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Add improved doctrings and doctests for math/perfect_number.py (#12830)

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* Add improved doctrings and doctests for math/perfect_number.py

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Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>
This commit is contained in:
NostraWho
2026-09-08 15:28:10 +02:00
committed by GitHub
co-authored by pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com> Christian Clauss
parent 301d111954
commit beca49787a
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maths/perfect_number.py
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@@ -2,13 +2,15 @@
== Perfect Number ==
In number theory, a perfect number is a positive integer that is equal to the sum of
its positive divisors, excluding the number itself.
For example: 6 ==> divisors[1, 2, 3, 6]
Excluding 6, the sum(divisors) is 1 + 2 + 3 = 6
So, 6 is a Perfect Number
Other examples of Perfect Numbers: 28, 486, ...
The first few perfect numbers are: 6, 28, 496, 8128, 33550336, ...
https://en.wikipedia.org/wiki/Perfect_number
https://oeis.org/A000396
"""
@@ -17,70 +19,286 @@ def perfect(number: int) -> bool:
Check if a number is a perfect number.
A perfect number is a positive integer that is equal to the sum of its proper
divisors (excluding itself).
divisors (positive divisors excluding the number itself).
The algorithm finds all divisors up to number//2 (since no proper divisor
can be greater than half the number) and sums them for comparison.
Time Complexity: O(sqrt(n)) with optimized divisor finding
Space Complexity: O(1)
Args:
number: The number to be checked.
number: The positive integer to be checked.
Returns:
True if the number is a perfect number otherwise, False.
Start from 1 because dividing by 0 will raise ZeroDivisionError.
A number at most can be divisible by the half of the number except the number
itself. For example, 6 is at most can be divisible by 3 except by 6 itself.
True if the number is a perfect number, False otherwise.
Raises:
ValueError: If number is not an integer.
Examples:
>>> perfect(27)
False
>>> perfect(28)
True
>>> perfect(29)
False
>>> perfect(6)
True
>>> perfect(12)
False
>>> perfect(496)
True
>>> perfect(8128)
True
>>> perfect(0)
False
>>> perfect(-1)
False
>>> perfect(33550336) # Large perfect number
True
>>> perfect(33550337) # Just above a large perfect number
False
>>> perfect(1) # Edge case: 1 is not a perfect number
False
>>> perfect("123") # String representation of a number
Traceback (most recent call last):
...
ValueError: number must be an integer
>>> perfect(12.34)
Traceback (most recent call last):
...
ValueError: number must be an integer
>>> perfect("Hello")
Traceback (most recent call last):
...
ValueError: number must be an integer
Basic perfect numbers:
>>> perfect(6)
True
>>> perfect(28)
True
>>> perfect(496)
True
>>> perfect(8128)
True
Large perfect number:
>>> perfect(33550336)
True
Non-perfect numbers:
>>> perfect(12)
False
>>> perfect(27)
False
>>> perfect(29)
False
>>> perfect(100)
False
Edge cases:
>>> perfect(1)
False
>>> perfect(2)
False
>>> perfect(0)
False
>>> perfect(-1)
False
>>> perfect(-6)
False
Numbers close to perfect numbers:
>>> perfect(5)
False
>>> perfect(7)
False
>>> perfect(27)
False
>>> perfect(29)
False
>>> perfect(495)
False
>>> perfect(497)
False
>>> perfect(33550335)
False
>>> perfect(33550337)
False
Type validation:
>>> perfect(12.34)
Traceback (most recent call last):
...
ValueError: number must be an integer
>>> perfect("123")
Traceback (most recent call last):
...
ValueError: number must be an integer
>>> perfect("Hello")
Traceback (most recent call last):
...
ValueError: number must be an integer
>>> perfect([6])
Traceback (most recent call last):
...
ValueError: number must be an integer
>>> perfect(None)
Traceback (most recent call last):
...
ValueError: number must be an integer
Testing divisor sum calculation for known cases:
>>> # For 6: divisors are 1, 2, 3 -> sum = 6
>>> sum(i for i in range(1, 6//2 + 1) if 6 % i == 0) == 6
True
>>> # For 28: divisors are 1, 2, 4, 7, 14 -> sum = 28
>>> sum(i for i in range(1, 28//2 + 1) if 28 % i == 0) == 28
True
>>> # For 12: divisors are 1, 2, 3, 4, 6 -> sum = 16 ≠ 12
>>> sum(i for i in range(1, 12//2 + 1) if 12 % i == 0) == 12
False
"""
if not isinstance(number, int):
raise ValueError("number must be an integer")
if number <= 0:
return False
return sum(i for i in range(1, number // 2 + 1) if number % i == 0) == number
# Special case: 1 has no proper divisors
if number == 1:
return False
# Find sum of all proper divisors
# We only need to check up to number//2 since no proper divisor
# can be greater than half the number
divisor_sum = sum(i for i in range(1, number // 2 + 1) if number % i == 0)
return divisor_sum == number
def perfect_optimized(number: int) -> bool:
"""
Optimized version of perfect number checker using mathematical properties.
