We present an algorithm for the generalized search problem (searching k marked items among N items) based on a continuous Hamiltonian and exploiting resonance.This resonant algorithm has the same time complexity O(√N/k) as the Grover algorithm.A natural extension of the algorithm,incorporating auxiliary "monitor" qubits,can determine k precisely,if it is unknown.The time complexity of our counting algorithm is O(√N),similar to the best quantum approximate counting algorithm,or better,given appropriate physical resources.