






from __future__ import annotations






def 							lowerCamelCase__ (       __lowerCamelCase     :	list[int]						):  # This function is recursive
  __UpperCAmelCase				:      Optional[Any]	 =    len(__lowerCamelCase						)
  # If the array contains only one element, we return it (it's the stop condition of
  # recursion)
  if array_length <= 1:
    return array
    # Else
  __UpperCAmelCase				:      str	 =    array[0]
  __UpperCAmelCase				:      int	 =    False
  __UpperCAmelCase				:      Tuple	 =    1
  __UpperCAmelCase				:      list[int]	 =    []
  while not is_found and i < array_length:
    if array[i] < pivot:
      __UpperCAmelCase				:      List[str]	 =    True
      __UpperCAmelCase				:      List[Any]	 =    [element for element in array[i:] if element >= array[i]]
      __UpperCAmelCase				:      List[str]	 =    longest_subsequence(__lowerCamelCase						)
      if len(__lowerCamelCase						) > len(__lowerCamelCase						):
        __UpperCAmelCase				:      str	 =    temp_array
    else:
      i += 1

  __UpperCAmelCase				:      Tuple	 =    [element for element in array[1:] if element >= pivot]
  __UpperCAmelCase				:      Union[str, Any]	 =    [pivot, *longest_subsequence(__lowerCamelCase						)]
  if len(__lowerCamelCase						) > len(__lowerCamelCase						):
    return temp_array
  else:
    return longest_subseq


if __name__ == "__main__":
       import doctest

       doctest.testmod()







'''simple docstring'''





SCREAMING_SNAKE_CASE__          =  256
# Modulus to hash a string
SCREAMING_SNAKE_CASE__          =  100_0003




def 							lowerCamelCase	(					_snake_case	:    str  ,_snake_case	:    str							):





    '''simple docstring'''


    lowercase__									=    len(_snake_case							)
    lowercase__									=    len(_snake_case							)
    if p_len > t_len:
        return False

    lowercase__									=    0
    lowercase__									=    0
    lowercase__									=    1

    # Calculating the hash of pattern and substring of text
    for i in range(_snake_case							):
        lowercase__									=    (ord(pattern[i]							) + p_hash * alphabet_size) % modulus
        lowercase__									=    (ord(text[i]							) + text_hash * alphabet_size) % modulus
        if i == p_len - 1:
            continue
        lowercase__									=    (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
        lowercase__									=    (
            (text_hash - ord(text[i]							) * modulus_power) * alphabet_size
            + ord(text[i + p_len]							)
        ) % modulus
    return False




def 							lowerCamelCase	(					):





    '''simple docstring'''


    lowercase__									=    "abc1abc12"
    lowercase__									=    "alskfjaldsabc1abc1abc12k23adsfabcabc"
    lowercase__									=    "alskfjaldsk23adsfabcabc"
    assert rabin_karp(_snake_case  ,_snake_case							) and not rabin_karp(_snake_case  ,_snake_case							)

    # Test 2)
    lowercase__									=    "ABABX"
    lowercase__									=    "ABABZABABYABABX"
    assert rabin_karp(_snake_case  ,_snake_case							)

    # Test 3)
    lowercase__									=    "AAAB"
    lowercase__									=    "ABAAAAAB"
    assert rabin_karp(_snake_case  ,_snake_case							)

    # Test 4)
    lowercase__									=    "abcdabcy"
    lowercase__									=    "abcxabcdabxabcdabcdabcy"
    assert rabin_karp(_snake_case  ,_snake_case							)

    # Test 5)
    lowercase__									=    "Lü"
    lowercase__									=    "Lüsai"
    assert rabin_karp(_snake_case  ,_snake_case							)
    lowercase__									=    "Lue"
    assert not rabin_karp(_snake_case  ,_snake_case							)
    print("Success."							)


if __name__ == "__main__":
 test_rabin_karp()




