Computer Science II Fall 2009

Transcription

1 Name: Computer Science II Fall 2009 Exam #2 Closed book and notes. This exam should have five problems and six pages. Problem 0: [1 point] On a scale of 0 5, where 5 is highest, I think I deserve a for overall class participation. (Feel free to justify your answer.) Problem 1: [20 points] Run-length encoding attempts to compress a sequence of values by replacing runs of identical values into pairs of values: the number of identical values in a row and the value itself. (For example, the sequence [30, 30, 20, 20, 20, 20] could be represented as [2, 30, 4, 20].) Write a static method called expand that takes a queue of integers representing a run-length encoded sequence, and returns a queue of integers containing the original, uncompressed sequence. You may assume that the input queue contains an even number of values. For full credit, the queue passed to expand should contain the same values after the call as it did before.

2 Problem 2: [24 points] Part a) Write a static method that takes two BinaryTree instances and returns true if their leftmost nodes contain identical values. (Put another way, if the input trees were ordered as Binary Search Trees, the method would be asking whether the smallest items in each of the trees are the same.) If one or both of the inputs are null your method should return false. For full credit, your solution should use recursion. I ll do the hard part to get you started: public static boolean sameleftmost(binarytree t1, BinaryTree t2) { Part b) What is the complexity of sameleftmost? That is, if the input trees contain N and M nodes respectively, how much work does sameleftmost do? Explain briefly.

3 Problem 3: [20 points] Part a) Below, draw the Binary Search Tree (BST) that would result from inserting the following sequence of values into an initially-empty BST: 50, 30, 80, 40, 45, 35, 90, 60, 85. (That is, first insert a 50 into an empty tree, then insert the 30 into the tree, etc.) Part b) Draw the BST that would result from removing the 30 and 45 from the tree above. Part c) Is it possible to create a full BST that contains the values from Part b? If so, draw the tree. If not, explain why not.

4 Problem 4: [15 Points] The code we wrote in class to evaluate postfix expressions is shown below. It assumes that all operators are binary operators that is, that each takes two arguments. Summarize the changes to the code that would be necessary if we wanted to introduce a unary minus operator for negation (we could use the symbol ~ to avoid confusion with subtraction). Please make notations next to the code explaing the changes. public static void main(string[] args) { Stack<Integer> operands = new Stack<Integer>(); Scanner keyboardinput = new Scanner(System.in); String theline = keyboardinput.nextline(); Scanner input = new Scanner(theLine); while (input.hasnext()) { if (input.hasnextint()) { operands.push(input.nextint()); else { int num2 = operands.pop(); int num1 = operands.pop(); char op = (input.next()).charat(0); switch (op) { case '+' : operands.push(num1+num2); case '-' : operands.push(num1-num2); case '*' : operands.push(num1*num2); case '/' : operands.push(num1/num2); default: System.out.println("Unknown op: "+op); System.out.println("Result is "+operands.pop());

5 Problem 5: [20 points] Your roommate was hard at work building a PriorityQueue when you came home the other night. He knows you re a CS whiz, and asked you for some advice: He s not sure whether it would be better to implement the PriorityQueue via a LinkedList, a Heap, or a Binary Search Tree. Below, fill in the worst case complexity estimates for the various implementation options. For full credit, briefly explain your answers. adding removing Linked List Heap BST

6 Class BinaryTree<E> java.lang.object BinaryTree<E> Class for a binary tree that stores type E objects. Author: Koffman and Wolfgang Constructor Summary BinaryTree() BinaryTree(E data, BinaryTree<E> lefttree, BinaryTree<E> righttree) Constructs a new binary tree with data in its root, lefttree as its left subtree and righttree as its right subtree. Method Summary E getdata() Return the data field of the root BinaryTree<E> getleftsubtree() Return the left subtree. BinaryTree<E> getrightsubtree() Return the right sub-tree boolean isleaf() Determine whether this tree is a leaf. String tostring() Constructor Detail BinaryTree public BinaryTree() BinaryTree public BinaryTree(E data, BinaryTree<E> lefttree, BinaryTree<E> righttree) Constructs a new binary tree with data in its root,lefttree as its left subtree and righttree as its right subtree. Method Detail getleftsubtree public BinaryTree<E> getleftsubtree() Return the left subtree. The left subtree or null if either the root or the left subtree is null getrightsubtree public BinaryTree<E> getrightsubtree() Return the right sub-tree the right sub-tree or null if either the root or the right subtree is null. getdata public E getdata() Return the data field of the root the data field of the root or null if the root is null isleaf public boolean isleaf() Determine whether this tree is a leaf. true if the root has no children tostring public String tostring() Overrides: tostring in class Object