David Feuer david.feuer at gmail.com
Wed Sep 2 04:55:00 UTC 2020

```Yes, the n not being inside the O is the point. These structures hold n
pointers in n words, plus a logarithmic term. Something like a linked list
or Data.Sequence will hold n pointers in around c*n words, where c>1. For a
list, c=3.

On Wed, Sep 2, 2020, 12:26 AM ☂Josh Chia (謝任中) <joshchia at gmail.com> wrote:

> Isn't a stack O(1) time for push & pop and O(n) space? What is the
> tradeoff being made here, where both space and time complexity increased?
>
> Or, am I missing something about the meaning of "n + O(log)", where the
> 'n' is not inside an 'O'. I don't really know what "n + O(log)" means
> exactly.
>
> On Wed, Sep 2, 2020 at 12:21 PM David Feuer <david.feuer at gmail.com> wrote:
>
>> Typical stacks, queues, and deques are designed to have O(1) operations.
>> These ones experiment in a different direction.
>>
>> On Wed, Sep 2, 2020, 12:19 AM ☂Josh Chia (謝任中) <joshchia at gmail.com>
>> wrote:
>>
>>> Could you elaborate on what the package does? The description is
>>> "Stacks, queues, and deques that take n + O(log n) space at the cost of
>>> having amortized O(log n) time complexity for basic operations." But why is
>>> it a 'cost' to have O(log n) instead of O(n) cost for basic operations on
>>> list-like structures (such as insert and delete presumably)? So, I didn't
>>> understand what the package is for.
>>>
>>> Do you mean "take amortized O(log n) time for basic operations at the
>>> cost of n + O(log n) space"? Or is it something else I didn't imagine?
>>>
>>>
>>>
>>> On Wed, Sep 2, 2020 at 4:17 AM David Feuer <david.feuer at gmail.com>
>>> wrote:
>>>
>>>> I am pleased to release the second version of the compact-sequences
>>>> package, now with deques!
>>>>
>>>> Changes:
>>>> * Change operator precedence.
>>>> * Add a test suite. Thanks to David Himmelstrup for setting up the
>>>> test and CI framework.
>>>> * Clean up internals somewhat.
>>>> * Add a proof of amortized bounds for the stack implementation.
>>>> Thanks, Li-Yao Xia.
>>>>
>>>> There are still plenty of things to work on, and help is always welcome.
>>>>
>>>> David Feuer
>>>> _______________________________________________