Answer the following questions about estimating the minimum complexity

for an algorithm that calculates the median of an array. You may assume

that the array has odd size, and in an array with odd size, the median

will be the middle element in sorted order $(2$nd smallest element in array

of size $3,3$rd smallest element for size $5,$ etc.$).$

$($a$)$ How many different possible solutions are there for an algorithm that

returns the index of the median of an array of size $n?$ Note that you

only need to count the distinct solutions to this problem $($different

problem instances may share the same solution$).$ Briefly justify your

answer.

$($b$)$ What is the minimum number of comparisons that a comparison$-$

based median algorithm would need to make in order to produce all

of these solutions? Justify your answer.