时间复杂度big-O、Big-Omega和big-Theta

我们有三种曲线：

 

A curve that we know is "above" the running time function when n is large. ( Big-O )

当n足够大时，曲线高于运行时间函数(big-o)

 

A curve that we know is "below" the running time function when n is large. (Big-Omega)

当n足够大时，曲线低于运行时间函数（big-omega）

 

If we can squeeze the curves that are "above" and "below" the running time function close enough, then we can figure out Big-Theta(big-theta)

 

Big-Theta 仅仅只是一个"Scaled"版本的运行曲线，big-theta仅仅只是scale最高序列的f(n)行为。big-theta仅仅只是一个曲线

 

 

Big-O 告诉你什么样的函数增长速度大于f(N)

Bit-Theta告诉你什么样的函数增长速度同f(N)

Big-Omega告诉你什么样的函数增长速度小于f(N)

 

Funcitons in Asymptotic notation

 

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所有公式都可以用这个来表示

 

Logarithms grow more slowly than polynomials

对数比指数增长慢

 

接下来是指数增长的顺序（由慢到快）：

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It would be convenient to have a form of asymptotic notation that means

运行时间最多增长这么多，但它可以增长的更慢

big-O asymptotic upper bounds:渐近上界

 

best case average/expected case worst case