CS200 Midterm 2 Fall 2007

Transcription

1 CS200 Midterm 2 Fall 2007 Name Topic Possible Received Generics, programming 10 Trees 35 Priority Queues, Heaps 30 Graphs 25 TOTAL 100

2 1. Generics/Programming [10 points] a. [4 points] Why is it important to create a tostring method in a new data structure implementation? b. [6 points] Spot the bugs in the following code. Underline each problem and suggest a fix for it. Make clear which problem is being fixed by which modification. ArrayList<Integer> somenums = new ArrayList(); somenums.add(0); ArrayList<Object> morenums = somenums; Integer first = morenums.get(0);. 2. Trees [35 points] a. [7 points] Circle T or F for True or False for the following statements. T F A preorder traversal of a binary search tree produces a lexicographic ordering of the vertices. T F A full (Rosen s definition) 3-ary tree with 49 vertices has 32 leaves. T F A full (either definition) binary tree with 64 leaves has 63 internal vertices. T F A tree is a graph. T F A preorder traversal of a heap produces a lexicographic ordering of the vertices. T F A binary tree with 256 vertices has a maximum height of 8. T F A balanced tree is a complete tree.

3 b. [15 points] Programming. Below is the code from Carrano and Prichard for BinarySearchTree. The instance variables and methods available to you are shown. You can use only these methods and methods built-in to Java. (You are not being given access to the protected methods in the class.) Fill in code for the insert method. If you need more space, use the back of the last page as well. public class BinarySearchTree<T extends KeyedItem<KT>, KT extends Comparable<? super KT>> extends BinaryTreeBasis<T> { // from BinaryTreeBasis, inherits isempty(), makeempty(), getrootitem(), // the use of the constructors and // instance variable protected TreeNode<T> root; // TreeNode has: TreeNode(T newitem, TreeNode<T> left, TreeNode<T> right) // getitem(),setitem(t newitem), getleft(),setleft(treenode<t> left), // getright(),setright(treenode<t> right) public BinarySearchTree(T rootitem) { public void setrootitem(t newitem) { public T retrieve(kt searchkey) { public void delete(kt searchkey) throws TreeException { public void insert(t newitem) {

4 c. [8 points] Draw the binary search tree that results i. from adding, in this order, the letters: M A I B D C T E F R ii. then draw the tree that results after removing the failing grades: D and F d. [5 points] Short Answer. Traversals are defined over ordered rooted trees. Why is it necessary to have ordered rooted trees? 3. Priority Queues/Heaps [30 points] a. [6 points] Short Answer. Carrano and Prichard describe a Priority Queue as a special case of the ADT Table. What is a Table? How can a Priority Queue be a Table?

5 b. [8 points] Circle T or F for True or False for the following statements. T F A binary search tree implementation of the Table ADT has non-linear Big-O for retrieval in average case. T F A Table cannot be implemented using a linked list. T F The array [5, 18, 101, 30, 22, 202, 101] is a heap with root as minimum value. T F When a value is removed from the heap [10, 101, 12, 231, 102, 72, 142], the array becomes [12, 101, 231, 102, 72, 142]. T F A semiheap is a complete binary tree. T F The rightmost leaf contains the first item to be removed from a heap implementation of a priority queue. T F Heapsort is O(n * log n) in the worst case. T F Heapsort can be made in place by iteratively constructing larger semi-heaps until the array becomes a heap. c. [10 points] Find and fix any bugs in the following code for heaprebuild, assume it is a maxheap. protected void heaprebuild(int root) { int child = 2 * root; if ( child < items.size() ) { int rightchild = child + 1; if (compareitems(items.get(root), items.get(child)) > 0) { T temp = items.get(root); items.set(root, items.get(child)); items.set(child, temp); heaprebuild(root);

6 d. [6 points] Construct a heap (represented as an array) with the inorder traversal of {13, 10, 18, 0, 21, 5, Graphs [25 points] a. [6 points] For which values of n (numbers of vertices) are the following special graphs bipartite? i. Complete ( K n ) ii. Cycle ( C n ) iii. Wheel (W n ) b. [4 points] Circle T or F for True or False if the following graphs can exist: T F A simple graph with 15 vertices each of degree 5 T F A multigraph with 10 vertices, 20 edges and 1 isolated vertex T F A simple directed graph with outdegree {1, 1, 1, 2 and indegree {1, 2, 2, 1 T F A directed multigraph with outdegree {1, 1, 1, 2 and indegree {1, 2, 2, 1 c. [6 points] Label each graph below with one of the following types: simple graph, multigraph, pseudograph, or none of these a b c

7 d. [9 points] For the following graph, f 5 a 3 b 6 4 c 7 e d i. show how it would be represented as an adjacency matrix. ii. show the depth first traversal starting from vertex e, assuming that 1) whenever a choice is offered, the alphabetically lower vertex is chosen and 2) the implementation is recursive so that the program stack is used when backtracking.