





'''simple docstring'''

def 						UpperCamelCase				(							_lowerCamelCase					:					list[list[int]]						,       _lowerCamelCase					:					int						,       _lowerCamelCase					:					int						,       _lowerCamelCase					:					list[int]       ):

    # 1. Validate that path exists between current and next vertices
    if graph[path[curr_ind - 1]][next_ver] == 0:
        return False

    # 2. Validate that next vertex is not already in path
    return not any(vertex == next_ver for vertex in path       )





def 						UpperCamelCase				(							_lowerCamelCase					:					list[list[int]]						,       _lowerCamelCase					:					list[int]						,       _lowerCamelCase					:					int       ):

    # Base Case
    if curr_ind == len(_lowerCamelCase       ):
        # return whether path exists between current and starting vertices
        return graph[path[curr_ind - 1]][path[0]] == 1

    # Recursive Step
    for next_ver in range(0						,       len(_lowerCamelCase       )       ):
        if valid_connection(_lowerCamelCase						,       _lowerCamelCase						,       _lowerCamelCase						,       _lowerCamelCase       ):
            # Insert current vertex  into path as next transition
            A__				=			next_ver
            # Validate created path
            if util_hamilton_cycle(_lowerCamelCase						,       _lowerCamelCase						,       curr_ind + 1       ):
                return True
            # Backtrack
            A__				=			-1
    return False





def 						UpperCamelCase				(							_lowerCamelCase					:					list[list[int]]						,       _lowerCamelCase					:					int = 0       ):
    A__				=			[-1] * (len(_lowerCamelCase       ) + 1)
    # initialize start and end of path with starting index
    A__				=			A__				=			start_index
    # evaluate and if we find answer return path either return empty array
    return path if util_hamilton_cycle(_lowerCamelCase						,       _lowerCamelCase						,       1       ) else []










'''simple docstring'''

from __future__ import annotations






class    UpperCAmelCase	:
 def __init__(				self      :Optional[int]						,       lowercase_      :int							)->							None:
     A__				=			order

     # a_{0} ... a_{k}
     A__				=			[1.0] + [0.0] * order
     # b_{0} ... b_{k}
     A__				=			[1.0] + [0.0] * order

     # x[n-1] ... x[n-k]
     A__				=			[0.0] * self.order
     # y[n-1] ... y[n-k]
     A__				=			[0.0] * self.order
 def      UpperCAmelCase_							(				self      :List[str]						,       lowercase_      :list[float]						,       lowercase_      :list[float]							)->							None:
     if len(lowercase_							) < self.order:
         A__				=			[1.0, *a_coeffs]

     if len(lowercase_							) != self.order + 1:
         A__				=			(
             F"Expected a_coeffs to have {self.order + 1} elements "
             F"for {self.order}-order filter, got {len(lowercase_							)}"
         )
         raise ValueError(lowercase_							)

     if len(lowercase_							) != self.order + 1:
         A__				=			(
             F"Expected b_coeffs to have {self.order + 1} elements "
             F"for {self.order}-order filter, got {len(lowercase_							)}"
         )
         raise ValueError(lowercase_							)

     A__				=			a_coeffs
     A__				=			b_coeffs



 def      UpperCAmelCase_							(				self      :Optional[int]						,       lowercase_      :float							)->							float:
     A__				=			0.0

     # Start at index 1 and do index 0 at the end.
     for i in range(1						,       self.order + 1							):
         result += (
             self.b_coeffs[i] * self.input_history[i - 1]
             - self.a_coeffs[i] * self.output_history[i - 1]
         )

     A__				=			(result + self.b_coeffs[0] * sample) / self.a_coeffs[0]

     A__				=			self.input_history[:-1]
     A__				=			self.output_history[:-1]

     A__				=			sample
     A__				=			result

     return result



