Big Oh，Big Omega和Big Theta之间的区别

先决条件–渐进符号，渐进符号的性质
1.大哦符号(O) ：
大哦符号用于描述渐近上限。

从数学上讲，如果f(n)描述算法的运行时间；如果存在正常数C，则f(n)为O(g(n))且不存在

0 <=f(n) <= c g(n) for all n>=n0

n =用于给上限提供一个函数。
如果一个函数为O(n)，它也将自动为O(n-square)！

Big oh(O)的图形示例：

2.大欧米符号(Ω)：
就像O符号提供渐近上限一样，Ω符号提供渐近下限。
令f(n)定义算法的运行时间；

如果存在正常数C和(n 0)使得f(n)为Ω(g(n))

O<= C g(n) <= f(n) for all n>=n 0

n =用于给定函数的下限
如果一个函数是O(n-square)，它也会自动成为O(n)。

大欧米茄(Ω)的图形示例：

3.大Theta表示法(Θ)：
令f(n)定义算法的运行时间。

如果f(n)为O(g(n))并且f(n)为Ω(g(n))，则f(n)称为Θ(g(n))。

数学上

O<=f(n)<=C 1 g(n) for n>=n 0

O<= C 2 g(n)<=f(n) for n >=n 0

合并这两个方程，我们得到：

O<=C 2 g(n)<=f(n)<=C 1 g(n) for n>=n 0

该方程式简单地意味着存在正常数C 1和C 2，使得f(n)夹在C 2 g(n)和C 1 g(n)之间。

大Theta(Θ)的图形示例：

Big oh，Big Omega和Big Theta之间的区别：

S.No.	Big Oh	Big Omega	Big Theta
1.	It is like <=  rate of growth of an algorithm is less than or equal to a specific value	It is like >=  rate of growth is greater than or equal to a specified value	It is like ==  meaning the rate of growth is equal to a specified value
2.	The upper bound of algorithm is represented by Big O notation. Only the above function is bounded by Big O. asymptotic upper bond is it given by Big O notation.	The algorithm’s lower bound is represented by Omega notation. The asymptotic lower bond is given by Omega notation	The bounding of function from above and below is represented by theta notation. The exact asymptotic behavior is done by this theta notation.
3.	Big oh (O) – Worst case	Big Omega (Ω) – Best case	Big Theta (Θ) – Average case
4.	Big-O is a measure of the longest amount of time it could possibly take for the algorithm to complete.	Big- Ω is take a small amount of time as compare to Big-O it could possibly take for the algorithm to complete.	Big- Θ is take very short amount of time as compare to Big-O and Big-? it could possibly take for the algorithm to complete.
5.	Mathematically – Big Oh is 0 <=f(n) <= c g(n) for all n>=n0	Mathematically – Big Omega is O<= C g(n) <= f(n) for all n>=n 0	Mathematically – Big Theta is O<=C 2 g(n)<=f(n)<=C 1 g(n) for n>=n 0