Welcome to OGeek Q&A Community for programmer and developer-Open, Learning and Share
Welcome To Ask or Share your Answers For Others

Categories

0 votes
1.5k views
in Technique[技术] by (71.8m points)

time complexity - Finding Big O of the Harmonic Series

Prove that

1 + 1/2 + 1/3 + ... + 1/n is O(log n). 
Assume n = 2^k

I put the series into the summation, but I have no idea how to tackle this problem. Any help is appreciated

Question&Answers:os

与恶龙缠斗过久,自身亦成为恶龙;凝视深渊过久,深渊将回以凝视…
Welcome To Ask or Share your Answers For Others

1 Reply

0 votes
by (71.8m points)

This follows easily from a simple fact in Calculus:

enter image description here

and we have the following inequality:

enter image description here

Here we can conclude that S = 1 + 1/2 + ... + 1/n is both Ω(log(n)) and O(log(n)), thus it is ?(log(n)), the bound is actually tight.


与恶龙缠斗过久,自身亦成为恶龙;凝视深渊过久,深渊将回以凝视…
OGeek|极客中国-欢迎来到极客的世界,一个免费开放的程序员编程交流平台!开放,进步,分享!让技术改变生活,让极客改变未来! Welcome to OGeek Q&A Community for programmer and developer-Open, Learning and Share
Click Here to Ask a Question

...