Solve problem 155.

python/e155.py

@@ -0,0 +1,40 @@
+from fractions import Fraction
+from functools import lru_cache
+
+C = 60
+
+def parallel(a, b):
+    return Fraction(a * b, a + b)
+
+
+def series(a, b):
+    return a + b
+    
+
+@lru_cache()
+def caps(n):
+    if n == 1:
+        return set([C])
+
+    cs = set()
+    for size_a in range(1, (n // 2) + 1):
+        size_b = n - size_a
+        for a in caps(size_a):
+            for b in caps(size_b):
+                cs.add(a)
+                cs.add(parallel(a, b))
+                cs.add(series(a, b))
+    return cs
+
+
+def euler_155():
+    assert len(caps(1)) == 1
+    assert len(caps(2)) == 3
+    assert len(caps(3)) == 7
+    return len(caps(18))
+
+
+if __name__ == "__main__":
+    solution = euler_155()
+    print("e155.py: " + str(solution))
+    assert solution == 3857447