Complexity of computing zk-SNARK Proofs
Its depend on the protocol used. The last and more efficient is Groth16 that use only 3 curve points in its proofs. You can see the size of the keys and the  the proofs in the table 2 of Groth's paper. The computation complexity of the pairing depends of whats curve is used. In general ZoKrates/Ethereum and ZCash use the bn256 curve paramters and the pairing algorithm used in their package (at least in the golang's one) is the algorithm 1 of the miller ate pairings. 

You see zk-SNARK is an amalgamation of various works and its complexity depends on the implementation that is evolving day to day.