  We give a new and constructive proof of the existence of a special class of
univariate polynomials whose graphs have preassigned shapes. By definition, all
the critical points of a Morse polynomial function are real and distinct and
all its critical values are distinct. Thus we can associate to it an
alternating permutation: the so-called Arnold snake, given by the relative
positions of its critical values. We realise any separable alternating
permutation as the Arnold snake of a Morse polynomial.
