Advent of Code 2019 Day 3

This year I have decided to try and do the code challenges on the Advent of Code website in Scala and possibly Spark if needed (or an interesting solution arises).
These are simple little coding challenges given once per day like an Advent Calendar before Christmas.

I did complete this challenge on the day but am only now managing to write about it!

Day 3: Part 1

Today’s challenge is again slightly more difficult than previous days.
I will again only try to paste the relevant parts of the challenge here.

We are presented with input that describes 2 wires coming out of a port and snaking around a grid.

Specifically, two wires are connected to a central port and extend outward on a grid. You trace the path each wire takes as it leaves the central port, one wire per line of text (your puzzle input).

And our job is to find the closest point they cross:

To fix the circuit, you need to find the intersection point closest to the central port. Because the wires are on a grid, use the Manhattan distance for this measurement. While the wires do technically cross right at the central port where they both start, this point does not count, nor does a wire count as crossing with itself.

Manhattan distance is a common distance metric used when dealing with grids and is also known as “Taxicab Geometry” because of the fact you measure the same way as a taxi would navigate through a city like Manhattan (a grid based city).
That means you measure your distance in each axis and add them up.
For example if you are at position (0, 1) and want to get to (10, 9) you take the x components and find the difference, 0 to 10 = 10, and do the same with the y components, 1 to 9 = 8, and add those results together, 8 + 10 = 18, and that is your Manhattan distance.

The wire paths are describe using what are essentially commands, for example:

For example, if the first wire’s path is R8,U5,L5,D3, then starting from the central port (o), it goes right 8, up 5, left 5, and finally down 3:

...........
...........
...........
....+----+.
....|....|.
....|....|.
....|....|.
.........|.
.o-------+.
...........

Then, if the second wire’s path is U7,R6,D4,L4, it goes up 7, right 6, down 4, and left 4:

...........
.+-----+...
.|.....|...
.|..+--X-+.
.|..|..|.|.
.|.-X--+.|.
.|..|....|.
.|.......|.
.o-------+.
...........

These wires cross at two locations (marked X), but the lower-left one is closer to the central port: its distance is 3 + 3 = 6.

So to begin we will need to be able to read and represent the wires in the text file.

I begin by creating some data structures to do this:

import scala.collection._

object Direction extends Enumeration {
  type Direction = Value
  val UP = Value("U")
  val RIGHT = Value("R")
  val DOWN = Value("D")
  val LEFT = Value("L")
}

import Direction.Direction

case class Command(direction: Direction, distance: Int)

type Wire = Seq[Command]

Here I have defined the direction as an enumerated type and commands as being a combination of directions and distance, with a wire simply being an ordered sequence of commands.

Now for parsing and reading I will again be using the Scala Source class and split this into several function to make it easier to read and think about the code:

def parseCommand(command: String): Option[Command] = {
  if (command.length < 2) {
    return None
  }
  try {
    val direction = Direction.withName(command.substring(0, 1))
    val distance = command.substring(1).toInt
    Some(Command(direction, distance))
  } catch {
    case _: Exception =>
      println(s"Unhandled command: $command")
      None
  }
}

First up I think about how I want to handle parsing a single command from the file I am given. These will be in forms similar to U1, R12, D3 and L23, basically a letter denoting direction followed by an integer denoting distance.
In my Direction enumerated object I defined each direction to have a name corresponding to the letters used in the input. I take the first character of the command and attempt to match it, then take the remainder and attempt to convert it to an integer.
If something goes wrong with the parsing I return a None that I can handle later and log the bad command.

def parseLine(line: String): Option[Wire] = {
  if (line == null || line.isEmpty) {
    return None
  }
  val commands: Seq[Option[Command]] = line.split(',')
    .map(part => parseCommand(part))

  if (commands.forall(item => item.isDefined)) {
    Some(commands.flatten)
  } else {
    println(s"Unhandled line: $line")
    None
  }
}

import scala.io.Source

def readInput(filename: String): Seq[Wire] = {
  val source = Source.fromFile(filename)
  val wires = source.getLines()
    .map(line => line.trim)
    .filter(line => line.nonEmpty)
    .map(line => parseLine(line))

  wires.flatten.toSeq
}

The next function is for parsing a whole line.
It splits the line up on the comma separator and uses the first function to extract a command from it.
It then checks all the results of parsing and sees if there were any errors with the command parsing. If there were it returns a None and logs an error, otherwise it flattens out all the Some[Command] instances into Command instances.

