Solve problem 265

python/e265.py

@@ -0,0 +1,47 @@
+def is_valid(circle_with_seen, n):
+    circle, seen = circle_with_seen
+    if len(circle) < n:
+        return True
+
+    end = tuple(circle[-n:])
+    if end in seen:
+        return False
+    seen.add(end)
+    return True
+
+
+def overlap_valid(circle_with_seen, n):
+    circle, seen = circle_with_seen
+    for i in range(1, n):
+        end = tuple(circle[-i:] + circle[: n - i])
+        if end in seen:
+            return False
+        seen.add(end)
+    return True
+
+
+def s(n):
+    length = 2**n
+    start = [0 for _ in range(n)]
+    xs = [(start, set([tuple(start)]))]
+    for _ in range(length - n):
+        nxs = []
+        for circle, seen in xs:
+            for d in [0, 1]:
+                nx = (circle + [d], seen.copy())
+                if is_valid(nx, n):
+                    nxs.append(nx)
+        xs = nxs
+    circles = [x[0] for x in xs if overlap_valid(x, n)]
+    return sum(int("".join(map(str, circle)), 2) for circle in circles)
+
+
+def euler_265():
+    assert s(3) == 52
+    return s(5)
+
+
+if __name__ == "__main__":
+    solution = euler_265()
+    print(f"e265.py: {solution}")
+    assert solution == 209110240768