Problem 2: The quaternary search algorithm is a modification of the binary search algorithm that splits the input not into two sets of almost-equal sizes, but into four sets of sizes approximately one-fourth.

a) Verbally describe and write pseudo-code for the quaternary search algorithm. b) Give the recurrence for the quaternary search algorithm c) Solve the recurrence to determine the asymptotic running time of the algorithm. How does the running time of the quaternary search algorithm compare to that of the binary search algorithm.

Problem 3: Design and analyze a divide and conquer algorithm that determines the minimum and maximum value in an unsorted list (array). a) Verbally describe and write pseudo-code for the min_and_max algorithm. b) Give the recurrence. c) Solve the recurrence to determine the asymptotic running time of the algorithm. How does the theoretical running time of the recursive min_and_max algorithm compare to that of an iterative algorithm for finding the minimum and maximum values of an array.