#### Rabin Karp

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

def rabin_karp(pattern: str, text: str) -> bool:
"""
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(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() -> None:
"""
>>> test_rabin_karp()
Success.
"""
# Test 1)
pattern = "abc1abc12"
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()
```  