  Within the framework of supersymmetric quantum mechanics, we study the
simplified version of potential algebra of shape invariance condition in k
steps, where k is an arbitrary positive integer. The associated potential
algebra is found to be equivalent to the generalized deformed oscillator
algebra that has a built-in Z_k-grading structure. The algebraic realization of
shape invariance condition in k steps is therefore formulated by the method of
Z_k-graded deformed oscillator. Based on this formulation, we explicitly
construct the general algebraic properties for shape invariant potentials in k
steps, in which the parameters of partner potentials are related to each other
by translation a_1 = a_0 + \delta. The obtained results include the cyclic
shape invariant potentials of period k as a special case.
