Consider the following recursive algorithm:

ALGORITHM Secret $($A$,$ lowIdx, highIdx$)$

$//$ Input:

$//-$ An array A$[1..$n$]$ of integer numbers

$//-$ integers lowIdx, highIdx

$//$ Variables:

$//-$ integers midIdx, temp$1,$ temp$2$

if lowIdx $==$ highIdx

return lowIdx

else

midIdx $=($lowIdx$+$highIdx$)/2$

temp$1$ Secret $($A$,$ lowIdx, midIdx$)$

temp$2$ Secret $($A$,$ midIdx$+1,$ highIdx$)$

if A$[$temp$1]>=$ A$[$temp$2]$

return temp$1$

else

return temp$2$

a$)[10$ points$]$ What does this algorithm return?

b$)[20$ points$]$ Set up a recurrence relation for the algorithm$$s running time and solve it$.$