Devise a divide$-$and$-$conquer algorithm that determines whether a candidate received a majority and,

ifso, determine who this candidate is$.[$Hint: Assume

that n is even and split the sequence of votes into

two sequences, each with n $/2$ elements. Note that a

candidate could not have received a majority of votes

without receiving a majority of votes in at least one of

the two halves.$]$

b$)$ Use the Master Theorem to estimate the number of

comparisons needed by the algorithm you devised in

part $($a$).$