Finally there is the readInput function that actually opens the file, reads it line by line and uses the parseLine method to generate whole wires.

With all that done we can now represent our wires in a way we can easily manipulate. It’s now time to consider how to determine where on a grid the wires actually live!
For this we need to represent positions somehow:

type Position = (Int, Int)

For now this simple tuple will suffice.

Now we need to convert the commands that make up a wire and convert them into all the positions they sit on a grid.
With our data structures this can be relatively simple:

def addCommand(start: Position, command: Command): Position = {
  val Command(direction: Direction, distance: Int) = command
  if (distance == 0) {
    return start
  }
  val (x, y) = start

  direction match {
    case Direction.UP => (x, y + distance)
    case Direction.DOWN => (x, y - distance)
    case Direction.RIGHT => (x + distance, y)
    case Direction.LEFT => (x - distance, y)
  }
}

The way this function works is that given a starting position and command it will determine where the command would cause the position to move to and return that as a result.

Of course if I used just this method I would only end up with positions where the wire changed direction (or got a new command), not all the points in between these positions.
For this reason I need a method of getting all the points between the starting position and the ending position of a command:

def pointsBetween(start: Position, end: Position): Seq[Position] = {
  val results = mutable.Buffer[Position]()
  val (x0, y0) = start
  val (x1, y1) = end
  val xStep = if (x0 > x1) -1 else 1
  val yStep = if (y0 > y1) -1 else 1
  for (x <- x0.to(x1, xStep)) {
    for (y <- y0.to(y1, yStep)) {
      val pos: Position = (x, y)
      // Don't add the start to the results
      if (x != x0 || y != y0) {
        results += pos
      }
    }
  }
  results
}

This method is relatively simple again, it’s basic interpolation between the two points.
I make use of a mutable Scala Buffer here to make things easier to read.

Now that I can get the points between 2 points I can bring this altogether to get all the points in a wire:

def getPositions(wire: Wire, origin: Position = (0, 0)): Seq[Position] = {
  val positions = mutable.Buffer[Position]()
  var lastPosition: Position = origin
  for (command <- wire) {
    val firstPosition: Position = lastPosition
    lastPosition = addCommand(firstPosition, command)
    // add all points between start (exclusive) and end (inclusive)
    positions ++= pointsBetween(firstPosition, lastPosition)
  }

  positions
}

This function starts at an origin and executes each command, using the start and end points of each, adding them all to a buffer and returning them all.

Now we can get all the points in a wire we need a way of finding out when wires intersect each other.
This is actually pretty simple:

def findIntersections(paths: Seq[Seq[Position]]): Seq[Position] = {
  val positionCounts: Map[Position, Int] =
    paths.flatMap(path => path.distinct)
      .groupBy(identity)
      .mapValues(_.size)

  positionCounts.filter(entry => entry._2 > 1).keys.toSeq
}

Since each path a wire takes now contains all the positions a wire can be in we just need to find where a position exists in both wires paths.
I have done this using some standard Scala code;

  1. First I get a distinct list of all positions in each path, that way I can avoid counting a wire crossing itself.
  2. Then I use flatmap to combine the paths into one list.
  3. Then I group them all by themselves (that’s the identity method I use) and convert the list into a Map[Position, Int] with the values being the count of occurrences of a given position.

This resulting map contains all the positions in both paths, if I then filter it down to only those that have a count greater than 1 I can find any intersections.

