feat: Solving day 16

docs/day16.md

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+
+## Day 16: Reindeer Maze
+
+It's time again for the Reindeer Olympics! This year, the big event is the Reindeer Maze, where the Reindeer compete for the lowest score.
+
+You and The Historians arrive to search for the Chief right as the event is about to start. It wouldn't hurt to watch a little, right?
+
+The Reindeer start on the Start Tile (marked `S`) facing East and need to reach the End Tile (marked `E`). They can move forward one tile at a time (increasing their score by `1` point), but never into a wall (`#`). They can also rotate clockwise or counterclockwise 90 degrees at a time (increasing their score by `1000` points).
+
+To figure out the best place to sit, you start by grabbing a map (your puzzle input) from a nearby kiosk. For example:
+
+```txt
+###############
+#.......#....E#
+#.#.###.#.###.#
+#.....#.#...#.#
+#.###.#####.#.#
+#.#.#.......#.#
+#.#.#####.###.#
+#...........#.#
+###.#.#####.#.#
+#...#.....#.#.#
+#.#.#.###.#.#.#
+#.....#...#.#.#
+#.###.#.#.#.#.#
+#S..#.....#...#
+###############
+```
+
+There are many paths through this maze, but taking any of the best paths would incur a score of only `7036`. This can be achieved by taking a total of `36` steps forward and turning 90 degrees a total of `7` times:
+
+```txt
+###############
+#.......#....E#
+#.#.###.#.###^#
+#.....#.#...#^#
+#.###.#####.#^#
+#.#.#.......#^#
+#.#.#####.###^#
+#..>>>>>>>>v#^#
+###^#.#####v#^#
+#>>^#.....#v#^#
+#^#.#.###.#v#^#
+#^....#...#v#^#
+#^###.#.#.#v#^#
+#S..#.....#>>^#
+###############
+```
+
+Here's a second example:
+
+```txt
+#################
+#...#...#...#..E#
+#.#.#.#.#.#.#.#.#
+#.#.#.#...#...#.#
+#.#.#.#.###.#.#.#
+#...#.#.#.....#.#
+#.#.#.#.#.#####.#
+#.#...#.#.#.....#
+#.#.#####.#.###.#
+#.#.#.......#...#
+#.#.###.#####.###
+#.#.#...#.....#.#
+#.#.#.#####.###.#
+#.#.#.........#.#
+#.#.#.#########.#
+#S#.............#
+#################
+```
+
+In this maze, the best paths cost `11048` points; following one such path would look like this:
+
+```txt
+#################
+#...#...#...#..E#
+#.#.#.#.#.#.#.#^#
+#.#.#.#...#...#^#
+#.#.#.#.###.#.#^#
+#>>v#.#.#.....#^#
+#^#v#.#.#.#####^#
+#^#v..#.#.#>>>>^#
+#^#v#####.#^###.#
+#^#v#..>>>>^#...#
+#^#v###^#####.###
+#^#v#>>^#.....#.#
+#^#v#^#####.###.#
+#^#v#^........#.#
+#^#v#^#########.#
+#S#>>^..........#
+#################
+```
+
+Note that the path shown above includes one 90 degree turn as the very first move, rotating the Reindeer from facing East to facing North.
+
+Analyze your map carefully. What is the lowest score a Reindeer could possibly get?

src/day16/day16.go

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+package day16
+
+import (
+	"slices"
+	"strings"
+)
+
+const EMPTY = '.'
+const END = 'E'
+const START = 'S'
+
+type direction uint8
+
+const (
+	EAST direction = iota
+	SOUTH
+	WEST
+	NORTH
+)
+
+type point struct {
+	x, y int
+}
+
+func (p point) valid(w, h int) bool {
+	return p.x >= 0 && p.y >= 0 && p.x < w && p.y < h
+}
+
+type maze struct {
+	emptySpaces map[point]bool
+	start       point
+	end         point
+	width       int
+	height      int
+}
+
+type thread struct {
+	p     point
+	dir   direction
+	moves uint
+	turns uint
+}
+
+func (t thread) cost() uint {
+	return t.moves + 1000*t.turns
+}
+
+func Solve(input string) uint {
+	m := parseInput(input)
+	return solve(m)
+}
+
+func parseInput(input string) maze {
+	var result maze
+	result.emptySpaces = make(map[point]bool)
+
+	result.height = len(input)
+	for j, line := range strings.Split(input, "\n") {
+		result.width = len(line)
+		for i, r := range line {
+			if r == EMPTY || r == START || r == END {
+				result.emptySpaces[point{x: i, y: j}] = true
+				if r == START {
+					result.start = point{x: i, y: j}
+				} else if r == END {
+					result.end = point{x: i, y: j}
+				}
+			}
+		}
+	}
+	return result
+}
+
+func solve(m maze) uint {
+	seenSpaces := make(map[point]uint)
+	seenSpaces[m.start] = 1
+	threads := []thread{{p: m.start, dir: EAST}}
+	var solution uint = 0
+
+	for {
+		nextThreads := make([]thread, 0)
+		for _, t := range threads {
+			if t.p == m.end {
+				if solution == 0 || t.cost() < solution {
+					solution = t.cost()
+				}
+			} else {
+				nextThreads = append(nextThreads, calcNextMoves(m, t, seenSpaces)...)
+			}
+		}
+
+		if len(nextThreads) == 0 {
+			if solution == 0 {
+				panic("No solution with no more spaces to check")
+			}
+			return solution
+		}
+		for i, t := range nextThreads {
+			if solution > 0 && t.cost() >= solution {
+				nextThreads = slices.Delete(nextThreads, i, i)
+			}
+			if seenSpaces[t.p] == 0 || t.cost() < seenSpaces[t.p] {
+				seenSpaces[t.p] = t.cost()
+			}
+		}
+		threads = nextThreads
+	}
+}
+
+func calcNextMoves(m maze, curr thread, seenSpaces map[point]uint) []thread {
+	nextMoves := make([]thread, 0)
+	possibilities := []thread{{p: point{x: curr.p.x + 1, y: curr.p.y}, dir: EAST, moves: curr.moves, turns: curr.turns},
+		{p: point{x: curr.p.x, y: curr.p.y + 1}, dir: SOUTH, moves: curr.moves, turns: curr.turns},
+		{p: point{x: curr.p.x - 1, y: curr.p.y}, dir: WEST, moves: curr.moves, turns: curr.turns},
+		{p: point{x: curr.p.x, y: curr.p.y - 1}, dir: NORTH, moves: curr.moves, turns: curr.turns}}
+	for i, t := range possibilities {
+		if t.p.valid(m.width, m.height) && m.emptySpaces[t.p] {
+			t.moves++
+			if i%2 != int(curr.dir)%2 {
+				t.turns++
+			} else if int(curr.dir) != i {
+				t.turns += 2
+			}
+			if seenSpaces[t.p] == 0 || t.cost() < seenSpaces[t.p] {
+				nextMoves = append(nextMoves, t)
+			}
+		}
+	}
+	return nextMoves
+}