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Finally, done. In last three days, I have been always thinking of D20 except for sleeping time(seriously).
I feel that D20 description is NOT easy to understand, and needed some assumption, to be honest. I'm writing what we need to understand to solve D20 in the below Spoiler.
For Part2, never try Brute Force, because it will just end up warming up your room temperature.
My WF
Part1
1) Receive pulses
One or more pulses are coming to conjunction module.
2) Update memory
Memory status low/high is updated to the same to the received pulse type. Conjunction module doe NOT send pulse to downstream until all of memory state are updated.
3) Send Pulse
Based on the memory state in the above 2), conjunction module send pulses. The number of pulses sent is the same as number of pulses received. For example, if it receives 2 pulses, and at least one memory is LOW, then it sends out 2 HIGH pulses at one time(HIGH-HIGH). So, conjunction module sends the single type of pulses at one time (never sends mixed type; LOW-LOW-HIGH)
In short, there may exist multiple pulses between two module, looking like a que due to this behavior of conjunction module.
Loop the process until no modules sends pulses. That is one cycle of pressing one button.
Part2
(This is just visualization purpose, and this tool doe not directly create the answer, so I believe it is not violation to Base A)
You can see 4(four) big circles and, other nodes locating near center.
Part2 question says "rx" sends LOW pulses. Let's see where rx is in this diagram.
"rx" is final termination nodes(no output module), and it receives from a conjunction module "ql", that receives from 4 different conjunction modules "fz", "mf", "ss", and "fh".
So we can interpret this problem as "When module "ql" sends LOW to "rx"", that is further equivalent question to "When 4 modules "fz", "mf", "ss", and "fh" send HIGH pulses at the same time?"
By modifying the WF of part1, get data of how many pressing buttons are needed to "ql" receives HIGH pulse from those 4 modules. In my dataset, no records appeared even after 1,000 press. So I run it again until 10,000 press, and finally got 8 records of HIGH pulses to "ql", 2record for each 4 senders in different timing. After that...please look carefully the result. You already have answer in your hand.
The idea of high pulses and low pulses immediately brought to mind computers and binary signals especially with Flip Flops and Conjunction modules that function like N-AND gates. @gawa has done a good job explaining the structure of the problem although, I would like to correct a couple things to hopefully not over complicate things for those who are attempting this problem. Every high/low pulse can be thought of as a singular entity that populates a queue, where each pulse will be evaluated one at a time in the order that they entered the queue. This means that the case @gawa included in his diagram for the conjunction module, where multiple signals enter the module at once will never occur, this is also true for the Flip Flop Modules. You do not need to think through or build a workflow that handles multiple synchronized inputs for any module because that will not happen. Just focus on one input at a time (it is actually the case that you will never even have two neighboring signals in the queue going to the same module):
| Queue Position | Instruction |
| 1 | Low to %A |
| 2 | High to %A |
| 3 | High to &B |
^The example above will never occur in solving this problem (if it does, something is wrong) because Position 1 and 2 both have signals going to %A, one immediately after the other. The following example is something you could see:
| Queue Position | Instruction |
| 1 | Low to %A |
| 2 | High to &B |
| 3 | High to %A |
Here is the structure/function of the Conjunction Module:
Hint for Part 2:
If you work through this chart, you'll notice something very interesting:
SUPER SPOILER
This ring forms a binary system, and since &X will only output a low signal when all inputs are high signals, this will occur in the example above when %A, %B, %G, %I, %J, %K, and %L have output a high signal (%A's input is what will actually trigger the Low signal output from &X).
Super interesting fact is that the frequency that this occurs at is the binary representation of the inputs to &X starting with %A in the position of 2^0 (Where input is 1 and output is 0 from &X). The above example is:
111101000011 = 3907
Do this for each ring, find the LCM of each of these and you will have your answer!
Workflow:
Iterative Macro (Part 1):
^ I enjoyed putting this macro together since it keeps track of everything: all the modules, the memory registers, and the signals being sent.
I have included my LCM macro.
Happy Solving!!!
I built python code first, and refer to reddit as well.
then convert to alteryx.
have to say that when change 1 or 2 lines/ variable. alteryx take much extra time to do it.
python less then 1 minute for both parts.
my alteryx workflow is take 7mins~ for part1 and 30mins~ for part2.
this time taken is hard to analysis or change...
1. split the iteration data to 2 parts, i.e. data and process.
(want to raise idea to handle variable, like simple low count and high count for this case)
2. then process 1-by-1 each, (that why my time speed is high)
note: ensure the sorting in union, new process should in the bottom.
Part2: Due to I already got answer in python. hence, I limit the flow to press button for 4000, to reduce time spent.
This is needed the most complex logic in this year's AoC. I made the iterative macro and dispose it many times .I am seriously wondering why there are NOT multiple repetitive inputs and outputs in Alteryx Iterative macro.
Viz by Network analysis tool
Yellow : Conjection
Red : button for stupid elf and broadcast module
The cause of my worries for part 2 :
I wanted to use the data below repeatedly.
Pulse :
Device status( flip flop status) :
Memory for conjection
So I unioned as follows.
On each repeat, I filtered them ans used them.
The macro to push the button. There are many macro output tools for debug.
This is outer macro for pusing 1000 times.
Workflow for part 1
Part 2: I needed the pulse pattern which is connected to rx module. After getting the pattern, we can use LCM. As a result, I pushed the button 5000 times and finally got the pattern.
Final workflow:
I spent a few days before the holidays trying to do this and picked it back up today. Logic in spoiler
P1:
1. I created two .yxdbs for inputs to update over time (one for flip flop modules and one for conjunctions)
2. I built out the iterative base macro to account for each possible step while forcing order one step at a time. I'm looping on the state (current module, signal, next module and order) while updating the .yxdbs and outputting the signal on each step to a macro output
3. The iterative macro has three categories to set up the logic flow: button, broadcaster, and non-button/broadcaster.
4. I took the base iterative macro and put it in another iterative macro to count the various steps
5. I put the nested macro in the main workflow and ran it.
P2:
1. I ran it 10k times and then found out the feeding modules once they hit high. Then I did LCM to solve it
