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102 lines
2.0 KiB
Python
102 lines
2.0 KiB
Python
"""
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https://en.wikipedia.org/wiki/Weird_number
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Fun fact: The set of weird numbers has positive asymptotic density.
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"""
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from math import sqrt
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def factors(number: int) -> list[int]:
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"""
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>>> factors(12)
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[1, 2, 3, 4, 6]
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>>> factors(1)
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[1]
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>>> factors(100)
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[1, 2, 4, 5, 10, 20, 25, 50]
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# >>> factors(-12)
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# [1, 2, 3, 4, 6]
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"""
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values = [1]
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for i in range(2, int(sqrt(number)) + 1, 1):
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if number % i == 0:
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values.append(i)
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if int(number // i) != i:
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values.append(int(number // i))
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return sorted(values)
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def abundant(n: int) -> bool:
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"""
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>>> abundant(0)
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True
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>>> abundant(1)
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False
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>>> abundant(12)
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True
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>>> abundant(13)
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False
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>>> abundant(20)
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True
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# >>> abundant(-12)
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# True
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"""
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return sum(factors(n)) > n
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def semi_perfect(number: int) -> bool:
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"""
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>>> semi_perfect(0)
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True
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>>> semi_perfect(1)
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True
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>>> semi_perfect(12)
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True
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>>> semi_perfect(13)
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False
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# >>> semi_perfect(-12)
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# True
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"""
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values = factors(number)
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r = len(values)
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subset = [[0 for i in range(number + 1)] for j in range(r + 1)]
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for i in range(r + 1):
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subset[i][0] = True
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for i in range(1, number + 1):
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subset[0][i] = False
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for i in range(1, r + 1):
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for j in range(1, number + 1):
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if j < values[i - 1]:
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subset[i][j] = subset[i - 1][j]
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else:
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subset[i][j] = subset[i - 1][j] or subset[i - 1][j - values[i - 1]]
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return subset[r][number] != 0
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def weird(number: int) -> bool:
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"""
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>>> weird(0)
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False
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>>> weird(70)
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True
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>>> weird(77)
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False
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"""
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return abundant(number) and not semi_perfect(number)
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if __name__ == "__main__":
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import doctest
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doctest.testmod(verbose=True)
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for number in (69, 70, 71):
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print(f"{number} is {'' if weird(number) else 'not '}weird.")
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