# Advent of Code 2021 in Kotlin - Day 19

## Introduction

In Day 19 we’re given a problem that is mostly related to the transformations in 3D space, including rotations and shifts of vectors. It’s been fun but also a hard work to implement it in Kotlin from basics in idiomatic way, so let’s see what the final solution is.

## Solution

The approach to given problem is somehow straightforward as we try pairing each pair of scanners and remember the transformations needed to go from one coordinates system to another. To do that, we remember a list of transformations for each scanner, that is required to transform its coordinate system to the system of the first scanner (collected in transform map). What’s more important we also remember if we’ve already check, if there is some relation between some pair of scanners (which is remembered in triedToPair). It’s important not to check multiple times for the same $\textnormal{fromId} \rightarrow \textnormal{toId}$ connection if there was no transformation found in the past. It cannot be deduced only from cahcedPair map because it has no value also if the pair was checked, and it was not found.

We search by starting from some start scanner that is the reference system and append next scanners, step by step, by finding next matching pairs between scanner from paired and toPair. Notice that we’ve implemented the new hashCode and equals to represent scanner by its id. This approach simplifies code a lot, so we don’t have to worry about indices when working with maps.

### Day19.kt

import V3.Companion.TRANSFORMS
import kotlin.math.absoluteValue

override fun solve() {
val data = reads<String>() ?: return
val scanners = data.groupSeparatedBy("") { it.toScanner() }

val matcher = ScannersMatcher(scanners, minCommon = 12)
val start = scanners.first()
val (beaconsFromStart, positioned) = matcher.findPairing(start)

beaconsFromStart.size.printIt()
sequence {
for ((s1, v1) in positioned) for ((s2, v2) in positioned)
if (s1 != s2) yield(v1 - v2)
}.maxOf { it.manhattanValue }.printIt()
}
}

private class ScannersMatcher(val scanners: List<Scanner>, val minCommon: Int) {

private data class FT(val from: Scanner, val to: Scanner)

private val cachedPair = mutableMapOf<FT, V3.T>()
private val triedToPair = DefaultMap<FT, Boolean>(false)

fun findPairing(start: Scanner): Pair<Set<V3>, Map<Scanner, V3>> {
val transform = DefaultMap<Scanner, List<V3.T>>(emptyList())
val beacons = start.beacons.toMutableSet()
val scan = mutableMapOf<Scanner, V3>().also { it[start] = V3.ZERO }

val paired = mutableSetOf(start)
val toPair = (scanners - paired).toMutableSet()

while (toPair.isNotEmpty()) {
[email protected] for (from in paired) for (to in toPair) {
val pairedShift = tryPair(FT(from, to)) ?: continue
transform[to] = transform[from] + pairedShift
beacons += to.beacons.map { transform[to](it) }
scan[to] = transform[to](V3.ZERO)
to.also { paired += it }.also { toPair -= it }
[email protected]
}
}
return Pair(beacons, scan)
}

private fun tryPair(ft: FT): V3.T? {
if (triedToPair[ft]) return cachedPair[ft]
triedToPair[ft] = true
for (t in TRANSFORMS) {
val to = t(ft.to)
val diffs = buildSet {
for (fb in ft.from.beacons) for (tb in to.beacons) add(tb - fb)
}
for (diff in diffs) {
val cnt = to.beacons.count { tb -> (tb - diff) in ft.from.beacons }
if (cnt >= minCommon) return t.copy(shift = -diff).also { cachedPair[ft] = it }
}
}
return null
}
}

private fun List<String>.toScanner() = Scanner(
first().removePrefix("--- scanner ").takeWhile { it.isDigit() }.toInt(),
drop(1).map { it.toBeacon() }.toSet()
)

private fun String.toBeacon() = split(",").map { it.toInt() }
.let { (x, y, z) -> V3(x, y, z) }

private data class V3(val x: Int, val y: Int, val z: Int) {
data class T(val id: Int, val shift: V3)

val manhattanValue = x.absoluteValue + y.absoluteValue + z.absoluteValue
private fun axeRotated(id: Int) = when (id) {
0 -> V3(x, y, z)
1 -> V3(-y, x, z)
2 -> V3(-x, -y, z)
3 -> V3(y, -x, z)
else -> error("Invalid axeRotate id")
}

private fun axeChanged(id: Int) = when (id) {
0 -> V3(x, y, z)
1 -> V3(x, z, -y)
2 -> V3(x, -z, y)
3 -> V3(x, -y, -z)
4 -> V3(-z, y, x)
5 -> V3(z, y, -x)
else -> error("Invalid axeChanged id")
}

infix fun transformedBy(by: T) = axeChanged(by.id / 4).axeRotated(by.id % 4) + by.shift

operator fun plus(v3: V3) = V3(x + v3.x, y + v3.y, z + v3.z)
operator fun minus(v3: V3) = V3(x - v3.x, y - v3.y, z - v3.z)
operator fun unaryMinus() = ZERO - this

companion object {
val ZERO = V3(0, 0, 0)
val TRANSFORMS = (0..23).map { T(it, ZERO) }
}
}

private class Scanner(val id: Int, val beacons: Set<V3>) {
override fun equals(other: Any?) = (other as? Scanner)?.id == id
override fun hashCode() = id
}

private operator fun List<V3.T>.invoke(v: V3) = foldRight(v) { t, v3 -> v3 transformedBy t }
private operator fun V3.T.invoke(s: Scanner) = Scanner(s.id, s.beacons.map { it transformedBy this }.toSet())

## Extra notes

We have used in the solution a few cool Kotlin features that are definitely worth mentioning. Let’s look at the:

1. Definitions of invoke functions that are declared as operators for transformations of vectors. In this way we got some cool syntax to actually applying transformation to vector or scanner.
2. We encoded the transformation on vector as a number from range 0..23 which includes the rotation and the change of the z axe of the coordinate system. It was pretty hard to express it in some good way, so we decided to do it explicitly with writing all possible transformations by hand. If it’s not readable, I encourage you to use your first 3 finger of your hand and see how these axes are transformed (that’s what I did in fact).
3. Take a look at the operator fun defined for V3 class representing the operations on vectors. They’re somehow obvious, but we have to remember that it’s convenient to define them as overloaded operators in Kotlin.
4. In the search of pair matches we used the named scope [email protected] - in this way we can exit the outer loop in Kotlin (and other modern programming languages) and it somehow simplifies the code.
5. Once again we’ve used the builders methods that’re new stable feature from Kotlin - building iterables with buildSet { } and sequence { } is really pleasant and straightforward.
###### Student of Computer Science

My interests include robotics (mainly with Arduino), mobile development for Android (love Kotlin) and Java SE/EE applications development.