Rewrite AoC 2024 day 19 part 1 solver to use iterables and yield to p…

…repare for part 2

lib/solvers/advent_of_code/2024/day_19_solver.dart

@@ -1,4 +1,3 @@
-import 'package:darq/darq.dart';
 import 'package:h3x_devtools/solvers/advent_of_code/2024/aoc_2024_solver.dart';
 
 class Day19Solver extends AdventOfCode2024Solver {
@@ -18,27 +17,24 @@ class Day19Solver extends AdventOfCode2024Solver {
     List<String> nonCompositablePatterns = [...towelPatterns];
     for (String pattern in towelPatterns) {
       nonCompositablePatterns.remove(pattern);
-      if (!_isDesignPossible('', pattern, nonCompositablePatterns)) nonCompositablePatterns.add(pattern);
+      if (!_getPossibleDesigns([], pattern, nonCompositablePatterns).isNotEmpty) nonCompositablePatterns.add(pattern);
     }
 
     // Now we check which designs are possible.
-    int possibleDesigns = desiredDesigns.where((design) => _isDesignPossible('', design, nonCompositablePatterns)).length;
+    int possibleDesigns = desiredDesigns.where((design) => _getPossibleDesigns([], design, nonCompositablePatterns).isNotEmpty).length;
 
     return 'Possible designs: $possibleDesigns';
   }
 
-  bool _isDesignPossible(String currentPattern, String desiredPattern, List<String> towelPatterns) {
+  Iterable<List<String>> _getPossibleDesigns(List<String> currentPattern, String desiredPattern, List<String> towelPatterns) sync* {
     for (String pattern in towelPatterns) {
-      String testingPattern = '$currentPattern$pattern';
+      String testingPattern = '${currentPattern.join()}$pattern';
       if (testingPattern == desiredPattern) {
-        return true;
+        yield [...currentPattern, pattern];
       } else if (testingPattern.length < desiredPattern.length && desiredPattern.startsWith(testingPattern)) {
-        bool isPossible = _isDesignPossible(testingPattern, desiredPattern, towelPatterns);
-        if (isPossible) return true;
+        yield* _getPossibleDesigns([...currentPattern, pattern], desiredPattern, towelPatterns);
       }
     }
-
-    return false;
   }
 
 }