armstrong numbers Algorithm
The Armstrong Numbers Algorithm is a mathematical algorithm that determines if a given number is an Armstrong number or not. Armstrong numbers, also known as pluperfect numbers or narcissistic numbers, are numbers that are equal to the sum of their digits when each digit is raised to the power of the number of digits in the number. For example, the number 153 is an Armstrong number because 1^3 + 5^3 + 3^3 = 153. Armstrong numbers are named after Michael F. Armstrong, who is credited with discovering this property of numbers.
The algorithm begins by converting the input number into a string or list of digits in order to determine the number of digits (n) it contains. Next, it iterates through each digit, raising it to the power of n and accumulating the sum of these powered digits. Once all digits have been processed, the algorithm compares the computed sum with the original number. If the sum is equal to the input number, then the number is an Armstrong number; otherwise, it is not. The Armstrong Numbers Algorithm is often used as an exercise in programming and mathematics education, as it requires knowledge of basic arithmetic and control structures, such as loops and conditionals.
"""
An Armstrong number is equal to the sum of the cubes of its digits.
For example, 370 is an Armstrong number because 3*3*3 + 7*7*7 + 0*0*0 = 370.
An Armstrong number is often called Narcissistic number.
"""
def armstrong_number(n: int) -> bool:
"""
Return True if n is an Armstrong number or False if it is not.
>>> armstrong_number(153)
True
>>> armstrong_number(200)
False
>>> armstrong_number(1634)
True
>>> armstrong_number(0)
False
>>> armstrong_number(-1)
False
>>> armstrong_number(1.2)
False
"""
if not isinstance(n, int) or n < 1:
return False
# Initialization of sum and number of digits.
sum = 0
number_of_digits = 0
temp = n
# Calculation of digits of the number
while temp > 0:
number_of_digits += 1
temp //= 10
# Dividing number into separate digits and find Armstrong number
temp = n
while temp > 0:
rem = temp % 10
sum += rem ** number_of_digits
temp //= 10
return n == sum
def narcissistic_number(n: int) -> bool:
"""Return True if n is a narcissistic number or False if it is not"""
expo = len(str(n)) # power, all number will be raised to
# each digit will be multiplied expo times
temp = [(int(i) ** expo) for i in str(n)]
# check if sum of cube of each digit is equal to number
return n == sum(temp)
def main():
"""
Request that user input an integer and tell them if it is Armstrong number.
"""
num = int(input("Enter an integer to see if it is an Armstrong number: ").strip())
print(f"{num} is {'' if armstrong_number(num) else 'not '}an Armstrong number.")
print(f"{num} is {'' if narcissistic_number(num) else 'not '}an Armstrong number.")
if __name__ == "__main__":
import doctest
doctest.testmod()
main()
