$(7$ points$)$

$($a$)$ Given a program which searches the farget data in a sequence of $6$ data, assume $($i$)$ without knowing the location of the target data, the CPU will examine the data one by one; $($ii$)$ the whole program can be executed parallelly and the program will stop immediately once the target data is found; and $($iii$)$ the program's running time except data searching can be ignored, please calculate:

$(1)$ If the target data is the $3^{id}$ in the sequence, what is the speedup gained by running the program using $2$ CPUs over running the program using $1$ CPU. Note: by default, the data will be equally dispatched to the CPUs $($i$.$e$.,$ CPU $1$ processes data $1,2,3$: CPU $2$ processes data $4,5$; $6,$ etc.$)$

$(2)$ It the target data is the $4^{th}$ in the sequence, what is the speedup by running the programing using $2$ CPUs?

$(3)$ If the target data is the $4^{th}$ in the sequence, what is the speedup by running the programing using $3$ CPUs?

$($b$)$ If the program of $($a$)$ can be executed completely parallelly, according to the Amdahl's law, what will be the speedup if we run it parallelly using $2$ threads $($i$.$e$.,$ two processors$)?$ Comparing it with the calculated results of the three cases above, do you see superlinear speedup in any of the three? If yes, which one$($s$)?$