





'''simple docstring'''






def   UpperCamelCase__ (						lowerCAmelCase    ):





      """simple docstring"""


      _lowerCAmelCase					=				[0 for i in range(len(lowerCAmelCase    )    )]

      # initialize interval's left pointer and right pointer
      _lowerCAmelCase	,				_lowerCAmelCase					=				0, 0

      for i in range(1				,      len(lowerCAmelCase    )    ):
            # case when current index is inside the interval
            if i <= right_pointer:
                  _lowerCAmelCase					=				min(right_pointer - i + 1				,      z_result[i - left_pointer]    )
                  _lowerCAmelCase					=				min_edge

            while go_next(lowerCAmelCase				,      lowerCAmelCase				,      lowerCAmelCase    ):
                  z_result[i] += 1

            # if new index's result gives us more right interval,
            # we've to update left_pointer and right_pointer
            if i + z_result[i] - 1 > right_pointer:
                  _lowerCAmelCase	,				_lowerCAmelCase					=				i, i + z_result[i] - 1

      return z_result
def   UpperCamelCase__ (						lowerCAmelCase				,      lowerCAmelCase				,      lowerCAmelCase    ):





      """simple docstring"""


      return i + z_result[i] < len(lowerCAmelCase    ) and s[z_result[i]] == s[i + z_result[i]]
def   UpperCamelCase__ (						lowerCAmelCase				,      lowerCAmelCase    ):





      """simple docstring"""


      _lowerCAmelCase					=				0
      # concatenate 'pattern' and 'input_str' and call z_function
      # with concatenated string
      _lowerCAmelCase					=				z_function(pattern + input_str    )

      for val in z_result:
            # if value is greater then length of the pattern string
            # that means this index is starting position of substring
            # which is equal to pattern string
            if val >= len(lowerCAmelCase    ):
                  answer += 1

      return answer


if __name__ == "__main__":
      import doctest

      doctest.testmod()













'''simple docstring'''






from __future__ import annotations

import numpy as np
def   UpperCamelCase__ (						lowerCAmelCase    ):





      """simple docstring"""


      _lowerCAmelCase	,				_lowerCAmelCase					=				np.shape(lowerCAmelCase    )
      if rows != columns:
            _lowerCAmelCase					=				(
                """'table' has to be of square shaped array but got a """
                f"{rows}x{columns} array:\n{table}"
            )
            raise ValueError(lowerCAmelCase    )

      _lowerCAmelCase					=				np.zeros((rows, columns)    )
      _lowerCAmelCase					=				np.zeros((rows, columns)    )
      for i in range(lowerCAmelCase    ):
            for j in range(lowerCAmelCase    ):
                  _lowerCAmelCase					=				sum(lower[i][k] * upper[k][j] for k in range(lowerCAmelCase    )    )
                  if upper[j][j] == 0:
                        raise ArithmeticError("""No LU decomposition exists"""    )
                  _lowerCAmelCase					=				(table[i][j] - total) / upper[j][j]
            _lowerCAmelCase					=				1
            for j in range(lowerCAmelCase				,      lowerCAmelCase    ):
                  _lowerCAmelCase					=				sum(lower[i][k] * upper[k][j] for k in range(lowerCAmelCase    )    )
                  _lowerCAmelCase					=				table[i][j] - total
      return lower, upper


if __name__ == "__main__":
      import doctest

      doctest.testmod()






