you forgot about updating the hashes of items after items which were modified , so while it could be slightly faster than O((n!×n)²) , not by much as my data shows .

in other words , every time you update the first hash you also need to update all the hashes after it , etcetera

so the complexity is O(n×n + n×(n-1)×(n-1)+…+n!×1) , though I dont know how to simplify that

actually all of my effort was wasted since calculating the hamming distance between two lists of n hashes has a complexity of O(n) not O(1) agh

I realized this right after walking away from my devices from this to eat something :(

edit : you can calculate the hamming distance one element at a time just after rehashing that element so nevermind

honestly I was very suspicious that you could get away with only calling the hash function once per permutation , but I couldn’t think how to prove one way or another.

so I implemented it, first in python for prototyping then in c++ for longer runs… well only half of it, ie iterating over permutations and computing the hash, but not doing anything with it. unfortunately my implementation is O(n²) anyway, unsure if there is a way to optimize it, whatever. code

as of writing I have results for lists of n ∈ 1 … 13 (13 took 18 minutes, 12 took about 1 minute, cant be bothered to run it for longer) and the number of hashes does not follow n! as your reasoning suggests, but closer to n! ⋅ n.

link for the desmos page

anyway with your proposed function it doesn’t seem to be possible to achieve O(n!²) complexity

also dont be so negative about your own creation. you could write an entire paper about this problem imho and have a problem with your name on it. though I would rather not have to title a paper “complexity of the magic lobster party problem” so yeah

unless the problem space includes all possible functions f , function f must itself have a complexity of at least n to use every number from both lists , else we can ignore some elements of either of the lists , therby lowering the complexity below O(n!²)

if the problem space does include all possible functions f , I feel like it will still be faster complexity wise to find what elements the function is dependant on than to assume it depends on every element , therefore either the problem cannot be solved in O(n!²) or it can be solved quicker

this would assume that finding the next prime is a linear operation , which is false

if I’m not mistaken , a example of a problem where O(n!²) is the optimal complexity is :

There are n traveling salespeople and n towns . find the path for each salesperson with each salesperson starting out in a unique town , such that the sum d₁ + 2 d₂ + … + n dₙ is minimised, where n is a positive natural number , dᵢ is the distance traveled by salesperson i and i is any natural number in the range 1 to n inclusive .

pre post edit, I realized you can implement a solution in 2(n!) :(

honestly what makes it even more funny is that she claims to be an anarchocapitalist

congrats on the 666th comment btw

Mozilla has a history of harming me. I’ve documented this as one more case of attacks from Mozilla to go along with everything else. I see no reason to put up with it or tolerate it. Mozilla should expect that one day they’re going to be held accountable. If people at Mozilla aren’t aware of the unethical behavior it regularly engages in including an exploitative approach to contributors, they should inform themselves.

- Daniel Micay (im the linked mailing list thread)

it doesn’t seem like Micay had feuds previous to 2019 with Mozilla , though I was unable to find what he is referring to unfortunately .

also I would recommend this video & and others by shounic

linky

I misread this as if it lacked the y and was slightly confused for a second

to be fair , neither the free software movement nor the open source movement (which are distinct ideologically) are explicitly socialist . in a way , especially the free software movement , they embody an extention of liberalism .

both of these movements focus on the individuals freedom and take issue not with developers/companies being systemically incentivized to develop closed source / nonfree software , but with individual developers/companies doing so . thus the solution taken is limited to the individual not to systemic change .

what does the octothorpe s mean in the top right ?

both Microsoft office and open/libre office files are zip files containing mostly XML so its not that bad actually , as long as you expose the files inside to git

LMMS isn’t really a DAW, as it can’t really manipulate audio easily, only midi.

IIRC it can use audio files as instruments though I never used that feature so idk how limited it is , I believe other DAWs can import audio more directly

most of the video was centred on the player

it wasn’t ?? haha , the movement in the beginning is there because I didn’t bother trimming the movement of the camera :P

pretty sure I have actually used it lol