what is continuous wavelet (cwt) ,wavelet packet (wpt) and stockwell (S-T) computational complexity?
For a dsicretized signal with N samples. In terms of complexity for the DWT it is O(N) and for WPT its O(Nlog(N)) REFER. For each scale one calculates a convolution and not a single correlation value and the scale values need to be integral values. They can be constrained by using the iterative structure of quadrature mirror LP and HP filters, which is basically a explicit way of coding the scaling function. This is basically because one needs a finite number of scalings of the wavelet to represent the signal (wavelet is overcomplete frame). REFER2. For the wavelet packet tree the extra cost is due to the encoding of the residue/detail coefficients. 

EDIT:
You are right the discretization of the scale function in the CWT parameter decides the number of levels of decomposition. Matlab implements the CWT and describes that the DFT can be used in calculating the CWT by zeropadding the wavelet and performing circular convolutions. 



Here Δt is the sampling interval (period) which basically discretizes the signal and the wavelet. So i guess you are right about the complexities for both the CWT and the WPT versions! Sorry about the mix up!