It has been known that the continuous quantum search algorithm (based on the Farhi-Gutmann Hamiltonian evolution) is analogous to the Grover (or discrete time quantum) algorithm. Recently we presented a continuous time algorithm based on the generalized quantum search Hamiltonian. The generalized quantum search Hamiltonian differentiates continuous time quantum search from discrete time quantum search by displaying the interaction between the initial state and the target one. This fact leads us to show that the interaction can improve quantum searched, and the interaction can save the perturbed Farhi-Gutmann Hamiltonian that would otherwise fail. Also we provide methods to improve adiabatic quantum search and discuss a way to speed up the quantum search by partial information.