= Solution
Choose $U$ to prepare the uniform superposition, so the marked-state probability is $p=1/4$. Apply the <marked-state phase oracle> $R_g^\pi$, followed by the reflection $UR_{00}^\pi U^\dagger$ about the prepared state. Part (iii) shows that this single <Grover search algorithm>[Grover iteration] produces $-|g\rangle$. A <projective measurement> in the four-item basis therefore returns the marked element with probability one. This is <exact Grover search on four entries>.
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