


"""simple docstring"""

def lowerCAmelCase_      (				UpperCamelCase__	: list[int]				,   UpperCamelCase__	: str ):






 """simple docstring"""







 __lowercase									=	int(UpperCamelCase__ )

 # Initialize Result
 __lowercase									=	[]

 # Traverse through all denomination
 for denomination in reversed(UpperCamelCase__ ):
  # Find denominations
  while int(UpperCamelCase__ ) >= int(UpperCamelCase__ ):
   total_value -= int(UpperCamelCase__ )
   answer.append(UpperCamelCase__ )  # Append the "answers" array

 return answer


# Driver Code
if __name__ == "__main__":
       UpperCAmelCase__  							=[]
       UpperCAmelCase__  							="0"

       if (
           input("Do you want to enter your denominations ? (yY/n): ").strip().lower()
           == "y"
       ):
              UpperCAmelCase__  							=int(input("Enter the number of denominations you want to add: ").strip())

              for i in range(0, n):
                     denominations.append(int(input(f"""Denomination {i}: """).strip()))
              UpperCAmelCase__  							=input("Enter the change you want to make in Indian Currency: ").strip()
       else:
              # All denominations of Indian Currency if user does not enter
              UpperCAmelCase__  							=[1, 2, 5, 10, 20, 50, 100, 500, 2000]
              UpperCAmelCase__  							=input("Enter the change you want to make: ").strip()

       if int(value) == 0 or int(value) < 0:
              print("The total value cannot be zero or negative.")

       else:
              print(f"""Following is minimal change for {value}: """)
              UpperCAmelCase__  							=find_minimum_change(denominations, value)
              # Print result
              for i in range(len(answer)):
                     print(answer[i], end=" ")




"""simple docstring"""

from collections.abc import Callable

import numpy as np


def lowerCAmelCase_      (				UpperCamelCase__	: Callable				,   UpperCamelCase__	: float				,   UpperCamelCase__	: float				,   UpperCamelCase__	: float				,   UpperCamelCase__	: float ):






 """simple docstring"""







 __lowercase									=	int(np.ceil((x_end - xa) / step_size ) )
 __lowercase									=	np.zeros((n + 1,) )
 __lowercase									=	ya
 __lowercase									=	xa

 for k in range(UpperCamelCase__ ):
  __lowercase									=	y[k] + step_size * ode_func(UpperCamelCase__				,   y[k] )
  x += step_size

 return y


if __name__ == "__main__":
       import doctest

       doctest.testmod()
