[leetcode] 507. Perfect Number @ python

判断完美数的算法实现

最新推荐文章于 2025-09-30 16:36:44 发布

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博客围绕判断完美数展开，完美数是指等于除自身外所有正因数之和的正整数。给出判断整数是否为完美数的问题，介绍了遍历的解法，时间复杂度为O(math.square(n))，空间复杂度为O(n)，还给出了示例。

原题

We define the Perfect Number is a positive integer that is equal to the sum of all its positive divisors except itself.

Now, given an integer n, write a function that returns true when it is a perfect number and false when it is not.
Example:
Input: 28
Output: True
Explanation: 28 = 1 + 2 + 4 + 7 + 14
Note: The input number n will not exceed 100,000,000. (1e8)

解法

遍历.
Time: O(math.square(n))
Space: O(n)

代码

class Solution:
    def checkPerfectNumber(self, num: int) -> bool:
        # base case
        if num <= 1: 
            return False
        
        divisors = [1]
        for i in range(2, int(math.sqrt(num))+1):
            if num % i == 0:
                divisors.extend([i, num/i])
        return num == sum(divisors)