如何分析这个特定版本的quicksort？

Question

I have this pseudocode and I want to analysis time complexity of this algorithm But I have no idea about it

Proc Sort(A,l,r)
 if(r-l+1<4)
    then Quicksort(A,l,r)
    else
     Sort(A,l,r-3)
     Sort(A,l+3,r)

So I know that if the element of an array is less than 4 we pass it through the quicksort else we reduce the size of the array by three and then pass the left and right part So we will do this untile we get exactly the array of size n<4 the problem is I can't get to the recurrence and I am not sure if this algorithm works better in the worst case analysis

Thank you for your help

Answer 1

Well, whether or not this sorting function actually works , the way to figure out the run time is pretty easy here:

You write down a mathematical expression for the run time as a function of array size:

T(N) = ???

Well, if N <= 4, then we call Quicksort. Now, we don't have the function definition available, but regardless of that, since it will only ever called with input of at most size 4, we can treat its run time as a constant and just call it C.

And if N >= 4, then we call Sort again, with arrays that are 3 smaller.

So:

T(N) for N >= 4 is 2 * T(N-3).

Now at this point that should give you all the information you need for runtime analysis. Why don't you try it from here and get back to us when you get stuck?