  Let $\mathbb{Z}$ be the integer numbers, $\mathbb{K}$ an algebraically closed
field, $\Lambda$ a finite dimensional $\mathbb{K}$-algebra, mod$\Lambda$ the
category of finitely generated right modules, proj$\Lambda$ the full
subcategory of mod$\Lambda$ consisting of all projective $\Lambda$-modules, and
$C_n(proj\Lambda)$ the bounded complexes of projective $\Lambda$-modules of
fixed size for any integer $n\geq2$. We find an algorithm to calculate the
strong global dimension of $\Lambda$, when $\Lambda$ is a finite strong global
dimension and derived discrete, using the Auslander-Reiten quivers of the
categories $C_n(proj\Lambda)$. Also, we show the relation between the
Auslander-Reiten quiver of the bounded derived category $D^b(\Lambda)$ and the
Auslander-Reiten quiver of $C_{\eta+1}(proj\Lambda)$, where
$\eta=s.gl.dim(\Lambda)$ (strong global dimension of $\Lambda$).
