2022 Day 12

2022/day12.swift

@@ -0,0 +1,273 @@
+import Foundation
+
+struct Matrix<Element> {
+    var width: Int
+    var height: Int
+    var data: [Element]
+    
+    init(width: Int, height: Int, data: [Element]) {
+        precondition(data.count == width * height)
+        self.width = width
+        self.height = height
+        self.data = data
+    }
+    
+    subscript(x: Int, y: Int) -> Element {
+        get {
+            precondition(0 <= x && x < width && 0 <= y && y < height)
+            return data[x + width * y]
+        }
+        set {
+            precondition(0 <= x && x < width && 0 <= y && y < height)
+            data[x + width * y] = newValue
+        }
+    }
+}
+
+extension Matrix {
+    func map<T>(_ transform: (Element) throws -> T) rethrows -> Matrix<T> {
+        Matrix<T>(width: width, height: height, data: try data.map(transform))
+    }
+    
+    func mapIndexed<T>(_ transform: (Int, Int, Element) throws -> T) rethrows -> Matrix<T> {
+        var newData: [T] = []
+        newData.reserveCapacity(data.count)
+        var index = 0
+        for y in 0..<height {
+            for x in 0..<width {
+                newData.append(try transform(x, y, data[index]))
+                index += 1
+            }
+        }
+        
+        return Matrix<T>(width: width, height: height, data: newData)
+    }
+
+    func find(where: (Element) throws -> Bool) rethrows -> [(Int, Int)] {
+        var result: [(Int, Int)] = []
+        var index = 0
+        for y in 0..<height {
+            for x in 0..<width {
+                if (try `where`(data[index])) {
+                    result.append((x, y))
+                }
+                index += 1
+            }
+        }
+
+        return result
+    }
+}
+
+enum MatrixError: Error {
+    case invalidShape
+}
+
+extension Matrix<Character> {
+    init(contentsOf url: URL) async throws {
+        var data: [Character] = []
+        var width: Int? = nil
+        var height = 0
+        
+        for try await line in url.lines {
+            guard width == nil || width == line.count else {
+                throw MatrixError.invalidShape
+            }
+            width = line.count
+            height += 1
+            data.append(contentsOf: Array(line))
+        }
+        
+        self.init(width: width ?? 0, height: height, data: data)
+    }
+}
+
+var startX = 0
+var startY = 0
+var goalX = 0
+var goalY = 0
+
+let input = try await Matrix(contentsOf: URL(fileURLWithPath: "day12.input")).mapIndexed { x, y, element in 
+    switch element {
+    case "S":
+        startX = x
+        startY = y
+        return 0
+        
+    case "E":
+        goalX = x
+        goalY = y
+        return Int(UInt8(ascii: "z") - UInt8(ascii: "a"))
+    
+    case "a"..."z":
+        return Int(UInt8(ascii: element.unicodeScalars.first!) - UInt8(ascii: "a"))
+        
+    default:
+        preconditionFailure("Invalid input")
+    }
+}
+
+protocol Map {
+    associatedtype Node: Hashable
+    associatedtype Distance: Comparable & AdditiveArithmetic = Int
+    
+    func neighbors(for node: Node) -> [Node]
+    func allNodes() -> [Node]
+
+    func distance(from: Node, to: Node) -> Distance
+}
+
+extension Map where Distance == Int {
+    func distance(from: Node, to: Node) -> Int { 
+        1 
+    }
+}
+
+struct PathFinder<M: Map> {
+    typealias Node = M.Node
+    typealias Distance = M.Distance
+    
+    let map: M
+    var distance: [Node: Distance] = [:]
+    var predecessors: [Node: Node] = [:]
+    var all: Set<Node>
+    
+    init(_ map: M) {
+        self.map = map
+        all = Set(map.allNodes())
+    }
+    
+    mutating func findPath(from: Node, to: Node) -> [Node]? {
+        distance[from] = .zero
+        
+        while true {
+            guard let next = popClosest() else { break } 
+            
+            for node in map.neighbors(for: next) where all.contains(node) {
+                updateDistance(from: next, to: node)
+            }
+        }
+        
+        let result = buildPath(to: to)
+        return result.first == from ? result : nil
+    }
+    
+    func buildPath(to node: Node) -> [Node] {
+        var path: [Node] = [node]
+        var current = node
+        while let next = predecessors[current] {
+            path.insert(next, at: 0)
+            current = next
+        }
+        return path
+    }
+    
+    mutating func popClosest() -> Node? {
+        // TODO: Priority queue based implementation.
+        let first = distance.filter { all.contains($0.key) }
+            .sorted { $0.value < $1.value }
+            .first?.key
+            
+        guard let node = first else {
+            return nil
+        }
+        
+        all.remove(node)
+        return node
+    }
+    
+    mutating func updateDistance(from: Node, to: Node) {
+        let alternative = distance[from]! + map.distance(from: from, to: to)
+        let previous = distance[to]
+        if previous == nil || alternative < previous! {
+            distance[to] = alternative
+            predecessors[to] = from
+        }
+    }
+}
+
+extension Map {
+    
+    func findPath(from: Node, to: Node) -> [Node]? {
+        var pathFinder = PathFinder(self)
+        return pathFinder.findPath(from: from, to: to)
+    }
+}
+
+
+struct FieldMap: Map {
+    struct Node: Hashable {
+        var x: Int
+        var y: Int
+    }
+    
+    var matrix: Matrix<Int>
+    
+    subscript(node: Node) -> Int {
+        matrix[node.x, node.y]
+    }
+    
+    func left(_ node: Node) -> Node? {
+        node.x > 0 ? Node(x: node.x - 1, y: node.y) : nil
+    }
+    
+    func right(_ node: Node) -> Node? {
+        node.x < matrix.width - 1 ? Node(x: node.x + 1, y: node.y) : nil
+    }
+    
+    func up(_ node: Node) -> Node? {
+        node.y > 0 ? Node(x: node.x, y: node.y - 1) : nil
+    }
+    
+    func down(_ node: Node) -> Node? {
+        node.y < matrix.height - 1 ? Node(x: node.x, y: node.y + 1) : nil
+    }
+    
+    func neighbors(for node: Node) -> [Node] {
+        var result: [Node] = []
+        result.reserveCapacity(4)
+        
+        let current = self[node] + 1
+        
+        if let up = up(node), self[up] <= current {
+            result.append(up)
+        }
+        
+        if let down = down(node), self[down] <= current {
+            result.append(down)
+        }
+        
+        if let left = left(node), self[left] <= current {
+            result.append(left)
+        }
+        
+        if let right = right(node), self[right] <= current {
+            result.append(right)
+        }
+        
+        return result
+    }
+    
+    func allNodes() -> [Node]  {
+        var result: [Node] = []
+        result.reserveCapacity(matrix.width * matrix.height)
+        for y in 0..<matrix.height {
+            for x in 0..<matrix.width {
+                result.append(Node(x: x, y: y))
+            }
+        }
+        return result
+    }
+}
+
+let map = FieldMap(matrix: input)
+print("Part 1: steps from start to goal: ", (map.findPath(from: .init(x: startX, y: startY), to: .init(x: goalX, y: goalY))?.count ?? 0) - 1)
+
+var shortest = Int.max
+for (x, y) in input.find(where: { $0 == 0 }) {
+    if let steps = map.findPath(from: .init(x: x, y: y), to: .init(x: goalX, y: goalY))?.count, steps < shortest {
+        shortest = steps
+    }
+}
+
+print("Part 2: Shortest path to goal: ", shortest - 1)