Solution to problem 12 in Python

src/Year_2021/P12.py

@@ -156,5 +156,66 @@ def part_1() -> None:
     print(f"There are {ans} paths visiting small caves")
 
 
+# --- Part Two ---
+
+# After reviewing the available paths, you realize you might have time to visit
+# a single small cave twice. Specifically, big caves can be visited any number
+# of times, a single small cave can be visited at most twice, and the remaining
+# small caves can be visited at most once. However, the caves named start and
+# end can only be visited exactly once each: once you leave the start cave, you
+# may not return to it, and once you reach the end cave, the path must end
+# immediately.
+
+# Now, the 36 possible paths through the first example above are:
+
+# start,A,b,A,b,A,c,A,end
+# start,A,b,A,b,A,end
+# start,A,b,A,b,end
+# start,A,b,A,c,A,b,A,end
+# start,A,b,A,c,A,b,end
+# start,A,b,A,c,A,c,A,end
+# start,A,b,A,c,A,end
+# start,A,b,A,end
+# start,A,b,d,b,A,c,A,end
+# start,A,b,d,b,A,end
+# start,A,b,d,b,end
+# start,A,b,end
+# start,A,c,A,b,A,b,A,end
+# start,A,c,A,b,A,b,end
+# start,A,c,A,b,A,c,A,end
+# start,A,c,A,b,A,end
+# start,A,c,A,b,d,b,A,end
+# start,A,c,A,b,d,b,end
+# start,A,c,A,b,end
+# start,A,c,A,c,A,b,A,end
+# start,A,c,A,c,A,b,end
+# start,A,c,A,c,A,end
+# start,A,c,A,end
+# start,A,end
+# start,b,A,b,A,c,A,end
+# start,b,A,b,A,end
+# start,b,A,b,end
+# start,b,A,c,A,b,A,end
+# start,b,A,c,A,b,end
+# start,b,A,c,A,c,A,end
+# start,b,A,c,A,end
+# start,b,A,end
+# start,b,d,b,A,c,A,end
+# start,b,d,b,A,end
+# start,b,d,b,end
+# start,b,end
+
+# The slightly larger example above now has 103 paths through it, and the even
+# larger example now has 3509 paths through it.
+
+# Given these new rules, how many paths through this cave system are there?
+
+
+def part_2() -> None:
+    ans = dfs("start", caves_map, {"start"}, already_visited=True)
+    print(f"There are {ans} paths in total")
+
+
 if __name__ == "__main__":
     part_1()
+    part_2()