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2023-24 - WIP
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@jurisk
jurisk committed Dec 25, 2023
1 parent 0b0a8b3 commit ef8438f
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200 changes: 131 additions & 69 deletions scala2/src/main/scala/jurisk/adventofcode/y2023/Advent24.scala
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Original file line number Diff line number Diff line change
Expand Up @@ -80,22 +80,25 @@ object Advent24 {
def dotProduct(a: Coordinates3D, b: Coordinates3D): Long =
a.x * b.x + a.y * b.y + a.z * b.z

def textually(data: List[PositionAndVelocity3D], num: Boolean): String = {
val vx = "A"
val vy = "B"
val vz = "C"

val px = "X"
val py = "Y"
val pz = "Z"

// val vx = "vx"
// val vy = "vy"
// val vz = "vz"
def dotCrossProductTextually(
data: List[PositionAndVelocity3D],
num: Boolean,
): String = {
// val vx = "A"
// val vy = "B"
// val vz = "C"
//
// val px = "px"
// val py = "py"
// val pz = "pz"
// val px = "X"
// val py = "Y"
// val pz = "Z"

val vx = "vx"
val vy = "vy"
val vz = "vz"

val px = "px"
val py = "py"
val pz = "pz"

def cp(
a: (String, String, String),
Expand Down Expand Up @@ -143,8 +146,8 @@ object Advent24 {
if (num) {
s"${dp(cp(extractStrings(rock.velocity), (vx, vy, vz)), sb(extractStrings(rock.position), (px, py, pz)))} = 0"
} else {
// s"${dp(cp(("rvx", "rvy", "rvz"), (vx, vy, vz)), sb(("rpx", "rpy", "rpz"), (px, py, pz)))} = 0"
s"${dp(cp(("d", "f", "g"), (vx, vy, vz)), sb(("h", "j", "k"), (px, py, pz)))} = 0"
s"${dp(cp(("rvx", "rvy", "rvz"), (vx, vy, vz)), sb(("rpx", "rpy", "rpz"), (px, py, pz)))} = 0"
// s"${dp(cp(("d", "f", "g"), (vx, vy, vz)), sb(("h", "j", "k"), (px, py, pz)))} = 0"
}
}
.mkString("\n")
Expand All @@ -163,7 +166,7 @@ object Advent24 {
List(ax / bx, ay / by, az / bz).distinct.size == 1
}

def normaliseToPosition(
private def normaliseToPosition(
data: List[PositionAndVelocity3D],
diff: Coordinates3D,
): Unit = {
Expand Down Expand Up @@ -194,27 +197,24 @@ object Advent24 {
}

def solvePart2(data: List[PositionAndVelocity3D]): PositionAndVelocity3D = {
printEquations(data)

// normaliseToPosition(data, Coordinates3D(24, 13, 10))

// anyoneIntersecting(data)

// println(textually(data, num = true))
// println()
// println(textually(data, num = false))
// println()

// For all rocks "r"
// (rvy * vz - rvz * vy) * (rpx - px) + (rvz * vx - rvx * vz) * (rpy - py) + (rvx * vy - rvy * vx) * (rpz - pz) = 0

// (rvy * C - rvz * B) * (rpx - X) + (rvz * A - rvx * C) * (rpy - Y) + (rvx * B - rvy * A) * (rpz - Z) = 0

// val limit = 1_000_000_000
val limit = 25
Axis.All foreach { axes =>
println(
s"Only by $axes: ${solvePart2CrudeOptimize(data, Set(axes), limit)}"
)
}
// Axis.All foreach { axes =>
// println(
// s"Only by $axes: ${solvePart2CrudeOptimize(data, Set(axes), limit)}"
// )
// }
solvePart2CrudeOptimize(data, Axis.All, limit)
}
// solvePart2DotCrossProducts(data.take(3), 100_000_000_000L)
Expand All @@ -239,9 +239,9 @@ object Advent24 {
data: List[PositionAndVelocity3D],
limit: Long,
): PositionAndVelocity3D = {
println(textually(data, num = true))
println(dotCrossProductTextually(data, num = true))
println()
println(textually(data, num = false))
println(dotCrossProductTextually(data, num = false))
println()

