Question 2: Recurrences a) Jonsider the the pseudo-code below for the recursive algorithm Test Rec(A. s. f), which takes is input an array A, indexed between s and f. Test Rec(A, s. f) if s + 2 91 = [] 92= [¹] Test Rec(A, s, q1) MergeSort (A, q1+1,92-1) Test Rec(A, q2, f) • Does this algorithm correctly sort the input array A? • Write the recurrence for the runtime T(n) of Test Ree when run on an array of size n. Determine the runtime of the algorithm using Master Method. Show the runtime is O(n log n) using the recursion tree.

Below is the recursive implementation of binary search from lab with one change (in red): the print statement at the top of the function which prints "BOO" There is also a main function which calls bsearchR on the sorted array data[] with 7 elements and searching for 10. QUESTION: How many BOOS will be printed by this program? // Recursive Binary Search Routine that does the "Real" Work int bsearchR(int a[], int lo, int hi, int x) { int m; printf("BO0\n"); // <<<<==== NEW STATEMENT if(hi < lo) return -1; m = (lo + hi) / 2; if(a[m] == x) return m; else if(x < a[m]) return bsearchR(a, lo, m-1, x); else return bsearchR(a, m+1, hi, x); } int main() { int data[] = {5, 8, 12, 15, 20, 25, 30}; int idx = bsearchR(data, e, 6, 10); return 0; }