  Let $\Lambda$ be a closed, connected Legendrian submanifold of the 1-jet
space of a smooth $n$-dimensional manifold. Associated to $\Lambda$ there is a
Legendrian invariant called Legendrian contact homology, which is defined by
counting rigid pseudo-holomorphic disks of $\Lambda$. Moreover, there exists a
bijective correspondence between rigid pseudo-holomorphic disks and rigid Morse
flow trees of $\Lambda$, which allows us to compute the Legendrian contact
homology of $\Lambda$ via Morse theory.
  If $\Lambda$ is spin, then the moduli space of the rigid disks can be given a
coherent orientation, so that the Legendrian contact homology of $\Lambda$ can
be defined with coefficients in $\mathbb Z$. In this paper we give an algorithm
for computing the corresponding orientation of the moduli space of rigid Morse
flow trees if the dimension of $\Lambda $ is greater than 1, and up to 4 signs
that depend on data that can be extracted from the vertices of the trees, but
which are not given explicitly, in the case $n=1$.
