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2020/day20/main.swift

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+import Foundation
+
+let input = loadData(day: 20)
+let scanner = Scanner(string: input)
+
+
+struct Tile {
+    var id: Int
+    var imageData: [Bool]
+    var size: Int
+
+    subscript (_ x: Int, _ y: Int) -> Bool {
+        get { imageData[x + y * size] }
+        set { imageData[x + y * size] = newValue }
+    }
+}
+
+
+extension Scanner {
+    func tile() -> Tile? {
+        guard string("Tile"),
+              let id = scanInt(),
+              string(":"),
+              let (image, size) = imageData()
+        else { return nil }
+        return Tile(id: id, imageData: image, size: size)
+    }
+
+    func imageData() -> ([Bool], Int)? {
+        var result: [Bool] = []
+        let set = CharacterSet(charactersIn: "#.")
+        var width: Int? = nil
+        while let line = scanCharacters(from: set) {
+            assert(width == nil || line.count == width)
+            width = line.count
+            result.append(contentsOf: line.map { $0 == "#" })
+        }
+
+        guard let w = width else { return nil }
+
+        return (result, w)
+    }
+
+    func tileSet() -> [Int: Tile]? {
+        var result: [Int: Tile] = [:]
+        while !isAtEnd {
+            guard let tile = self.tile() else { return nil }
+            result[tile.id] = tile
+        }
+        return result
+    }
+}
+
+let tilesById = scanner.tileSet()!
+
+struct TileReference: Hashable {
+    enum Rotation: CaseIterable {
+        case rotate0, rotate90, rotate180, rotate270
+    }
+
+    var id: Int
+    var flipped: Bool
+    var rotation: Rotation
+
+    subscript (x: Int, y: Int) -> Bool {
+        get {
+            let tile = tilesById[id]!
+
+            var coord = flipped ? (x: tile.size - 1 - x, y: y) : (x: x, y: y)
+            coord = rotation.get(x: coord.x, y: coord.y, size: tile.size)
+
+            return tile[coord.x, coord.y]
+        }
+    }
+
+    var end: Int { tilesById[id]!.size - 1 }
+}
+
+extension TileReference.Rotation {
+    func get(x: Int, y: Int, size: Int) -> (x: Int, y: Int) {
+        let e = size - 1
+        switch self {
+        case .rotate0: return (x, y)
+        case .rotate90: return (y, e - x)
+        case .rotate180: return (x, e - y)
+        case .rotate270: return (e - y, x)
+        }
+    }
+}
+
+struct Board {
+    struct Cell {
+        var possible: Array<TileReference>
+    }
+
+    var size: Int
+    var cells: [Cell]
+
+    init<T>(tiles: T) where T: Sequence, T.Element == Int {
+        let orientations = [true, false].flatMap { flipped in TileReference.Rotation.allCases.map { (flipped, $0) } }
+        let allOptions = tiles.flatMap { id in orientations.map { TileReference(id: id, flipped: $0.0, rotation: $0.1 ) } }
+        size = Int(sqrt(Double(tilesById.count)))
+        cells = Array(repeating: Cell(possible: allOptions), count: size*size)
+        assert(size * size == tilesById.count)
+    }
+
+    subscript(x: Int, y: Int) -> Cell {
+        get { cells[x + y * size] }
+        set { cells[x + y * size] = newValue }
+    }
+
+    func coordinate(_ cell: Int) -> (x: Int, y: Int) {
+        let (y, x) = cell.quotientAndRemainder(dividingBy: size)
+        return (x, y)
+    }
+
+    func solve(startingAt: Int = 0) -> Board? {
+        if startingAt >= cells.count { return self }
+
+        let coord = coordinate(startingAt)
+        let left = coord.x > 0 ? self[coord.x - 1, coord.y].chosen! : nil
+        let above = coord.y > 0 ? self[coord.x, coord.y - 1].chosen! : nil
+
+        func matchLeft(_ ref: TileReference) -> Bool {
+            guard let left = left else { return true }
+            return (0...ref.end).allSatisfy { left[left.end, $0] == ref[0, $0] }
+        }
+
+        func matchAbove(_ ref: TileReference) -> Bool {
+            guard let above = above else { return true }
+            return (0...ref.end).allSatisfy { above[$0, above.end] == ref[$0, 0] }