// Find such px, py, pz, vx, vy, vz that for all rocks
Expand Down Expand Up @@ -537,15 +537,73 @@ object Advent24 {
println(s"px + t$idx * vx = ${r.p.x} ${sgn(r.v.x)} * t$idx")
println(s"py + t$idx * vy = ${r.p.y} ${sgn(r.v.y)} * t$idx")
println(s"pz + t$idx * vz = ${r.p.z} ${sgn(r.v.z)} * t$idx")
println()
}

def printNice(r: PositionAndVelocity3D, idx: String, axis: Axis): String =
axis match {
case Axis.X => s"px ${sgn(-r.p.x)} = t$idx * (${r.v.x} - vx)"
case Axis.Y => s"py ${sgn(-r.p.y)} = t$idx * (${r.v.y} - vy)"
case Axis.Z => s"pz ${sgn(-r.p.z)} = t$idx * (${r.v.z} - vz)"
}

println(s"Same r.v.x: ")
data.groupBy(_.v.x).values.filter(_.size >= 2).foreach { list =>
println(s"r.v.x equal:")
list foreach { r =>
println(printNice(r, "?", Axis.X))
}
println()
}

println(s"Same r.v.y: ")
data.groupBy(_.v.y).values.filter(_.size >= 2).foreach { list =>
println(s"r.v.y equal:")
list foreach { r =>
println(printNice(r, "?", Axis.Y))
}
println()
}

println(s"Same r.v.z: ")
data.groupBy(_.v.z).values.filter(_.size >= 2).foreach { list =>
println(s"r.v.z equal:")
list foreach { r =>
println(printNice(r, "?", Axis.Z))
}
println()
}

data.zipWithIndex foreach { case (r, id) =>
val idx = id + 1
println(s"px ${sgn(-r.p.x)} = t$idx * (${r.v.x} - vx)")
println(s"py ${sgn(-r.p.y)} = t$idx * (${r.v.y} - vy)")
println(s"pz ${sgn(-r.p.z)} = t$idx * (${r.v.z} - vz)")
println()
}

println()

println(s"${3 + 3 + data.length} variables")
println(s"${data.length * 3} equations")

println()
println(s"x + t_n * a = rpx + rvx * t_n")
println(s"y + t_n * b = rpy + rvy * t_n")
println(s"z + t_n * c = rpz + rvz * t_n")
println(s"px + t_n * vx = rpx + rvx * t_n")
println(s"py + t_n * vy = rpy + rvy * t_n")
println(s"pz + t_n * vz = rpz + rvz * t_n")

println()

// println(s"Line equations:")
// data.foreach { r =>
// println(s"(x ${sgn(-r.p.x)}) / ${r.v.x} == (y ${sgn(-r.p.y)}) / ${r.v.y} == (z ${sgn(-r.p.z)}) / ${r.v.z}")
// }
// println()

println(dotCrossProductTextually(data, num = true))
println()
println(dotCrossProductTextually(data, num = false))
println()

// (t_n * a) - (rvx * t_n) = rpx - x
// t_n * (a - rvx) = rpx - x
Expand All @@ -554,38 +612,48 @@ object Advent24 {

// x = 24, y = 13, z = 10, a = -3, b = 1, c = 2

val x = 24
val y = 13
val z = 10
val a = -3
val b = 1
val c = 2
val px = 24
val py = 13
val pz = 10
val vx = -3
val vy = 1
val vz = 2

List(
(1 * vz - -2 * vy) * (19 - px) + (-2 * vx - -2 * vz) * (13 - py) + (-2 * vy - 1 * vx) * (30 - pz) == 0,
(-1 * vz - -2 * vy) * (18 - px) + (-2 * vx - -1 * vz) * (19 - py) + (-1 * vy - -1 * vx) * (22 - pz) == 0,
(-2 * vz - -4 * vy) * (20 - px) + (-4 * vx - -2 * vz) * (25 - py) + (-2 * vy - -2 * vx) * (34 - pz) == 0,
(-2 * vz - -1 * vy) * (12 - px) + (-1 * vx - -1 * vz) * (31 - py) + (-1 * vy - -2 * vx) * (28 - pz) == 0,
(-5 * vz - -3 * vy) * (20 - px) + (-3 * vx - 1 * vz) * (19 - py) + (1 * vy - -5 * vx) * (15 - pz) == 0,
) foreach { b =>
assert(b)
}

