Perfect Number

Unit 4 Session 1 (Click for link to problem statements)

U-nderstand

Understand what the interviewer is asking for by using test cases and questions about the problem.

• What if n is 1 or less?
  • The function should return False since 1 and any non-positive numbers do not have proper divisors that sum up to themselves.

P-lan

Plan the solution with appropriate visualizations and pseudocode.

General Idea: Iterate through all numbers up to half of n to find its divisors, sum them, and compare the sum to n.

1) Check if n is 1 or less, return False if so
2) Initialize the sum of divisors to 0
3) Loop through numbers from 1 up to n/2
  a) If a number divides n evenly, add it to the sum of divisors
4) After the loop, compare the sum of divisors to n
5) Return True if they are equal, otherwise False

⚠️ Common Mistakes

• Forgetting to exclude n itself from its list of divisors.
• Not handling the case when n is less than or equal to 1 correctly.

I-mplement

def is_perfect_number(n):
    if n <= 1:
        return False
    sum_divisors = 0
    i = 1
    while i <= n // 2:
        if n % i == 0:
            sum_divisors += i
        i += 1
    return sum_divisors == n