Divide and Conquer You have a list A[1...n] of n integers. A local minimum of a list is an index i such that A[i] < A[i −1] and A[i] < A[i +1]. A[1] and A[n] are local minimums only if they are less than their single neighbor. You will develop an algorithm to find one local minimum in a list (there may be more than one in the list but you only have to find one). a) Circle the local minimums in this list. A= [10,7,5,3,5,7,9,6,4,2
b) Write a formal statement of this problem. That is, state the input and output criteria as precisely as possible.
c) Let LM(A[a...b) express the output of the local minimum problem. State a self-reduction relating the solution to the main problem to solutions to its sub-problems.
d) What is the worst case running time of the algorithm you have designed.

Write a program that uses a random number generator to generate a two digit positive integer and allows the user to perform one or more of the following operations: a. double the number. b. reverse the digits of the number. c. raise the number to the power of 2, 3, or 4. d. sum the digits of the number. e. if the number is a two-digit number, then raise the first digit to the power of the second digit. f. if the number is a three-digit number and the last digit is less than or equal to 4, then raise the first two digits to the power of the last digit. after performing an operation if the number is less than 10, add 10 to the number. also, after each operation determine if the number is prime. each successive operation should be performed on the number generated by the last operation. your program should not contain any global variables and each of these operations must be implemented by a separate function. also, your program should be menu driven. 7. (fraction calculator) write a program that