(a) Implement (in Java) the RadixSort algorithm to sort in increasing order an array of integer keys. (c) How many edges does a graph have if its degree sequence is 5, 2, 2, 2, 2, 1? Draw such a graph (d) The definition of a topological ordering of a graph G- is an ordering of the vertices from 1 to n such that if (i,j) is in E then i j. Give an example of a graph with a topological ordering such that the converse statement"ific j then edge (i,j) is in ?" is false. public void radixSort(int arr]) In your implementation you must consider that each key contains only even digits (0, 2, 4 6, and 8). Your program must detect the case of odd digits in the keys, and, in this case, abort (e) Does Prims and Kruskals algorithms work if some edges have negative weights? Justify (prove or give counter example) in each case. You may assume distinct edge weights. Note: To storage and process the bucket lists, use an ArrayList structure. (b) What is the running time complexity of your radixSort method? Justify. (f) Consider the following graph. If there is ever a decision between multiple neighbor nodes in the BFS or DFS algorithms, assume we always choose the letter closest to the beginning of the alphabet first (a) Given the following list of numbers: trace the execution for quicksort with median-of-three partitioning and a cutoff of 3 (b) The processing time of an algorithm is described by the following recurrence equation (c 3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5 is a positive constant) What is the running time complexity of this algorithm? Justify. (c) You decided to improve insertion sort by using binary search to find the position p where the new insertion should take place (c.1) what is the worst-case complexity of your improved insertion sort if you take account of only the comparisons made by the binary search? (c.2) What is the worst-case complexity of your improved insertion sort if only swaps/inversions of the data values are taken into account? (f.1) In what order will the nodes be visited using a Breadth First Search? (f.2) In what order will the nodes be visited using a Depth First Search? #3: (45 (a) Model the following situation a graphs. Draw the graph, and give the corresponding adjacency matrix. Ann and Bob are friends. Ann is also friends with Carla and David. Bob, Carla and Evans are all friends of each other (b) Either draw a graph with the following specified properties, or explain why no such graph exists: A simple graph with five vertices with degrees 2, 3, 3, 3, and 5