Add new algorithm for Armstrong numbers (TheAlgorithms#4474)

* Add a new algorithm for Armstrong numbers * FAILING = (-153, -1, 0, 1.2, 200, "A", [], {}, None) Co-authored-by: Christian Clauss <cclauss@me.com>

Author: AndersonTorres

maths/armstrong_numbers.py

@@ -1,26 +1,24 @@
 """
-An Armstrong number is equal to the sum of its own digits each raised
-to the power of the number of digits.
+An Armstrong number is equal to the sum of its own digits each raised to the
+power of the number of 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.
+
+Armstrong numbers are also called Narcissistic numbers and Pluperfect numbers.
+
+On-Line Encyclopedia of Integer Sequences entry: https://oeis.org/A005188
 """
+PASSING = (1, 153, 370, 371, 1634, 24678051, 115132219018763992565095597973971522401)
+FAILING = (-153, -1, 0, 1.2, 200, "A", [], {}, None)
 
 
 def armstrong_number(n: int) -> bool:
  """
  Return True if n is an Armstrong number or False if it is not.
 
- >>> armstrong_number(153)
+ >>> all(armstrong_number(n) for n in PASSING)
  True
- >>> armstrong_number(200)
- False
- >>> armstrong_number(1634)
- True
- >>> armstrong_number(0)
- False
- >>> armstrong_number(-1)
- False
- >>> armstrong_number(1.2)
+ >>> any(armstrong_number(n) for n in FAILING)
  False
  """
  if not isinstance(n, int) or n < 1:
@@ -43,15 +41,46 @@ def armstrong_number(n: int) -> bool:
  return n == sum
 
 
-def narcissistic_number(n: int) -> bool:
- """Return True if n is a narcissistic number or False if it is not"""
+def pluperfect_number(n: int) -> bool:
+ """Return True if n is a pluperfect number or False if it is not
+
+ >>> all(armstrong_number(n) for n in PASSING)
+ True
+ >>> any(armstrong_number(n) for n in FAILING)
+ False
+ """
+ if not isinstance(n, int) or n < 1:
+ return False
+
+ # Init a "histogram" of the digits
+ digit_histogram = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
+ digit_total = 0
+ sum = 0
+ temp = n
+ while temp > 0:
+ temp, rem = divmod(temp, 10)
+ digit_histogram[rem] += 1
+ digit_total += 1
+
+ for (cnt, i) in zip(digit_histogram, range(len(digit_histogram))):
+ sum += cnt * i ** digit_total
+
+ return n == sum
 
- 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 narcissistic_number(n: int) -> bool:
+ """Return True if n is a narcissistic number or False if it is not.
+
+ >>> all(armstrong_number(n) for n in PASSING)
+ True
+ >>> any(armstrong_number(n) for n in FAILING)
+ False
+ """
+ if not isinstance(n, int) or n < 1:
+ return False
+ expo = len(str(n)) # the power that all digits will be raised to
+ # check if sum of each digit multiplied expo times is equal to number
+ return n == sum(int(i) ** expo for i in str(n))
 
 
 def main():
@@ -61,6 +90,7 @@ def main():
  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.")
+ print(f"{num} is {'' if pluperfect_number(num) else 'not '}an Armstrong number.")
 
 
 if __name__ == "__main__":