+        }
+
+        for option in cells[startingAt].possible.lazy.filter({ matchLeft($0) && matchAbove($0) }) {
+            var result = self
+            result.cells[startingAt].possible = [option]
+
+            let next = startingAt + 1
+
+            for cell in next..<cells.count {
+                result.cells[cell].possible = result.cells[cell].possible.filter {
+                    return $0.id != option.id
+                }
+
+                if result.cells[cell].possible.isEmpty {
+                    return nil
+                }
+            }
+
+            if let solution = result.solve(startingAt: next) {
+                return solution
+            }
+        }
+
+        return nil
+    }
+}
+
+
+extension Board.Cell {
+    var chosen: TileReference? {
+        guard let result = possible.first, possible.count == 1 else {
+            return nil
+        }
+
+        return result
+    }
+}
+let start = Date()
+guard let solution = Board(tiles: tilesById.keys).solve() else { fatalError() }
+let end = Date()
+
+print("Took", end.timeIntervalSince(start))
+
+let e = solution.size - 1
+
+print(solution[0,0].chosen!.id)
+
+print(
+    solution[0,0].chosen!.id *
+    solution[e,0].chosen!.id *
+    solution[0,e].chosen!.id *
+    solution[e,e].chosen!.id
+)
+
+extension Board {
+    struct CompleteImage {
+        let board: Board
+        var flipped = false
+        var rotation = TileReference.Rotation.rotate0
+    }
+
+    var completeImage: CompleteImage {
+        CompleteImage(board: self)
+    }
+
+    func completeImage(flipped: Bool, rotation: TileReference.Rotation) -> CompleteImage {
+        CompleteImage(board: self, flipped: flipped, rotation: rotation)
+    }
+}
+
+
+extension Board.CompleteImage {
+    var size: Int {
+        board.size * (board.cells[0].chosen!.end - 1)
+    }
+
+    subscript(x: Int, y: Int) -> Bool {
+        get {
+            var coord = flipped ? (x: size - 1 - x, y: y) : (x: x, y: y)
+            coord = rotation.get(x: coord.x, y: coord.y, size: size)
+
+            let tileSize = board.cells[0].chosen!.end - 1
+            let (tileX, offsetX) = coord.x.quotientAndRemainder(dividingBy: tileSize)
+            let (tileY, offsetY) = coord.y.quotientAndRemainder(dividingBy: tileSize)
+            let tile = board[tileX, tileY].chosen!
+            return tile[offsetX + 1, offsetY + 1]
+        }
+    }
+}
+
+for y in 0..<solution.completeImage.size {
+    for x in 0..<solution.completeImage.size {
+        print(solution.completeImage[x, y] ? "#" : ".", terminator: "")
+    }
+    print()
+}
+
+
+extension Board.CompleteImage {
+    func seaMonster(x: Int, y: Int) -> Bool {
+        return self[x + 18, y] &&
+            self[x + 0, y + 1] && self[x + 5, y + 1] && self[x + 6, y + 1] && self[x + 11, y + 1] && self[x + 12, y + 1] && self[x + 17, y + 1] && self[x + 18, y + 1] && self[x + 19, y + 1]  &&
+            self[x + 1, y + 2] && self[x + 4, y + 2] && self[x + 7, y + 2] && self[x + 10, y + 2] && self[x + 13, y + 2] && self[x + 16, y + 2]
+    }
+
+    func countMonsters() -> Int {
+        var count = 0
+        for y in 0..<size - 2 {
+            for x in 0..<size - 19 {
+                if seaMonster(x: x, y: y) {
+                    count += 1
+                }
+            }
+        }
+        return count
+    }
+
+    func countOnes() -> Int {
+        var count = 0
+        for y in 0..<size {
+            for x in 0..<size {
+                count += self[x, y] ? 1 : 0
+            }
+        }
+        return count
+    }
+}
+
+let ones = solution.completeImage.countOnes()
+outer: for flipped in [true, false] {
+    for rotation in TileReference.Rotation.allCases {
+        let monsters = solution.completeImage(flipped: flipped, rotation: rotation).countMonsters()
+        if monsters > 0 {
+            let monsterTiles = monsters * 15
+            let result = ones - monsterTiles
+            print(result)
+            break outer
+        }
+    }
+}
+