Consider the following algorithm: search(a, first, last, key) 1 if a[first] = key 2 return true 3 if first > = last 4 return false 5 middle = (first + last)/2 6 left = search(a, first, middle, key) 7 right = search(a, middle+1, last, key) 8 return (left or right)write down a recurrence that counts the number of times the comparison in line 1 is performed on an array of length n. write down the asymptotic version of the running time.

Write a program that inserts the digits of an integer into an array in originalorderfollowed by reverse order. first, promptthe user to enter a positive integer(> 0). determine the number of digits of the integer. create a dynamically allocated integer arrayof a size twice the number of digits. now insert the digits in original order which will occupy half of the array. then, insert the digits in reverse order. finally, output thedigits in thearray. use at least two functions to organize your program.