All Possible Sorting algorithm analysis

Question

The “APS” (All Possible Sorting) algorithm sorts an array A of size n by generating all possible sequences of elements of n, and for each sequence, checking to see if the elements are in sorted (ascending) order.

a) What is the worst-case time complexity of APS? Explain your logic / show your work.

My answer:

Worst case is O(n!) because it generates all possible sequences and then checks if sorted.

Preferably, I would like someone to tell me if I'm right or wrong and how to get to the answer. This big O stuff confuses me.

Joe F · Accepted Answer · 2013-04-19 00:26:51Z

3

APS is generating all possible permutations of N elements, which gives you n! different possible sortings, so you are correct.

Proving that it is O(n!) just requires you to prove that the runtime is asymptotically upper-bounded by n!, which basically means you have to prove that:

f(n) = O(n!) if, for some m and c, |f(n)| < |m * n!| for all n > c.

Proving this is easier if you have the actual algorithm written out, but if you walk through your logic it should do the trick.

answered Apr 19, 2013 at 0:26

Joe F

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