AoC 2024 day 19 part 2

aoc2024/src/day19/python/solution.py

@@ -17,19 +17,41 @@
 
 @cache
 def _is_possible(design: str, patterns: frozenset[str], candidate: str = '') -> bool:
+  """Returns true if the design can be made with the available patterns."""
   for pattern in patterns:
     testee = candidate + pattern
-    if testee == design:
+    if testee == design or (design.startswith(testee) and _is_possible(design, patterns, testee)):
       return True
-    if design.startswith(testee):
-      if _is_possible(design, patterns, testee):
-        return True
   return False
 
 
+@cache
+def _count_distinct_arrangements(design: str, patterns: frozenset[str], prefix: str, k: int) -> int:
+  """Returns the number of distinct arrangements that can be made to create a 'design'
+  from available 'patterns'.
+  Example: given design 'brwrr' and patterns 'b','r','br','wr',
+  it can be made in 2 different ways: b+r+wr+r or br+wr+r."""
+  if k == 0:  # Base case
+    return 1
+  return sum(
+    _count_distinct_arrangements(design=design,
+                                 patterns=patterns,
+                                 prefix=prefix + pattern,
+                                 k=k - len(pattern))
+    if design.startswith(prefix + pattern)
+    else 0
+    for pattern in patterns)
+
+
 def num_possible_designs(input: Sequence[str]) -> int:
-  patterns: frozenset[str] = frozenset(input[0].split(', '))
-  result = 0
-  for design in input[2:]:
-    result += 1 if _is_possible(design, patterns) else 0
-  return result
+  """Returns the total number of designs that can be made with the available patterns."""
+  patterns: frozenset[str] = frozenset(input[0].split(', '))  # First line has comma-separated patterns.
+  return sum(1 if _is_possible(design, patterns) else 0
+             for design in input[2:])  # Designs start on the third line.
+
+
+def num_possible_options(input: Sequence[str]) -> int:
+  """Returns the total number of different ways the designs can be made with the available patterns."""
+  patterns: frozenset[str] = frozenset(input[0].split(', '))  # First line has comma-separated patterns.
+  return sum(_count_distinct_arrangements(design=design, patterns=patterns, prefix='', k=len(design))
+             for design in input[2:])  # Designs start on the third line.

aoc2024/test/day19/python/test_solution.py

@@ -14,7 +14,7 @@
 import unittest
 
 from common.python3.AdventOfCodeTestCase import AdventOfCodeTestCase
-from aoc2024.src.day19.python.solution import num_possible_designs
+from aoc2024.src.day19.python.solution import num_possible_designs, num_possible_options
 
 
 class TestSolution(AdventOfCodeTestCase):
@@ -28,6 +28,12 @@ def test_part1_withExample_success(self):
   def test_part1_withPuzzleInput_success(self):
     self.assertEqual(365, num_possible_designs(self.input))
 
+  def test_part2_withExample_success(self):
+    self.assertEqual(16, num_possible_options(self.examples[0]))
+
+  def test_part2_withPuzzleInput_success(self):
+    self.assertEqual(730121486795169, num_possible_options(self.input))
+
 
 if __name__ == '__main__':
   unittest.main()