Runtime of Algorithm

Question

An algorithm to sort a list L1 of length n:

1) Create new List L2

2) Move biggest element of L1 to beginning of L2

3) Do 2) until L1 is empty

4) Print L2

Can someone figure out what the O() complexity of this is? First I thought it was O(n*log(n)) but I an not so sure anymore, now I think its O(n^2).

Why did you think it was O(n log n), and why do you now think it is O(n^2)? — kaya3
– kaya3, Commented Mar 5, 2020 at 22:54
Well actually initially looking at the problem I thought it was O(n^2) but I realized that L1 gets smaller as Elements are moved to L2 so then I did some research and thought it would be in O(n*log(n)) but after some simple testing in python I figured thats not right so I went back to O(n^2). — SK4P3
– SK4P3, Commented Mar 5, 2020 at 22:58

Michał Urbaniak · Accepted Answer · 2020-03-06 04:36:08Z

1

Let's say you have a list of 10 elements.

In step 2 you have to scan the whole list first to find the biggest element and move to it to list no 2.

So, scanning the whole list is (10 + 9 + 8 + ... + 1) operations = 55.

For 100 elements it will be (100 + 99 + ... + 1) which is 5050

Now for n elements, you will have (n + (n-1) + ... + 1) operations which is (n+1)*n/2 = O(n^2)

answered Mar 6, 2020 at 4:36

Michał Urbaniak

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1 Comment

Ohh wow I was too stupid to see the sum from 1 to n because it was backwards... Thank you very much! :D