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f37d415227
* Add a new algorithm for Armstrong numbers
* FAILING = (-153, -1, 0, 1.2, 200, "A", [], {}, None)
Co-authored-by: Christian Clauss <cclauss@me.com>
101 lines
3.0 KiB
Python
101 lines
3.0 KiB
Python
"""
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An Armstrong number is equal to the sum of its own digits each raised to the
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power of the number of digits.
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For example, 370 is an Armstrong number because 3*3*3 + 7*7*7 + 0*0*0 = 370.
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Armstrong numbers are also called Narcissistic numbers and Pluperfect numbers.
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On-Line Encyclopedia of Integer Sequences entry: https://oeis.org/A005188
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"""
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PASSING = (1, 153, 370, 371, 1634, 24678051, 115132219018763992565095597973971522401)
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FAILING = (-153, -1, 0, 1.2, 200, "A", [], {}, None)
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def armstrong_number(n: int) -> bool:
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"""
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Return True if n is an Armstrong number or False if it is not.
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>>> all(armstrong_number(n) for n in PASSING)
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True
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>>> any(armstrong_number(n) for n in FAILING)
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False
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"""
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if not isinstance(n, int) or n < 1:
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return False
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# Initialization of sum and number of digits.
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sum = 0
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number_of_digits = 0
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temp = n
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# Calculation of digits of the number
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while temp > 0:
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number_of_digits += 1
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temp //= 10
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# Dividing number into separate digits and find Armstrong number
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temp = n
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while temp > 0:
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rem = temp % 10
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sum += rem ** number_of_digits
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temp //= 10
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return n == sum
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def pluperfect_number(n: int) -> bool:
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"""Return True if n is a pluperfect number or False if it is not
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>>> all(armstrong_number(n) for n in PASSING)
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True
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>>> any(armstrong_number(n) for n in FAILING)
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False
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"""
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if not isinstance(n, int) or n < 1:
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return False
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# Init a "histogram" of the digits
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digit_histogram = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
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digit_total = 0
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sum = 0
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temp = n
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while temp > 0:
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temp, rem = divmod(temp, 10)
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digit_histogram[rem] += 1
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digit_total += 1
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for (cnt, i) in zip(digit_histogram, range(len(digit_histogram))):
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sum += cnt * i ** digit_total
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return n == sum
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def narcissistic_number(n: int) -> bool:
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"""Return True if n is a narcissistic number or False if it is not.
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>>> all(armstrong_number(n) for n in PASSING)
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True
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>>> any(armstrong_number(n) for n in FAILING)
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False
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"""
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if not isinstance(n, int) or n < 1:
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return False
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expo = len(str(n)) # the power that all digits will be raised to
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# check if sum of each digit multiplied expo times is equal to number
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return n == sum(int(i) ** expo for i in str(n))
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def main():
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"""
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Request that user input an integer and tell them if it is Armstrong number.
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"""
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num = int(input("Enter an integer to see if it is an Armstrong number: ").strip())
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print(f"{num} is {'' if armstrong_number(num) else 'not '}an Armstrong number.")
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print(f"{num} is {'' if narcissistic_number(num) else 'not '}an Armstrong number.")
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print(f"{num} is {'' if pluperfect_number(num) else 'not '}an Armstrong number.")
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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main()
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