day 19 note

day19/sol2.py

@@ -12,6 +12,14 @@ def solve(file):
             n += 1
         if len(x) > 1:
             for i in range(1,len(x)):
+                # note: i originally tried to compute this as
+                # n += ways(x[i:]) * ways(x[i:])
+                # however that gives an overcount as, for example,
+                # rrr can be broken up as (r)[(r)(r)] or [(r)(r)](r) but
+                # for the purpose of the puzzle those are both equivalent -
+                # only the leaf nodes count (r r r), not the structure of the tree.
+                # the fix is to only recurse on one side of the cut (doesn't
+                # matter which one).
                 if x[:i] in ds:
                     n += ways(x[i:])
         #print("ways(%s) = %s"%(x,n))