the after takes less than double the time of the before

aoc2021-12-computed.diff

diff --git a/12.py b/12.py
index 8cb48a8..e6097ae 100644
--- a/12.py
+++ b/12.py
@@ -8,39 +8,39 @@ for line in data.splitlines():
     G.add_edge(a, b)
 
 
-def find_paths(G, so_far, visited, from_="start"):
+def find_paths(G, so_far, from_="start"):
     edges = G[from_]
 
     for node in edges:
         if node == "end":
             yield [*so_far, "end"]
-        elif node.islower() and node in visited:
+        elif node.islower() and node in so_far:
             continue
         else:
-            yield from find_paths(G, [*so_far, node], {*visited, node}, from_=node)
+            yield from find_paths(G, [*so_far, node], from_=node)
 
 
-print(len(list(find_paths(G, ["start"], {"start"}))))
+print(len(list(find_paths(G, ["start"]))))
 
 
-def find_paths(G, so_far, visited, from_="start", twice=False):
+def find_paths(G, so_far, from_="start"):
     edges = G[from_]
+    smalls = [n for n in so_far if n.islower()]
+    twice = len(set(smalls)) != len(smalls)
 
     for node in edges:
         if node == "start":
             continue
         elif node == "end":
             yield [*so_far, "end"]
-        elif node.islower() and node in visited and twice:
+        elif node.islower() and node in so_far and twice:
             continue
         else:
             yield from find_paths(
                 G,
                 [*so_far, node],
-                {*visited, node},
                 from_=node,
-                twice=twice or (node.islower() and node in visited),
             )
 
 
-print(len(list(find_paths(G, ["start"], {}))))
+print(len(list(find_paths(G, ["start"]))))