// (19 - x) / (a + 2) = (13 - y) / (b - 1) = (30 - z) / (c + 2)
// (18 - x) / (a + 1) = (19 - y) / (b + 1) = (22 - z) / (c + 2)
// (20 - x) / (a + 2) = (25 - y) / (b + 2) = (34 - z) / (c + 4)
// (12 - x) / (a + 1) = (31 - y) / (b + 2) = (28 - z) / (c + 1)
// (20 - x) / (a - 1) = (19 - y) / (b + 5) = (15 - z) / (c + 3)

data foreach { r =>
if ((a != r.v.x) && (b != r.v.y) && (c != r.v.z)) {
val e1 = (r.p.x - x).toDouble / (a - r.v.x)
val e2 = (r.p.y - y).toDouble / (b - r.v.y)
val e3 = (r.p.z - z).toDouble / (c - r.v.z)

println(s"$e1, $e2, $e3")
}

println(s"(${r.p.x} - x) / (a ${sgn(-r.v.x)}) = (${r.p.y} - y) / (b ${sgn(
-r.v.y
)}) = (${r.p.z} - z) / (c ${sgn(-r.v.z)})")
println()
}

println(s"${3 + 3 + data.length} variables")
println(s"${data.length * 3} equations")

println()
// data foreach { r =>
// if ((a != r.v.x) && (b != r.v.y) && (c != r.v.z)) {
// val e1 = (r.p.x - x).toDouble / (a - r.v.x)
// val e2 = (r.p.y - y).toDouble / (b - r.v.y)
// val e3 = (r.p.z - z).toDouble / (c - r.v.z)
//
// println(s"$e1, $e2, $e3")
// }
//
// println(s"(${r.p.x} - x) / (a ${sgn(-r.v.x)}) = (${r.p.y} - y) / (b ${sgn(
// -r.v.y
// )}) = (${r.p.z} - z) / (c ${sgn(-r.v.z)})")
// println()
// }
//
// println(s"${3 + 3 + data.length} variables")
// println(s"${data.length * 3} equations")
//
// println()
}

def solvePart2CrudeOptimize(
Expand Down Expand Up @@ -630,12 +698,12 @@ object Advent24 {
)

val t = data.indices map { idx =>
o.labeledReal(s"t_$idx")
o.labeledInt(s"t_$idx")
}

t foreach { t_n =>
o.addConstraints(
t_n >= o.realConstant(0)
t_n >= o.constant(0)
)
}

Expand All @@ -651,25 +719,19 @@ object Advent24 {

if (axes.contains(Axis.X)) {
o.addConstraints(
o.intToReal(px) + t_n * o.intToReal(vx) === o.intToReal(
px_n
) + t_n * o.intToReal(vx_n)
px + t_n * vx === px_n + t_n * vx_n
)
}

if (axes.contains(Axis.Y)) {
o.addConstraints(
o.intToReal(py) + t_n * o.intToReal(vy) === o.intToReal(
py_n
) + t_n * o.intToReal(vy_n)
py + t_n * vy === py_n + t_n * vy_n
)
}

if (axes.contains(Axis.Z)) {
o.addConstraints(
o.intToReal(pz) + t_n * o.intToReal(vz) === o.intToReal(
pz_n
) + t_n * o.intToReal(vz_n)
pz + t_n * vz === pz_n + t_n * vz_n
)
}
}
Expand Down
11 changes: 10 additions & 1 deletion scala2/src/test/scala/jurisk/adventofcode/y2023/Advent24Spec.scala
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Original file line number Diff line number Diff line change
Expand Up @@ -7,7 +7,9 @@ import org.scalatest.matchers.should.Matchers._

class Advent24Spec extends AnyFreeSpec {
// https://www.math3d.org/G5JHCaIly
private def testData = parseFile(fileName("-test"))
private def testData = parseFile(fileName("-test"))
private def testNormalisedData = parseFile(fileName("-test-normalised"))

private def realData = parseFile(fileName(""))

val expectedTestAnswer: PositionAndVelocity3D = PositionAndVelocity3D(
Expand Down Expand Up @@ -104,6 +106,13 @@ class Advent24Spec extends AnyFreeSpec {
}

"part 2" - {
"test normalised" in {
solvePart2(
testNormalisedData
).velocity shouldEqual expectedTestAnswer.velocity
part2(testNormalisedData) shouldEqual 0
}

"test" in {
solvePart2(testData).position shouldEqual expectedTestAnswer.position
part2(testData) shouldEqual 47
Expand Down

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