I can use the above methods to get me this far like so:

val wires = readInput("day3.input.txt")
val wireToPositions = wires.map(wire => (wire, getPositions(wire))).toMap
val intersections = findIntersections(wireToPositions.values.toSeq)

Now I need to actually use the manhattan distance to find out which of the intersections is the closest.
The code fot the manhattan distance in Scala is simple:

def manhattanDistance(origin: Position, other: Position): Int = {
  val x: Int = math.abs(origin._1 + other._1)
  val y: Int = math.abs(origin._2 + other._2)
  x + y
}

I can then find the closest intersection like so:

def findClosestIntersection(
    origin: Position,
    intersections: Seq[Position]
    ): (Position, Int) = {
  val withDistances =
    intersections.map(pos => (pos, manhattanDistance(origin, pos)))

  withDistances.minBy(f => f._2)
}

What this does is similar to finding the intersections initially; it takes each position and gets it’s distance from the origin, then simply returns the one with the smallest distance.

I can then use this command like so to answer part 1:

val closest = findClosestIntersection(
  (0, 0),
  intersections
)
println(s"Closest intersection ${closest._1} distance=${closest._2}")

Day 3: Part 2

Finally onto part 2.
We now need to use a different measurement on the intersections:

To do this, calculate the number of steps each wire takes to reach each intersection; choose the intersection where the sum of both wires’ steps is lowest. If a wire visits a position on the grid multiple times, use the steps value from the first time it visits that position when calculating the total value of a specific intersection.

The number of steps a wire takes is the total number of grid squares the wire has entered to get to that location, including the intersection being considered. Again consider the example from above:

...........
.+-----+...
.|.....|...
.|..+--X-+.
.|..|..|.|.
.|.-X--+.|.
.|..|....|.
.|.......|.
.o-------+.
...........

In the above example, the intersection closest to the central port is reached after 8+5+5+2 = 20 steps by the first wire and 7+6+4+3 = 20 steps by the second wire for a total of 20+20 = 40 steps.

However, the top-right intersection is better: the first wire takes only 8+5+2 = 15 and the second wire takes only 7+6+2 = 15, a total of 15+15 = 30 steps.

With our code this is actually pretty easy.
Since we have a list of all the positions in a wire we can use it with the intersections we uncovered before to find out their distances by simply counting the steps it takes to get to them:

val wireToIntersectionDistances: Map[Wire, Map[Position, Int]] =
  wireToPositions.map(entry => {
    val wire = entry._1
    val positions = entry._2
    val positionsToDistance = intersections.map(
      // remember to +1 as we excluded the origin from our original list
      intersection => (intersection, positions.indexOf(intersection) + 1)
    ).toMap
    (wire, positionsToDistance)
  })

Then with this map of wires to their intersections and their distances we can do some more calculations to find out the total steps taken from both wires for each intersection and then find the lowest:

val intersectionsToTotalDistances: Map[Position, Int] =
  wireToIntersectionDistances.foldLeft(Map[Position, Int]())((sum, map) => {
    val otherMap = map._2
    (sum.keySet ++ otherMap.keySet).map { key: Position =>
      (key, sum.getOrElse(key, 0) + otherMap.getOrElse(key, 0))
    }.toMap
  })

val minDistanceIntersection = intersectionsToTotalDistances.minBy(f => f._2)

println(s"Min distance intersection at ${minDistanceIntersection._1} distance=${minDistanceIntersection._2}")

Now admittedly that foldLeft block of code does look quite complex but what it does is fairly simple:

  1. The first set of arguments contains the initial, empty, value for what we want to eventually return, a map of positions to the total amount of steps taken.
  2. The next set of arguments contains the function that keeps the running summarized map and the current map being processed from the wireToIntersectionDistances map entries.
  3. The rest of the code then sums up the maps values within based on their keys, which are the positions.
  4. Finally we get the minimum entry like before.

And that’s part 2 of Day 3 done!

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