Agh I made a mistake in my code:

if (recalc || numbers[i] != (hashstate[i] & 0xffffffff)) {
	hashstate[i] = hasher.hash(((uint64_t)p << 32) | numbers[i]);
}

Since I decided to pack the hashes and previous number values into a single array and then forgot to actually properly format the values, the hash counts generated by my code were nonsense. Not sure why I did that honestly.

Also, my data analysis was trash, since even with the correct data, which as you noted is in a lineal correlation with n!, my reasoning suggests that its growing faster than it is.

Here is a plot of the incorrect ratios compared to the correct ones, which is the proper analysis and also clearly shows something is wrong.

Anyway, and this is totally unrelated to me losing an internet argument and not coping well with that, I optimized my solution a lot and turns out its actually faster to only preform the check you are doing once or twice and narrow it down from there. The checks I’m doing are for the last two elements and the midpoint (though I tried moving that about with seemingly no effect ???) with the end check going to a branch without a loop. I’m not exactly sure why, despite the hour or two I spent profiling, though my guess is that it has something to do with caching?

Also FYI I compared performance with -O3 and after modifying your implementation to use sdbm and to actually use the previous hash instead of the previous value (plus misc changes, see patch).

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!) :(

lmao the “high priority bug” is just a user error

honestly I use .hh/.cc which is quite nice IMO . you can also use .hpp/.cpp but I don’t like it personally

reminder that .H can be used as a c++ header extension , along with .C for source files

honesty I never understood why people consider malbolge so bad . sure its difficult AF to do anything in and the complexity gets quite higher still , but IMHO its just to abstract to be painful , it feels to different to feel like something you should be able to understand .

honesty struggling to write simple operations in some of my own esolangs was way more mind-bendingly horrid than I think malbolge could be without making a compiler to it , while still feeling like I was programming .

to be fair I also made ArrayFuck so yeah

don’t worry , it can always get worse . source : I implemented a esoteric programming language of my own making with just a parser (no lexer !) and a tree walking interpreter while reimplementing a standard library and depending on undefined behavior in python . honestly I fear that code more each time I look at it

Honestly I feel like PHP regex may be able to parse html but not entirely sure

I’m think the answer there does not apply to the PHP version of regex though I’m not entirely sure

I pretty much grew up on Ubuntu’s default polish layout - a modified version of the polish programmer’s keyboard , which itself is a modified version of ANSI

(the preview is slightly broken , but oh well)

I cannot begin to stress how used I am t o having an extra key layer accessible by just pressing alt . Note that the current version I have has some dead keys as well on the third and fourth layer .

honestly I’ve been working on a side project in plain c , while I usually do c++ with a large amount of c libraries and I can’t say I prefer it . The OOP features c++ gives really feel absent and I really feel like my code could be cleaner with them .

especially as OP is comming from Java , c++ is likely a better option than c

While I agree with you , the Open Software Initiative doesn’t :

Open source doesn’t just mean access to the source code.

So according to the OSI’s definition of open source , a project being public on github , but with out a license or with a license which does not comply with the requirements set out by the OSI

no it still doesn’t because unless that ai will code in assembly (which you could argue is a statically typed programming language with just one type , but lets not be pedantic) , it will still use programming languages , which means it will still matter if a language something is made is statically or dynamically typed .

even with the assumption that AI will be able to efficiency code in assembly , lets entertain the exponential growth version of ai often shown in fiction , it will still not be worth for that super intelligence to write in assembly (except for what we humans would call fun or for small cases where its necessary like os headers etc) because a compiler will do it faster and likely good enough , especially as it will then be able to make a better compiler . it will also likely not want to spend time/focus to scan the assembly code which is another advantage to not writing in pure assembly .

making that statement requires a complete lack of understanding how programming works along with an over"optimistic" view on the future of ai nya

to be fair , making a simple os is a fun side project , though I would recommend going with a toy VM rather than actual hardware

Not that it will matter in the AI future

that statement makes so little sense I feel like Mount stupid does not give it justice .