Quaternary search is like binary search, but divides the array into four parts instead$$of two. After quarterly dividing the array, the four divisors are compared to the input value. If it$$matches the index is returned. If not the algorithm is recursively called on the subarray that$$contains the value.$($a$)$ What design technique is this algorithm based on$?($b$)$ Set up a recurrence for the number of key comparisons in the worst case. You may assume$$that n $=4$k$,$ for some none$($c$)$ Solve the recurrence for n $=4$k$.($d$)$ Compare this algorithm$$s efficiency with that of binary search.