Hi.

Please do not take my solutions tooo seriousely. The OP asked for a not linear algorithm.

Simulation of atomic forces are not linear, they are quadratic, ... whatever. So just build a graph out of the linked list. Each connection should yield in forces to the connected elements that they will try to get to the distance "1". Additionaly all elements have a very low pushing force to each other element (nonlinear force of course :-). A little bit of nonlinear friction also should be added.

If you simulate this threedimensional over a few thousend cycles there may be different results.
1. It will not converge to a stable solution. The distance of some list elements will keep growing. --> there are at least two not connected parts of the list wich travel through space. --> no cyclic list.

2. it will converge to a stable solution. Then add a little power wich will attract the graph to the x-y-plane. After a few thousend additional iterations print the parallel projection of the graph to the x-y-plane and perform a Blob analysis of the resulting picture. There are four possible results:
a. the graph has no hole. --> no circle, no linked list.
b. the graph has more than one hole --> no circular list.
c. the graph has exact one hole, and the area is about pi r^2 with r = number of nodes / 2*pi --> the graph is circular
d. as c, but with smaller area --> the graph looks like a 6 or like a § or something else, but not like an o.

Maybe this ist not the fastest algorithm, but it will result in the prettiest pictures :-)

And you can do all of the things above nonlinear.


GMarco