Algorithm 3 Modified g-database algorithm.
Input:${|0\rangle }^{\otimes N}{|0\rangle }^{\otimes N}$, classical query access to g Output: The g-database $$|r_g\rangle =|x\rangle |g\left(x\right)\rangle$$  1: H-gate operations are performed on $\rho$ qubits (not necessarily continuous) for the front ${|0\rangle }^{\otimes N}$. $${|x\rangle |0\rangle }^{\otimes N}$$  2: For each $x\in {\{0,1\}}^N$, $2^{\rho }$ classical queries $g\left(x\right)$ are performed, and then the $g\left(x\right)$ unitary operator is applied in the second register.
3: Return $|x\rangle |g\left(x\right)\rangle$	▷ Return the g-database $|r_g\rangle$