Final Review Announcements

• PA4 is due tonight at 11pm • PA3 re-grade requests due by Monday • Study guide and pracce final posted on course website (website was upgraded to be mobile friendly). • Review session tomorrow from noon to 1pm • Secon A: If you have mulple finals (three or more) on Friday and need to take the exam on Wed, send me an email (with the necessary proof). • Secon B: If you have mulple finals (three or more) on Wed and need to take the exam on Friday, please respond to my Piazza poll Final Exam… • 4 Parts • Part 1: Basic knowledge of data structures and C++ – 20% to 30% of final score – Mulple choice • Part 2: Applicaon, Comparison and Implementaon of the data structures – 20% to 30% of final score – Short answers • Part 3: Simulang algorithms and run me analysis – 20% to 30% of final score – Short answers • Part 4: C++ and programming assignments

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/Part 2: B-trees ˜galles/visualization/BTree.html 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 Insert the value 42 into the following BTree. 4. Consider the following set of initially unrelated elements is S=0,1,2,3,4,5,6, 7, 8, 9, 10, 11, 12. Assume that the initial union-ﬁnd data structure is shown here, a forest of 12 singleton nodes with the header array initialized as shown.

0 1 2 3 4 5 6 7 8 9 10 11 12

-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 4. Consider the following set of initially unrelated elements is S=0,1,2,3,4,5,6, 7, 8, 9, 10, 11, 12. Assume(a) Draw that the the final initial forest union-find of up-trees that data results structure from the is following shown here, sequence a forest of operations of 12 singleton using union- nodes with the headerby-size. array initialized Break ties by as keeping shown. the first argument as the root. Union(0,2), Union(3,4), Union(9,7), Union(9,3), Union (6,8), Union(6,0), Union(12,6), Union(1,11), Union(9,6)

0 1 2 3 4 5 6 7 8 9 10 11 12

-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1

(a) Draw the ﬁnal forest of up-trees that results from the following sequence of operations using union- by-size. Break ties by keeping the ﬁrst argument as the root. Union(0,2), Union(3,4), Union(9,7), Union(9,3), Union (6,8), Union(6,0), Union(12,6), Union(1,11), Union(9,6)

(b) Draw the new forest of up-trees that results from doing a Find(4) with path compression on your forest of up-trees from (a).

(b) Draw the new forest of up-trees that results from doing a Find(4) with path compression on your forest of up-trees from (a). 4. Consider the following set of initially unrelated elements is S=0,1,2,3,4,5,6, 7, 8, 9, 10, 11, 12. Assume that the initial union-ﬁnd data structure is shown here, a forest of 12 singleton nodes with the header array initialized as shown.

0 1 2 3 4 5 6 7 8 9 10 11 12

-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1

(b) Draw the new forest of up-trees that results from doing a Find(4) with path compression on your forest of up-trees from (a).

9 8 12 0

3 7 2

4 1

11 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

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(a) Consider the following algorithm operating of a graph G(V, E) and a source vertex s i. Initially, set the visited field of all vertices in V as FALSE ii. Start at source vertex, s. Set the visited field of s as TRUE, set counter to 1 iii. Enqueue s into a queue iv. While the queue is not empty or counter less than or equal to V | | A. Dequeue the vertex v from the head of the queue B. For each of v0s neighbor vertex, w (with visited FALSE): • Mark the visited field of w as TRUE • Increment counter by 1 • Enqueue w into the queue i. Identify the above graph algorithm.

ii. Assume the graph is implemented as an adjacency list. Write the Big O running time of each step of the algorithm (against each line of above) and derive the tightest overall Big O bound. Data structure Comparison

Is operaon K faster in data structure X or data structure Y? Data structure Comparison Of the following pairs of data structures, which of the pair is the beer choice for... (circle 1 in each set)

• Inserng a list of sorted elements: Randomized search tree / Binary search tree / They are about equal • Ease of implementaon (assume it’s not built in): Skip list / Red-Black tree (RBT) / about equal • In-order traversal of elements: Hashtable / Binary search tree / They are about equal • Smallest average-case (Big-O) me to ﬁnd an element: Hashtable / AVL tree / They are about equal • Fastest actual me to ﬁnd an element from secondary storage (NOT big-O): RBT / AVL tree / B-trees/They are all about equal • Requires less space: Mul-way trie / Ternary tree / They are about equal • Congratulaons on pulling through – you are a survivor ! • Hope you go on to do wonderful things with your knowledge of advanced data structures.

Good luck with PA4, the ﬁnal and life in general J