Min / Max Combinator circuit help

Don't know how to use a machine? Looking for efficient setups? Stuck in a mission?
MrDrummer
Fast Inserter
Fast Inserter
Posts: 132
Joined: Sat Nov 22, 2014 2:51 pm
Contact:

Min / Max Combinator circuit help

Post by MrDrummer »

So when I played Factorio last, it was 0.14 and there was a mod called Math Co-Processor, which allowed getting the min, max and random signal from the values on the poles ajacent to it.

This allowed for getting the min/max of any number of different signals.

This mod has since stopped development.

How would I do this with combinators? I had tried it myself back along, but my brain fried. Plus the way i did everything meant exponentially more combinators the more values I wish to compare.

Context: I'd like to get the lowest storage depot quantity for my iron, copper, coal and stone. But ideally a blueprint that can be used elsewhere.
quyxkh
Smart Inserter
Smart Inserter
Posts: 1031
Joined: Sun May 08, 2016 9:01 am
Contact:

Re: Min / Max Combinator circuit help

Post by quyxkh »

How tricky are you prepared to get with your wiring? With isolated inputs (input wires not already driving other inputs) you can select the signal set from n sets that has the min/max of a particular signal in 3n-3 combinators and log_2 n time.

Start with the basic trick that leads to 3n-3 combinator usage and linear time: negate the second set (Each×-1⇒Each) and wire the result and the first set to an (Iron<0⇒Everything) comparator, then wire the second set and the comparator result to an (Each-0⇒Each) isolator:
Select the signal set having the smallest iron signal
Select the signal set having the smallest iron signal
snap@T1700752=512x160-2-18.25,z2.jpg (5.35 KiB) Viewed 25429 times
The second set's signals are on the isolator's green input, so if the comparator doesn't do anything that'll be your output. The comparator sees the first set minus the second set, but only outputs the difference if the second set's iron was greater, so the isolator sees B (on the green wire) + (A-B) (on the red wire) with the difference added only if (A-B)'s iron is < 0. B+A-B is A, so you get all of A's values if A's iron is least, B's otherwise.

This gets the correct result 3 ticks worst case 0 ticks best: best case is some A values change but B's iron remains least, if some B values change but B's iron remains least then tick 0 B stays the best, tick 1 the isolator's outputting any new B values; worst case is tick 0 B's iron becomes less than A's, tick 1 the negator result's live, tick 2 the comparator result's live, tick 3 the isolator result's live. To add another input, the bottom right isolator's output is your new A signal, make a new row and wire it up:
Same, for three sets
Same, for three sets
snap@T1778538=528x224-2.25-18.25,z2.jpg (8.59 KiB) Viewed 25429 times
If linear time's okay, having the right result as of say half a second ago with ten inputs doesn't leave you wishing you could get the delay down under a quarter second, you can just drag-spam the bottom two rows there and the least will show up on your bottom right isolator otuputs. But the log time wiring change is obvious: for each set of four inputs, wire the pairs up separately and treat their outputs as the A and B inputs to the middle:
Logarithmic-time wiring for four sets, readout's in the middle.
Logarithmic-time wiring for four sets, readout's in the middle.
snap@T1855492=560x304-2.5-19.5,z2.jpg (12.32 KiB) Viewed 25429 times
and your least-iron signal set readout is the middle isolator.

This does sometimes have transients, if a B signal changes to have greater iron it'll take a couple ticks for the lesser value to overtake it, so if tick one the A set is iron 43 and the B set is iron 12, then tick 2 the B set gets iron 600, on tick 3 and 4 you'll see the 600-iron set until the negator/comparator pair's result catches up. If that's intolerable you can put a pulse converter and a delay on there, don't output anything if the iron value has risen in the last two ticks, but generally you're dealing with small per-tick changes, one inserter hand capacity at a time, and calculation results lagging a little isn't worth worrying about.

Edit: I keep thinking it's doable with 2n-1 combinators, that just looks _so_ sparse, are any of the isolators but the last really necessary?

Edit 2: the setup's pretty easy to adapt, if instead of delivering the signal set with the smallest value for iron youi want to deliver the largest value presented for each signal regardless of origin, change the comparators from Iron < 0 ⇒ Everything to Each > 0 ⇒ Each, that might be what your "min/max of an arbitrary number of signals" means.
MrDrummer
Fast Inserter
Fast Inserter
Posts: 132
Joined: Sat Nov 22, 2014 2:51 pm
Contact:

Re: Min / Max Combinator circuit help

Post by MrDrummer »

Thank you so much for spending time helping me with my problem!

