Solve problem 265

python/e265.py

@@ -0,0 +1,68 @@
+def is_valid(circle, seen, n):
+    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, seen, n):
+    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 align(circle, n):
+    needle = [0 for _ in range(n)]
+
+    for i in range(len(circle) - n):
+        if circle[i : i + n] == needle:
+            return circle[i:] + circle[:i]
+    return []
+
+
+def s(n):
+    length = 2**n
+    circles = [[[], set()]]
+    for i in range(length):
+        new_circles = []
+        for circle, seen in circles:
+            for d in [0, 1]:
+                new_circle = circle + [d]
+                new_seen = seen.copy()
+                if is_valid(new_circle, new_seen, n):
+                    new_circles.append([new_circle, new_seen])
+        circles = new_circles
+    valid_circles = []
+    valid_seen = set()
+    for circle, seen in circles:
+        if overlap_valid(circle, seen, n):
+            aligned = align(circle, n)
+            aligned_tuple = tuple(aligned)
+            if aligned and aligned_tuple not in valid_seen:
+                valid_circles.append(aligned)
+                valid_seen.add(aligned_tuple)
+
+    t = 0
+    for circle in valid_circles:
+        s = int("".join(map(str, circle)), 2)
+        print(circle, s)
+        t += s
+    return t
+
+
+def euler_265():
+    assert s(3) == 52
+    return s(5)
+
+
+if __name__ == "__main__":
+    solution = euler_265()
+    print(f"e265.py: {solution}")
+    assert solution == 209110240768