Reachability in restricted walk on integers

We prove that two conditions are sufficient, and with three exceptions also necessary, for reachability of any position in restricted walk on integers in which the sizes of the moves to the left and to the right are constant but need not be equal. A method to compute the length of the shortest path between any two positions, as well as a shortest path algorithm when the reachability conditions are true are given. Also a complete characterization for Hamiltonian restricted walks between absorbing boundaries is given.