ANSWER THE $3$rd PART $,$ thanks

One$-$out$-$of$-$four search. Let $f$:$\{0,1{\}}^2\{0,1\}$ be a black$-$box function taking the value $1$

on exactly one input. The goal of the one$-$out$-$of$-$four search problem is to find the unique $(x_1,x_2)in\{0,1{\}}^2$

such that $f(x_1,x_2)=1.$

$(7$ points$)$ Suppose $f$ is given as a quantum black box $U_f$ acting as

$|x_1,x_2,y$:

Determine the output of the following quantum circuit for each of the possible black$-$box functions $f$ :