  Using "complexity=action" proposal we study complexity growth of certain
gravitational theories containing higher derivative terms. These include
critical gravity in diverse dimensions. One observes that the complexity growth
for neutral black holes saturates the proposed bound when the results are
written in terms of physical quantities of the model. We will also study
effects of shock wave to the complexity growth where we find that the presence
of massive spin-2 mode slows down the rate of growth.
