Take a look at Pollard's rho algorithm. It's not quite the same problem, but maybe you'll understand the logic from it, and apply it for linked lists.
(if you're lazy, you can just check out cycle detection -- check the part about the tortoise and hare.)
This only requires linear time, and 2 extra pointers.
In Java:
boolean hasLoop( Node first ) {
if ( first == null ) return false;
Node turtle = first;
Node hare = first;
while ( hare.next != null && hare.next.next != null ) {
turtle = turtle.next;
hare = hare.next.next;
if ( turtle == hare ) return true;
}
return false;
}
(Most of the solution do not check for both next and next.next for nulls. Also, since the turtle is always behind, you don't have to check it for null -- the hare did that already.)
