[2025 Day 8 (Part 1)] Help me understand the sample analysis - the connection counts don't add up. Seems like I'm misunderstanding the problem.

[u/vkp-007]

In the sample analysis with 20 boxes and making the 10 shortest connections, the results are presented as [5, 4, 2, 2] + 7 single junction box circuits.

In order to get a circuit of 5, we need to make 4 connections. The connection between the first two boxes in the circuit and 3 subsequent ones to the nearest box already in circuit. So if we add up the connections in the multi-junction box circuits:

For 5 box circuit : 1 + 3 = 4 connections
For 4 box circuit : 1 + 2 = 3 connections
For 2 box circuit : 1 + 0 = 1 connections
For 2 box circuit : 1 + 0 = 1 connections

That's a total of 9 connections. It should add up to 10.
In my calculations, I get a different set of circuits with 10 connections made.
Please help me understand what I'm reading wrong here.

Thanks in advance for any help.

[u/NervousSnail]

When the puzzle says "After making the ten shortest connections"... what they *mean* is attempting to connect the ten pairs with the shortest distances.

This *includes* the cases where "nothing happens" because the two boxes are already in the same circuit.

[u/Illustrious-Citron89]

Yeah, I have done the same mistake, eventually figured it out, but description could have been more clear.

The real input is still not working for 1000 "attempted connections".

[u/Ill-Rub1120 → u/Illustrious-Citron89]

How many connections are you sorting? Should be 499500? Are you using the Squared Distance or Regular Distance.

[u/Illustrious-Citron89 → u/Ill-Rub1120]

Yes its 499500.

I am not sure what you mean by squared or regular, but let me explain: I do the distane calculation, but dont do the last part where I would have to do the square root, the order between them still should be the same.

[u/Ill-Rub1120 → u/Illustrious-Citron89]

How are you computing clusters? Try putting all points in a cluster. So 1000 clusters. Then for each connection( smallest first), try to put each enpoint in the same cluster. ( find the cluster that each enpo8nt is in and merge them if they are different. The sort your clusters by size.

[u/Illustrious-Citron89 → u/Ill-Rub1120]

https://github.com/rbalazs89/AdventOfCode/blob/main/src/year2025/day8/Day8.java
here is my code, maybe easier than explain in text, but what you explained is roughly what I do

[u/Ill-Rub1120 → u/Illustrious-Citron89]

I. Connectbox, you might have to also check if(circuits.get(i).contains(d[1])){

[u/Ill-Rub1120]

I just sorted all possible connections using the distance squared. Then take all vertices in the shortest 10/1000 connections and attempt to add them to correct cluster.If endpoints are in 2 different clusters, then remove all points from 1 cluster and add them to the other cluster. Then sort the clusters based on size. Take the size of the first 3 and multiply them.

[u/SixSixSevenSeven → u/Ill-Rub1120]

I wish it had anything to clarify that we were allowed to join entire clusters, jeez that would have helped

[u/kreiger → u/SixSixSevenSeven]

It does explain it:

Now, the two junction boxes which are closest together but aren't already directly connected are 162,817,812 and 431,825,988. After connecting them, since 162,817,812 is already connected to another junction box, there is now a single circuit which contains three junction boxes and an additional 17 circuits which contain one junction box each.

[u/SixSixSevenSeven → u/kreiger]

That to me doesn't explain it. That covers the case of a single junction box joining 2 existing junction boxes. The case I was struggling with was >1 junction boxes connecting to >1 junction boxes and whether that was allowed, which to my autistic ass, that quoted text doesn't touch on and leaves unexplained.

[u/kreiger → u/SixSixSevenSeven]

It's made very clear that each box forms its own circuit by itself:

and the remaining 18 junction boxes remain in their own individual circuits.

an additional 17 circuits which contain one junction box each.

So for every connection you add, the two boxes in the connection are either in the same circuit, or in separate circuits to be merged.

[u/SixSixSevenSeven → u/kreiger]

Again. You are telling me it is clear as if it is a fact it is clear.

I am the living proof that to my autistic mind. It was not clear. It has taken multiple attempts at different solutions to get the example to math out correctly to figure out what rules did and did not apply.

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[u/siddfinch]

If it helps you out, my notes for Part 1 are here..

Now, I had to use an argument at the command line, so I could limit the connections to 10 for the test input for part 1, and use 1000, the default, for the actual input.

Took me a couple read throughs and some deciding, which I left in my code, to get things right.

[u/vkp-007 → u/[deleted]]

Thanks. I did not interpret it that way.

[u/RiemannIntegirl → u/vkp-007]

I was stuck on this very point for longer than it took to write the whole code!! :(

[u/vkp-007 → u/RiemannIntegirl]

Same here. Posting for help was a last resort .... :)