算法分析之函数渐近分析
首要原则，三点：
#1 最坏的情况分析。"worst – case analysis" : our running time bound holds for every input of length n.
BONUS : worst case usually easier to analyze.
#2 不关心常数。低阶项。Won't pay much attention to constant factors, lower-order terms
#3 渐近分析。Asymptotic Analysis: focus on running time for large input sizes n
Justification: Only big problems are interesting!
渐近分析。Asymptotic Analysis
上图即原则#2.
Example: Equate 6n log2(n) + 6 with just n log n.
Terminology: Running time is O (n log n) ["big-Oh" of n log n]
where n = input size (e.g. length of input array).
Examples:
Loops：O (n) Two Nested Loops：O (n^2)
Big-O-notation
O-notation is an asymptotic upper bound.
Basic Examples：
#1： 
#2: 
Omega-notation
Ω-notation provides an asymptotic lower bound.
Theta-notation
We say that g(n) is an asymptotically tight bound for f (n).
Theta里的内容取不同的两个系数可表示函数渐近上、下界。
看三者关系：
Little o-notation
We use o-notation to denote an upper bound that is not asymptotically tight.
小o表示非渐近紧确的上界。而大O可能是也可能不是渐近紧确的。
小o就是函数极限的定义符号。
w-notation
小w表示非渐近紧确的下界。和小o定义相反。因此：
Examples
#1 
#2 
#3 
ANNOUNCEMENTS:
DO NOT USE THE CONTENTS OF THIS BOLG FOR COMMERCIAL PURPOSE, AND I USE THE CONTENTS FORM INFERENCES JUST FOR STUY.
THIS BOLG IS FORM: http://www.cnblogs.com/JayZen/p/4073235.html
Referances
Course: Algorithms: Design and Analysis, Part 1 by Tim Roughgarden at Stanford from Coursera
《Introduction to Algorithms》
