Automatic computation of crosscap number of alternating knots

We specify the computational complexity of crosscap numbers of alternating knots by introducing an automatic computation. For an alternating knot $K$, let $\mathcal{E}$ be the number of edges of its diagram. Then there exists a code such that the complexity of this computation of the crosscap number of $K$ is estimated by $O({\mathcal{E}}^{\mathcal{3}})$.