Final Review 1 Final Exam (Out of 70) • Part A: Basic knowledge of data structures – 20 points – MulEple choice • Part B: Applicaon, Comparison and Implementaon of the data structures – 20 points – Apply supported operaons (like find and insert) to data structures we have covered like: BST, AVL, RBTs, MulEway trie, Ternary Trie, B trees, skip lists. Also essenEal concepts in Huffman codes • Part C: Simulang algorithms and run Eme analysis – 15 points – Graph algorithms: BFS, DFS, Dijkstra, Prims’, Kruskals’. Also union find • Part D: C++ and programming assignments – 15 points – Short answer 2 Final Exam Practice Questions CSE 100 (Fall 2014) CSE Department University of California, San Diego Part A: The Basics This section tests your basic knowledge of data structures via multiple choice questions. Sample questions include all the iclicker and reading quiz questions covered in class. Please make sure you review them. Part B: Application, Comparison and Implementation This section tests how well you understand what goes on under the hood of the data structures covered during the course, their strengths and weaknesses and their applications. The format is short answers and fill in the blanks. 1. B-trees. (a) Construct a 2-3 tree by inserting the following keys in the order shown: 10, 15, 20, 25, 17, 30. You can check your answers and experiment with trees of your own design at the following web sites: https://www.cs.usfca.edu/˜galles/visualization/BTree.html B-trees http://ats.oka.nu/b-tree/b-tree.manual.html (b) Which of the following are legal 2,3 trees (B tree of order 3)? For a tree that is not a valid 2,3 tree, state a reason why. 22 50 22 52 8 30 64 5 9 24 53 54 22 12 50 79 5 9 1 7 4 7 30 64 69 84 102 3 Insert the value 42 into the following BTree. 4 Ternary Tries 5. Ternary search Trees. (a) Consider the following ternary search tree. Nodes with double circles have their end bits set to true. Circle all of the words from the list on the right that are in the tree and write in any words that are missing. At the end you should have a complete list of all words found in the tree, and only those words. a n l d s air, all, a, and, as i l t r (b) Does the height of this tree depend on the order in which the keys have been inserted? (c) Briefly explain why you would prefer to use a ternary search tree rather than a binary search tree to implement getAllValidWords() in PA4. 5 Part C: Simulating Algorithms and Run Time Analysis This section tests how well you understand the algorithms during the course. The focus is on simulating well known graph algorithms and the application of data structures to achieve fast run times. You will also be tested on analyzing the running time of these algorithms. The format is short answers and fill in the blanks. 1. Graphs. Given the following graph, run Dijkstra’s algorithm on it, with source node A. Alongside the graph is the data structure for eachWrite the sequence of verEces visited when running DFS on the node that you will modify, see below. D following graph. Assume the link to the vertex with the A: dist = 0 prev= -1 done= f adj: ((B,5),(D,10),(E,6)) 0 minimum edge weight is chosen when mulEple choices are available B: dist = prev= -1 done= f adj: ((D,3)) C 3 4 1 10 C: dist = prev= -1 done= f adj: ((D,0)) B 1 E 1 D: dist = prev= -1 done= f adj: () 5 6 1 A E: dist = prev= -1 done= f adj: ((C,3)) Write the sequence of verEces visited when running BFS on the following graph. Assume the link to the vertex with the 1 The boxes below represent the priority queue which is used in the algorithm. Each set of boxes represents the priority queue after the firstminimum edge weight is chosen when mulEple choices are pair has been dequeued and its associated node has been fully expanded (i.e. its neighbors, along withavailable their distances, have been added to the priority queue as appropriate). You will fill these in. Run Dijkstra’s algorithm by (1) modifying the values in the dist, prev, done and done fields (above) as the algorithm runs, and (2) showing the values stored in the priority queue after each new node is expanded. For the data structures at the top, you should cross off old values as you replace them. For the priority queue, you should show the contents of the whole queue in the next set of boxes after you have fully expanded/explored from the node that you just removed from the front of the queue in the previous step. The initial priority queue and initial values are already filled in for you. You may stop the process when each node has been marked as done. You may not need all of the queues. If you do need more, just draw them in below the final array, to the side, or on the scratch page. 6 Which of the following are AVL trees? B C 42 A 42 42 10 67 67 10 67 10 11 53 90 53 90 53 90 87 87 D. A&C E. A&B&C Annotate the trees with balance factors 7 AVL Rotaons 0 30 -1 1 15 70 0 0 20 60 Insert 50. Then insert 66. Draw the resulEng AVL tree. 8 Red Black trees 30 15 70 20 60 How can we make the above tree a valid red-black tree Insert 50. Then insert 66. Draw the resulEng RBT. 9 Data structure Comparison Insert Find Avg Worst Avg Worst Sorted array Sorted Linked list Queue Skip list BST AVL/RBT Min-heap Hash table B-trees 10 Data structure Comparison Which of the following pairs of data structures, which of the pair is the beger choice for. • InserEng a list of sorted elements (worst case): A. AVL tree B. Binary search tree C. They are about equal • In-order traversal of elements: A. Hashtable B. Binary search tree C. They are about equal 11 Data structure Comparison Which of the following pairs of data structures, which of the pair is the beger choice for. • Smallest average-case (Big-O) Eme to find an element: A. Hashtable B. AVL tree C. They are about equal • Fastest actual Eme to find an element from secondary storage (NOT big-O) A. RBT B. AVL tree C. B-trees D. They are all about equal • Requires less space: A. MulE-way trie B. Ternary tree C. They are about equal 12 Some comic relief… hp://xkcd.com/1185/ 13 Some comic relief… hp://xkcd.com/1185/14 Good luck with the final! 15 .