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TDDC32 Tryout Exam Rules: • • • • • • No materials allowed A total of 21 points can be opbtained. For a grade of 3 the number of points required is 11. For a grade of 4 it’s 14 and for a grade of 5 it’s 17. For every assignment you get 3 points. If there are 2 subassinments per assignment you get 1.5 points per subassinment. If there are 3 subassinments then you get 1 point per subassinment. Note that the number of assignments and the points per assignment may change in the real exam. The problem 7 is to be added . Happy exercising Assignments: 1) OOAD principles: 1. Describe 2 principles of OOAD 2. What is a method signature and how does it relate to polymorphism? 2) UML 1. What are use case diagrams and where are they used? 2. What is the similarity and difference between a sequence diagram and a collaboration diagram 3) AVL trees 1. Construct an AVL tree, when the following values, arriving in the following order: 9 6 7 2 1 11 10 3 8 4 5: 2. What is a FIBONACCI tree and why is it important? 4) Splay trees: 1. What is the advantage of using splay trees over AVL trees? 2. Show, step by step how a removal of the value 5 occurs in the following splay tree: 1 2 7 6 5 3 4 5) Hashtables 1. Why/when does one want to increase the size of a hashtable? 2. For a hashtable of size 11 the primary hash function is h(k) = k % 11. Choose a dual hash function d(k), explain your choice if different from the standard one, and insert: 11 76 22 44 91 84 47 75 14 55. Show the final hashtable, h(k), d(k), and the probed locations in the hashtable for all the values to be inserted. 6) Skip Lists & Heaps 1. What is the advantage of skip lists over lists implemented with a) arrays b) linked lists with respect to find() and insert()? 2. How many children can a node have in a heap and what is the heap order property? 7) (a,b) Trees 1. Show what happens step by step when you remove the values 20, 3 from the following (2,5) tree. 20 10 3 6 30 18 23 26 27 40 50 33 39 42 44 53 56 2. Show what happens step by step when you add the values 62, 63, 24, 25 to the following (2,5) tree: 59 20 10 3 6 30 18 23 26 27 40 50 33 39 42 44 53 56 59 3. Show that when you have a split of an (inner) node in an (a, b) tree, the number of children of any of the 2 resulting nodes is larger than the minimum number of children allowed. A node is splitted if it has at least b+1 children. As we promote he median key, the smaller of the nodes resulting in the split will have the number of children, denoted here as c as follows. If b is odd then c = (b+1)/2. If b is even then c = b / 2. From the definition of (a,b) trees we know that a ≤ (b+1)/2. Now if b is odd then it’s immediately visible that c ≥ a. If b is even then a ≤ b/2, so again c ≥ a. q.e.d.