.__multiplier + + return hash + + def __rel_hash(self, s: str, prev_hash: int, idx: int, length: int) -> int: + assert(0 < idx < len(s)) + + return (prev_hash - s[idx - 1]) // self.__multiplier + s[idx + length - 1] * self.__multiplier + + def find(self, t: str, p: str) -> List[int]: + len_t = len(t) + len_p = len(p) + if len_p > len_t: + return [] + + # 1. find hash functions for t and p + hash_p = self.__abs_hash__(p, len_p) + hash_t = self.__abs_hash__(t, len_p) + + # 2. find all occurences + occurences = [] + if hash_p == hash_t: + occurences.append(0) + for idx in range(1, len_t): + hash_t = self.__rel_hash(t, hash_t, idx, len_p) + if hash_p == hash_t and p == t[idx:idx+len_p]: + occurences.append(idx) + + return occurences + + + + + \ No newline at end of file pFad - Phonifier reborn

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