$(10\%)$ In the prune and search algorithm we introduced in the class to solve the selection

problem, the input elements are divided into groups of $5$ elements. Please explain the reason

why this algorithm can be considered as a prune and search algorithm? $(5\%)$ Will this

algorithm still work in linear time if the input elements are divided into groups of $7$ elements?

$(5\%)$ Note that you need to explain the reason for your answer.