如何从Leetcod理解快乐数问题解的空间复杂性

Question

我在理解Happy Number Question from Leet code的一个解决方案的空间复杂性分析时遇到了一些困难，对于我对复杂性分析的疑问，我用粗体标记了它们，非常感谢您的建议

问题是：

链接：https://leetcode.com/problems/happy-number/

问题：

Write an algorithm to determine if a number is "happy". A happy number is a number defined by the following process: Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1. Those numbers for which this process ends in 1 are happy numbers.

示例：

输入：19

输出：真

说明：

1^2（1的平方）+9^2=82

8^2+2^2=68

6^2+8^2=100

1^2+0^2+0^2=1

代码如下：

class Solution(object):
    def isHappy(self, n):
        #getnext function will compute the sum of square of each digit of n
        def getnext(n):
            totalsum = 0
            while n>0:
                n,v = divmod(n,10)
                totalsum+=v**2
            return totalsum
        #we declare seen as a set to track the number we already visited
        seen = set()
        #we stop checking if: either the number reaches one or the number was visited #already(ex.a cycle)
        while n!=1 and (n not in seen):
            seen.add(n)
            n = getnext(n)
        return n==1

注意：如果我需要解释代码的工作原理，请随时告诉我

解决方案说空间复杂度是logN，有人能给我一些建议说明为什么会这样吗？