  We investigate the early-time light-curves of a large sample of 223 type II
supernovae (SNe) from the Sloan Digital Sky Survey and the Supernova Legacy
Survey. Having a cadence of a few days and sufficient non-detections prior to
explosion, we constrain rise-times, i.e. the durations from estimated first to
maximum light, as a function of effective wavelength. At restframe g-band
(4722A), we find a distribution of fast rise-times with median of (7.5+/-0.3)
days. Comparing these durations with analytical shock models of Rabinak and
Waxman (2013); Nakar and Sari (2010) and hydrodynamical models of Tominaga et
al. (2009), which are mostly sensitive to progenitor radius at these epochs, we
find a median characteristic radius of less than 400 solar radii. The inferred
radii are on average much smaller than the radii obtained for observed red
supergiants (RSG). Investigating the post-maximum slopes as a function of
effective wavelength in the light of theoretical models, we find that massive
hydrogen envelopes are still needed to explain the plateaus of SNe II. We
therefore argue that the SN II rise-times we observe are either a) the shock
cooling resulting from the core collapse of RSG with small and dense envelopes,
or b) the delayed and prolonged shock breakout of the collapse of a RSG with an
extended atmosphere or embedded within pre-SN circumstellar material.
