  We show that the Density of States (DoS) for lattice Self Avoiding Walks can
be estimated by using an inverse algorithm, called flatIGW, whose step-growth
rules are dynamically adjusted by requiring the energy histogram to be locally
flat. Here, the (attractive) energy associated with a configuration is taken to
be proportional to the number of non-bonded nearest neighbor pairs (contacts).
The energy histogram is able to explicitly direct the growth of a walk because
the step-growth rule of the Interacting Growth Walk \cite{IGW} samples the
available nearest neighbor sites according to the number of contacts they would
make. We have obtained the complex Fisher zeros corresponding to the DoS,
estimated for square lattice walks of various lengths, and located the $\theta$
temperature by extrapolating the finite size values of the real zeros to their
asymptotic value, $\sim 1.49$ (reasonably close to the known value, $\sim 1.50$
\cite{barkema}).