I have not built this in my test save quite yet, but how does it handle two lowest values that are the same?

copper: 1,000,000
iron: 2,000,000
coal: 500,000
stone: 500,000

I used to use the Random combinator from the mentioned mod, but I guess I need to figure out a way to pick one. (or is that what the "any" selector does?)

As far as compactness goes, I don't really care - this will be used in a master controller anyway. I just want to be able to slap down a blueprint and configure the values i want. (And possibly be able to disect it to expand if needed)

I'll be sure to play around using your explanation in the near future :)
quyxkh
Smart Inserter
Smart Inserter
Posts: 1031
Joined: Sun May 08, 2016 9:01 am
Contact:

Re: Min / Max Combinator circuit help

Post by quyxkh »

Okay, for picking the signal that has the lowest numeric value from a single set, not max coal from a lot of mixed-inventory sets but max item from a single mixed-inventory set, that one I don't know. Pretty sure I remember XKnight and maybe DaveMcW in a discussion about that, their conclusion was ~it's hard~. Best way to isolate a single item signal from a set I know of is feeding the set to a set-filter stack-filter-inserter that has the items available, but that won't be random and might not be greatest or least. See viewtopic.php?t=52697 for my take on that, it's unwieldy though.

Maybe a little mental aikido, is there some way to achieve your ends (some kind of load balancing, but what?) that uses combinators' strengths?
phi1010
Inserter
Inserter
Posts: 46
Joined: Sat Aug 20, 2016 3:31 pm
Contact:

Re: Min / Max Combinator circuit help

Post by phi1010 »

I just built a maximum calculator, trading space for time: viewtopic.php?f=193&t=71845

You might be able to calculate a minimum with this too, if you:
Change the rounding to floor instead of ceil:
* remove the S := -1 constant calculator
* Change the sum from M := Each/N to M := S/N
and request values lower instead of higher than average:
* change the >= filter to =<

Or simply try to negate the input (and maybe add the sum of all items to each, to enforce positive values) -- I haven't tested it for negative values yet, usually this might either trigger inability to distinguish between large numbers with small differerences, e.g. {-9,-8}, or elimination of the maximum itself, causing an empty result.

Getting a random item's value is probably impossible, since there is no way to apply a distinguishing filter operation to one that doesn't apply to the other too, if both items have the same value. A constant combinator with different signals for each item would be a minimum requirement -- or a signal where every item can occur independently, e.g. from sushi belt.
WilliamR
Manual Inserter
Manual Inserter
Posts: 2
Joined: Wed Oct 17, 2018 4:08 pm
Contact:

Re: Min / Max Combinator circuit help

Post by WilliamR »

So,... Is there a chance that we simply get a min / max operator for the arithmetic combinator? Seems like this is a no brainer and an easy extension...
User avatar
DaveMcW
Smart Inserter
Smart Inserter
Posts: 3718
Joined: Tue May 13, 2014 11:06 am
Contact:

Re: Min / Max Combinator circuit help

Post by DaveMcW »

Suggestion Forum is this way: viewforum.php?f=6
MrDrummer
Fast Inserter
Fast Inserter
Posts: 132
Joined: Sat Nov 22, 2014 2:51 pm
Contact:

Re: Min / Max Combinator circuit help

Post by MrDrummer »

Figured i'd post an update on my original purpose of this thread...

I have got a train controller working! The Min/Max shown at the start of this thread is used all the time! Very helpful :)

My main purpose for removing an item from a min/max "test" was to prevent trains going to a coal outpost for example when I have plenty in storage.

I think the easy solution is to just disable the resulting min signal from doing anything when the item in question is over a large number (10mil for arguments sake), and when you want to disable an item that is being compared, just set it to be over that threshold. This would be for min, in the context of "go to the ore pickup station for the ore we have the least of in storage"

Then, since uranium or coal is above everything else that we care about (under 10mil), the others will get priority. If everything is over the magic number (10mil), then nothing happens with the chosen output.

