更新时间:2023-09-16 23:31:58
您可以将循环扩展为以下内容:
You can expand the loops to something like this:
i = 1 ——> 1,2,3,…,b b
i = 2 ——> 1,3,5,…,b (b/2)
i = 3 ——> 1,4,7,…,b (b/3)
i = 4 ——> 1,5,9,…,b (b/4)
…
i = b ——> 1, b (b/b = 1)
这会扩展为以下形式的总和:
This expands into a sum of the form:
b + b/2 + b/3 + … + b/b = b * (1 + 1/2 + 1/3 + … + 1/b)
您可能认识到第二个因素是谐波系列.然后,使用以下SO答案的结果:找到谐波系列的Big O您可以获得嵌套循环的大哦":
You might recognize the second factor as the Harmonic Series. Then, using the result from the following SO answer: Finding Big O of the Harmonic Series you can get the Big Oh of your nested loops:
O(b * log(b))