




from __future__ import annotations

from collections import namedtuple
from dataclasses import dataclass





@dataclass
class 					__lowerCamelCase			:




    """simple docstring"""

    snake_case__   = 42
    snake_case__   = None
    snake_case__   = None






UpperCamelCase								=	namedtuple('CoinsDistribResult', 'moves excess')



def 				_A  (		lowerCAmelCase_	:   TreeNode | None     ):
     """simple docstring"""

     if root is None:
          return 0

     # Validation
     def count_nodes(lowerCAmelCase_	:   TreeNode | None     ) -> int:
          if node is None:
               return 0

          return count_nodes(node.left     ) + count_nodes(node.right     ) + 1

     def count_coins(lowerCAmelCase_	:   TreeNode | None     ) -> int:
          if node is None:
               return 0

          return count_coins(node.left     ) + count_coins(node.right     ) + node.data

     if count_nodes(lowerCAmelCase_     ) != count_coins(lowerCAmelCase_     ):
          raise ValueError("The nodes number should be same as the number of coins"     )

     # Main calculation
     def get_distrib(lowerCAmelCase_	:   TreeNode | None     ) -> CoinsDistribResult:

          if node is None:
               return CoinsDistribResult(0  ,							1     )

          lowerCAmelCase__      ,						lowerCAmelCase__            =					get_distrib(node.left     )
          lowerCAmelCase__      ,						lowerCAmelCase__            =					get_distrib(node.right     )

          lowerCAmelCase__            =					1 - left_distrib_excess
          lowerCAmelCase__            =					1 - right_distrib_excess

          lowerCAmelCase__            =					(
              left_distrib_moves
              + right_distrib_moves
              + abs(lowerCAmelCase_     )
              + abs(lowerCAmelCase_     )
          )
          lowerCAmelCase__            =					node.data - coins_to_left - coins_to_right

          return CoinsDistribResult(lowerCAmelCase_  ,							lowerCAmelCase_     )

     return get_distrib(lowerCAmelCase_     )[0]


if __name__ == "__main__":
     import doctest

     doctest.testmod()




import math

import qiskit

def 			lowerCAmelCase__					(     a__:						int = 1     ,    a__:						int = 1     ,    a__:						int = 1			)    ->						qiskit.result.counts.Counts:


							'''simple docstring'''





							if (
							    isinstance(a__     ,    a__			)
							    or isinstance(a__     ,    a__			)
							    or isinstance(a__     ,    a__			)
							):
														raise TypeError('inputs must be integers.'			)

							if (input_a < 0) or (input_a < 0) or (carry_in < 0):
														raise ValueError('inputs must be positive.'			)

							if (
							    (math.floor(a__			) != input_a)
							    or (math.floor(a__			) != input_a)
							    or (math.floor(a__			) != carry_in)
							):
														raise ValueError('inputs must be exact integers.'			)

							if (input_a > 2) or (input_a > 2) or (carry_in > 2):
														raise ValueError('inputs must be less or equal to 2.'			)

							# build registers
							_UpperCAmelCase											=     qiskit.QuantumRegister(4     ,    'qr'			)
							_UpperCAmelCase											=     qiskit.ClassicalRegister(2     ,    'cr'			)
							# list the entries
							_UpperCAmelCase											=     [input_a, input_a, carry_in]

							_UpperCAmelCase											=     qiskit.QuantumCircuit(a__     ,    a__			)

							for i in range(0     ,    3			):
														if entry[i] == 2:
																					quantum_circuit.h(a__			)  # for hadamard entries
														elif entry[i] == 1:
																					quantum_circuit.x(a__			)  # for 1 entries
														elif entry[i] == 0:
																					quantum_circuit.i(a__			)  # for 0 entries

    # build the circuit
							quantum_circuit.ccx(0     ,    1     ,    3			)  # ccx = toffoli gate
							quantum_circuit.cx(0     ,    1			)
							quantum_circuit.ccx(1     ,    2     ,    3			)
							quantum_circuit.cx(1     ,    2			)
							quantum_circuit.cx(0     ,    1			)

							quantum_circuit.measure([2, 3]     ,    a__			)  # measure the last two qbits

							_UpperCAmelCase											=     qiskit.Aer.get_backend('aer_simulator'			)
							_UpperCAmelCase											=     qiskit.execute(a__     ,    a__     ,    shots=1_0_0_0			)

							return job.result().get_counts(a__			)


if __name__ == "__main__":
		print(f'''Total sum count for state is: {quantum_full_adder(1, 1, 1)}''')