A combinator mode for min/max (maybe even random) would be cool too :)
Honktown
Smart Inserter
Smart Inserter
Posts: 1042
Joined: Thu Oct 03, 2019 7:10 am
Contact:

Re: Min / Max Combinator circuit help

Post by Honktown »

10 mil in storage? yikes! Every level of Mining Productivity you lost another million ore. Sure it might be like, one patch worth you're losing, but the efficiency!
I have mods! I guess!
Link
MrDrummer
Fast Inserter
Fast Inserter
Posts: 132
Joined: Sat Nov 22, 2014 2:51 pm
Contact:

Re: Min / Max Combinator circuit help

Post by MrDrummer »

It's more because I have not got the processing for said ore up and running yet. I'd rather everything comes to a halt than for trains to back up because the stations meant to unload are chocka!
quyxkh
Smart Inserter
Smart Inserter
Posts: 1031
Joined: Sun May 08, 2016 9:01 am
Contact:

Re: Min / Max Combinator circuit help

Post by quyxkh »

To pick a single highest or lowest: burst the wire out through N pairs, once for each signal you're interested in, the pairs forward that signal to itself and to signal-I. The outputs from each pair are the inputs to the above selection network, which will pick exactly one (I, resource) pair having the desired value, if coal is lowest at 723 it'll output {coal=723,I=723}. If there's duplicates it'll pick one fairly arbitrarily, you can work out the priority.
pic
If anybody's still interested, thinking I couldn't be the first person to invent that, I googled for it and discovered an everything comparison *does not compare a signal against itself* so you can get all highest or lowest values (or no value if duplicates exist) much more easily, everything<coal output coal does in fact output coal if that's the highest value. This is much more useful than my read on what the wiki says, "The Everything input functions as a logical AND, and will return true only if ALL non-zero inputs pass the conditional.", because if coal is a non-zero signal it does not pass that "< Coal" conditional. I hope the wiki's wrong.
MrDrummer
Fast Inserter
Fast Inserter
Posts: 132
Joined: Sat Nov 22, 2014 2:51 pm
Contact:

Re: Min / Max Combinator circuit help

Post by MrDrummer »

Thanks! Will save this for when I next take a crack at Factorio.
telephotorocket
Manual Inserter
Manual Inserter
Posts: 2
Joined: Sat Mar 11, 2023 9:27 pm
Contact:

Re: Min / Max Combinator circuit help

Post by telephotorocket »

It is time! this thread will be revived, we have found an answer, a circuit build that can calculate MAX() can recalculate whenever a higher value is put in, can ignore updates from anything under max being updated, and will clear itself when input is turned off, best of all it fits inside a 5x5.

https://factorioprints.com/view/-NQHYf_XCsdl_ChkKKMW
User avatar
disentius
Filter Inserter
Filter Inserter
Posts: 694
Joined: Fri May 12, 2017 3:17 pm
Contact:

Re: Min / Max Combinator circuit help

Post by disentius »

what is the difference with this one?
https://factoriobin.com/post/2blkEgmK
thelordodin
Fast Inserter
Fast Inserter
Posts: 153
Joined: Fri Jan 06, 2017 1:54 am
Contact:

Re: Min / Max Combinator circuit help

Post by thelordodin »

I think I have a better solution to this, without jumping through loops.

All circuits in this blueprints can be fed with both green or red wires.

The blueprints:

Code: Select all

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
This is the main idea behind my blueprints:
First you build a filter circuit.
It gets "input" wire and "filter" wire, then it outputs all signals from input but only if the same signal is positive in "filter".
My implementation handles both positive and negative signals (from -1 billion up to 1 billion)

Filter circuit is done using this ideas:
1) Use condition combinator to get positive signals from "filter"
2) Multiply that by -2 billion (or any other big negative value)
3.1) Merge it with "input" on next combinator, so you effectively get input -2 billion * filter
3.2) Use condition combinator to get values above -1 billion
4) Now add back 2 billions

So it takes only 4 combinators to build (see numbers above, 3.1 and 3.2 is done on one decider combinator).

Also build "excluder" circuit
It's simmilar to "filter" but it excludes the second wire from the first one.
It can be build with 4 combinators (or less).
The ideas are same, so I won't describe it again, just here is the blueprint.

The blueprints are functional BUT I didn't even tryed to optimize them. I think if one wants to, than 3-4 combinators can be thrown away from them.
I'll appriciate if someone does that - please post updated versions.

Notes for thouse crazy guys who read this far and really wants to understand how it's done:

The idea behind max (min is roughly the same):
You have A and B wires and have to select max signals from them.
So basically
- First we make A<=B, this is essentially (B + 1) * (-1) + A < 0
- I.e. feed B into arithmetic +1, Arithmetic *-1, merge wires with A on next comb, decider <0 emit 1
- Now we have all "good" signals types from A, so just use "filter" circuit on A to get them

- Now we just exclude this "good" signals from B using "excluder
- And after that merge two parts
Done. You have good results

What won't work (the naive approach I tried at first but it didn't work):
- Using (A-B) <= 0 to filter A
and
- Using (A-B) > 0 to filter B
and then merge
Tried this. It won't work for equal signals.
Last edited by thelordodin on Sat Dec 23, 2023 9:43 am, edited 1 time in total.
Tertius
Filter Inserter
Filter Inserter
Posts: 948
Joined: Fri Mar 19, 2021 5:58 pm
Contact:

Re: Min / Max Combinator circuit help

Post by Tertius »

thelordodin wrote: Fri Dec 22, 2023 11:24 am What won't work (the naive approach I tried at first but it didn't work):
- Using (A-B) <= 0 to filter A
and
- Using (A-B) > 0 to filter B
and then merge
Tried this. It won't work for equal signals.
The naive approach indeed works, you probably got the "filter X" part wrong.