This version uses the fact that divisors come in pairs (d, n/d) to reduce
the search space to sqrt(n).
Time Complexity: O(sqrt(n))
Space Complexity: O(1)
Args:
number: The positive integer to be checked.
Returns:
True if the number is a perfect number, False otherwise.
Examples:
>>> perfect_optimized(6)
True
>>> perfect_optimized(28)
True
>>> perfect_optimized(496)
True
>>> perfect_optimized(12)
False
>>> perfect_optimized(1)
False
>>> perfect_optimized(0)
False
>>> perfect_optimized(-1)
False
"""
if not isinstance(number, int):
raise ValueError("number must be an integer")
if number <= 1:
return False
divisor_sum = 1 # 1 is always a proper divisor for n > 1
# Check divisors up to sqrt(number)
i = 2
while i * i <= number:
if number % i == 0:
divisor_sum += i
# Add the paired divisor if it's different from i
if i != number // i:
divisor_sum += number // i
i += 1
return divisor_sum == number
def find_perfect_numbers(limit: int) -> list[int]:
"""
Find all perfect numbers up to a given limit.
Args:
limit: The upper bound to search for perfect numbers.
Returns:
List of perfect numbers up to the limit.
Examples:
>>> find_perfect_numbers(10)
[6]
>>> find_perfect_numbers(30)
[6, 28]
>>> find_perfect_numbers(500)
[6, 28, 496]
>>> find_perfect_numbers(0)
[]
>>> find_perfect_numbers(1)
[]
"""
if not isinstance(limit, int) or limit < 0:
raise ValueError("limit must be a non-negative integer")
return [n for n in range(1, limit + 1) if perfect(n)]
def get_divisors(number: int) -> list[int]:
"""
Get all proper divisors of a number (excluding the number itself).
Args:
number: The positive integer to find divisors for.
Returns:
List of proper divisors in ascending order.
Examples:
>>> get_divisors(6)
[1, 2, 3]
>>> get_divisors(28)
[1, 2, 4, 7, 14]
>>> get_divisors(12)
[1, 2, 3, 4, 6]
>>> get_divisors(1)
[]
>>> get_divisors(7)
[1]
"""
if not isinstance(number, int) or number <= 0:
raise ValueError("number must be a positive integer")
if number == 1:
return []
return [i for i in range(1, number // 2 + 1) if number % i == 0]
if __name__ == "__main__":
from doctest import testmod
testmod()
print("Program to check whether a number is a Perfect number or not...")
try:
number = int(input("Enter a positive integer: ").strip())
except ValueError:
msg = "number must be an integer"
raise ValueError(msg)
print("Running doctests...")
testmod(verbose=True)
print(f"{number} is {'' if perfect(number) else 'not '}a Perfect Number.")
print("\nPerfect Number Checker")
print("=" * 40)
print("A perfect number equals the sum of its proper divisors.")
print("Examples: 6 (1+2+3), 28 (1+2+4+7+14), 496, 8128, ...")
print()
while True:
try:
user_input = input("Enter a positive integer (or 'q' to quit): ").strip()
if user_input.lower() == "q":
break
number = int(user_input)
if number <= 0:
print("Please enter a positive integer.")
continue
is_perfect = perfect(number)
divisors = get_divisors(number)
divisor_sum = sum(divisors)
print(f"\nNumber: {number}")
print(f"Proper divisors: {divisors}")
print(f"Sum of divisors: {divisor_sum}")
print(f"Is perfect: {'Yes' if is_perfect else 'No'}")
if is_perfect:
print(f"✓ {number} is a Perfect Number!")
else:
print(f"✗ {number} is not a Perfect Number.")
print("-" * 40)
except ValueError as e:
if "invalid literal" in str(e):
print("Please enter a valid integer.")
else:
print(f"Error: {e}")
except KeyboardInterrupt:
print("\nGoodbye!")
break