struct Hand {
    let dominos: Set<Domino>
    
    func trains(startingWith: Int) -> Array<Train> {
        var t = Array<Train>()
        let starts = dominos.filter { $0.connectsTo(startingWith) }
        for start in starts {
            let remaining = dominos.subtracting([start])
            let train = Train(start: startingWith, path: [start])
            t.append(contentsOf: buildTrains(train, remaining: remaining))
        }
        return t
    }
    
    private func buildTrains(_ soFar: Train, remaining: Set<Domino>) -> Array<Train> {
        var built = [soFar]
        
        let start = soFar.final
        let connections = remaining.filter { $0.connectsTo(start) }
        
        for connect in connections {
            let remainingForTrain = remaining.subtracting([connect])
            let thisTrain = Train(start: soFar.start, path: soFar.path + [connect])
            let trains = buildTrains(thisTrain, remaining: remainingForTrain)
            built.append(contentsOf: trains)
        }
        
        return built
    }
    
    func print() {
        let hasVertical = dominos.filter { $0.isDouble }.count > 0
        var printedLines = Array<Array<Character>>(repeating: [], count: hasVertical ? 5 : 3)
        for t in dominos {
            var lines = t.tile().split(separator: "\n").map { Array($0) }
            if hasVertical == true && t.isDouble == false {
                lines.insert(Array(repeating: " ", count: Domino.horizontalTileWidth), at: 0)
                lines.append(Array(repeating: " ", count: Domino.horizontalTileWidth))
            }
            
            // append a space after this tile
            printedLines = printedLines.enumerated().map {
                $1 + lines[$0] + [" "]
            }
        }
        
        for l in printedLines { Swift.print(String(l)) }
    }
}