# Numbers of alphabet which we call base
alphabet_size = 256
# Modulus to hash a string
modulus = 1000003


def rabin_karp(pattern, text):
 """
 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.

 This will be the simple version which only assumes one pattern is being searched
 for but it's not hard to modify

 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
 """
 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:
 continue
 modulus_power = (modulus_power * alphabet_size) % modulus

 for i in range(0, 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:
 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


def test_rabin_karp():
 """
 >>> test_rabin_karp()
 Success.
 """
 # Test 1)
 pattern = "abc1abc12"
 text1 = "alskfjaldsabc1abc1abc12k23adsfabcabc"
 text2 = "alskfjaldsk23adsfabcabc"
 assert rabin_karp(pattern, text1) and 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()