Do this for MAX(A,B):
Create difference B-A
Output A.
If difference > 0, add difference to output (by using a decider combinator and "input count").

Similar for MIN(A, B):
Create difference B-A
Output A.
If difference < 0, add difference to output (by using a decider combinator and "input count").


This is a blueprint book with all kinds of * OP * operations:


It's from this forum, but unfortunately, I'm unable to find the original post and the original poster to give credit.

The blueprint contains many NOP combinators. These are present to uncouple input from output and to make the latency equal for every case - you might omit some, if the use case allows this.
mmmPI
Smart Inserter
Smart Inserter
Posts: 3680
Joined: Mon Jun 20, 2016 6:10 pm
Contact:

Re: Min / Max Combinator circuit help

Post by mmmPI »

thelordodin wrote: Fri Dec 22, 2023 11:24 am What won't work (the naive approach I tried at first but it didn't work):
- Using (A-B) <= 0 to filter A
and
- Using (A-B) > 0 to filter B
and then merge
Tried this. It won't work for equal signals.
Are you using mods ? when i tried to import the blueprint it only import 4 combinators connected and 2 constant a little aside, and it's telling me "unknown signal note interface" or "unknown virtual signal name".

I wanted to see if there was some difference with the book i used, which is similar to the one Tertius linked, with some additions, it was made from Nidan at first from this post viewtopic.php?f=193&t=103567
thelordodin
Fast Inserter
Fast Inserter
Posts: 153
Joined: Fri Jan 06, 2017 1:54 am
Contact:

Re: Min / Max Combinator circuit help

Post by thelordodin »

mmmPI wrote: Sat Dec 23, 2023 1:49 am Are you using mods ? when i tried to import the blueprint it only import 4 combinators connected and 2 constant a little aside, and it's telling me "unknown signal note interface" or "unknown virtual signal name".

I wanted to see if there was some difference with the book i used, which is similar to the one Tertius linked, with some additions, it was made from Nidan at first from this post viewtopic.php?f=193&t=103567
Yes I use mods, but the circuts will work just fine without any mods.
Where combinatiors is input, the right side is output. Min/Max output is right bottom corner.

I've updated the bluprint in my post above - get the new book.
The only mod left is "Attach notes" with comments.
But again you don't need to install it, all will work fine without it, you just won't see the comments.
mmmPI
Smart Inserter
Smart Inserter
Posts: 3680
Joined: Mon Jun 20, 2016 6:10 pm
Contact:

Re: Min / Max Combinator circuit help

Post by mmmPI »

thelordodin wrote: Sat Dec 23, 2023 9:41 am I've updated the bluprint in my post above - get the new book.
The only mod left is "Attach notes" with comments.
But again you don't need to install it, all will work fine without it, you just won't see the comments.
i'm fine with mods, i tried without any mod of my own, i thought it wouldn't matter , then maybe it does, but now i definitely think there is a problem in the blueprint, i see the updated book and to me it's only one blueprint inside , in the second position , the filter made of 4 combinators with the description of it as a filter . I don't get anything else
bpmissingmaybe.png
bpmissingmaybe.png (173.39 KiB) Viewed 7942 times
thelordodin
Fast Inserter
Fast Inserter
Posts: 153
Joined: Fri Jan 06, 2017 1:54 am
Contact:

Re: Min / Max Combinator circuit help

Post by thelordodin »

mmmPI wrote: Sat Dec 23, 2023 10:24 am i'm fine with mods, i tried without any mod of my own, i thought it wouldn't matter , then maybe it does, but now i definitely think there is a problem in the blueprint, i see the updated book and to me it's only one blueprint inside , in the second position , the filter made of 4 combinators with the description of it as a filter . I don't get anything else

bpmissingmaybe.png
Ooops... I forgot about the icons... and it deletes blueprint if he don't know icon for.

Can you try this?

Code: Select all

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
Post Reply

Return to “Gameplay Help”