Algorithm doubt

Question

Which of the following statements is/are valid?
1. Time Complexity of QuickSort is Θ(n^2)
2. Time Complexity of QuickSort is O(n^2)
3. For any two functions f(n) and g(n), we have f(n) = Θ(g(n)) if and only if f(n) = O(g(n)) and f(n) = Ω(g(n)).
4. Time complexity of all computer algorithms can be written as Ω(1)

Comments

Time complexity of all computer algorithms can be written as $\Omega \left ( 1 \right )$

$\Rightarrow$it is as good as saying that All algorithm should at least take constant time.

$\Rightarrow$ It is as good as saying that All algorithm's best case will be atleast constant .

$\Rightarrow$ $1$ i.e contant time is lower bound for any algorithm .

That's right, no matter how efficient an algorithm is, it will take at least constant time .

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:) thanks alot

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I think first is not valid: Time Complexity of QuickSort is Θ(n^2)  

The worst case of Quicksort has Time Complexity  Θ(n^2) and Quicksort has a lower bound of Ω(n.lg(n)) on best case not Ω(n^2). Time Complexity of QuickSort is between  Ω(n.lg(n)) and O(n^2)  

Answer 1

2 is right answer .

Comments

2 and 3 option is correct

4 th is wrong if time complete of any algorithm =1/n

First is wrong n^2 is upper bound for quite sort