  The gravitational collapse of a massless scalar field enclosed with a
perfectly reflecting wall in a spacetime with a cosmological constant $\Lambda$
is investigated. The mass scaling for the gapped collapse $ M_{AH}-M_g \propto
(\epsilon_c-\epsilon)^\xi$ is confirmed and a new time scaling for the gapped
collapse $T_{AH}-T_g\propto(\epsilon_c-\epsilon)^\zeta$ is found. We find that
both of these two critical exponents depend on the combination $\Lambda R^2$,
where $R$ is the radial position of the reflecting wall. Especially, we find an
evolution of the critical exponent $\xi$ from $0.37$ in the confined asymptotic
dS case with $\Lambda R^2=1.5$ to $0.7$ in asymptotic AdS case ($\Lambda
R^2\rightarrow-\infty$), while the critical exponent $\zeta$ varies from $0.10$
to $0.26$, which shows the new critical behavior for the gapped collapse is
essentially different from the one in the Choptuik's case.
