Need help with any of these questions. Data analysis/algorithms. Thank you:

Solve the following recurrences using the Master Theorem. State the case and the constant values used: T\left(n ight)=12T\left(\frac{n}{3} ight)+n^4\lg n T(n)=12T(n3)+n4lgn T\left(n ight)=4T\left(\frac{n}{2} ight)+\lg n T(n)=4T(n2)+lgn T\left(n ight)=2T\left(\frac{n}{4} ight)+\sqrt{n} T(n)=2T(n4)+n T\left(n ight)=T\left(\sqrt[4]{n^3} ight)+5T(n)=T([4]n3)+5. Use the change of variable m=lg(n). Upload a file with your solution.

Let A[1..n] and B[1..n] be two arrays sorted in increasing order. Assume that both A and B have no duplicate elements. Write the pseudocode of an algorithm which computes A B. More specifically the algorithms prints the elements which are in A and are not in B. The running time of the algorithm must be O(n). Upload a file with your solution.

Design an efficient algorithm for finding and deleting an element of the smallest value in a max-heap A[1..n] where n \ge 1. What is the running time of your algorithm? Upload a file with your solution.

We implement a max-priority queue using the max-heap A. Assume that A = <200, 80, 160, 40, 70, 30, 50, 3, 25, 5>. Write A after each of the following two operations: HEAP-INCREASE-KEY(A, 9, 100) HEAP-INSERT(A, 180) Apply the second operation to the max-heap resulted from applying the first operation. Upload a file with your solution.

We are running the Quicksort algorithm on the array A = < 5, 3, 25, 6, 10, 17, 1, 2, 18, 8>. (7 pts) Write A after the first PARTITION() call. (3 pts) Write A after the second PARTITION() call.

Use Quicksort to sort the array A = < E, X, E, R, C, I, S, E> in alphabetical order. Draw the tree of the recursive calls made. Upload a file with your solution.

Select all the statements below which are TRUE: Insertion sort is an asymptotically optimal comparison sort. Any comparison sort algorithm requires (nlgn) comparisons in the worst case. Any sorting algorithm has running time (n) since it has to traverse the sequence of elements. Quick sort is not a comparison sort because it calls the PARTITION function. Heapsort and Merge sort are asymptotically optimal comparison sorts. Bucket sort is not a comparison sort.