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CS 240 Computer Science II Exam 3 Page 1 Spring ‘03 April 2, 2003 Name_____________________________ 1. Linked lists. a) Fill in the Java inner class below to support the implementation of a linked list in which each node holds one String and a next reference. [5 pts] private class Node { private _______ info; private _______ next; private Node(String s){ info = _______; _________ = ________; } } b) Indicate how the head pointer instance variable of the linked list is declared and start as the empty list. The linked list starts with a dummy head node. [4 pts] ___________ head = new _______________________; c) Draw a box and pointer diagram to represent the ordered list (“cat”, “dog”, “fish”) as pointed to by head. The linked list starts with a dummy head node. [5 pts] d) Fill in the blanks so that Java code that would add the value “ant” as a new first node of this ordered list. [5 pts] Node temp = new Node (“ant”); temp. _______ = _______ . ________; head.______ = ______ ; 2. Fill in the code below to complete the enqueue operation using a singly linked list implementation (no dummy head node). [5 pts] public void enqueue(Object item){ if (item == null) throw new IllegalArgumentException ("Trying to insert null onto the queue"); Node node = new Node (______); if (size == 0){ head = _________; } else { tail._______ = _______; } tail = node; size_____; } CS 240 Computer Science II Exam 3 Page 2 3. Give the time complexities, O(1) or O(n) for each of the operations of the implied data structure that are implemented as a linked list. _________ pop() [8 pts] _________ insert(item) //into a sorted list _________ dequeue() _________ insert(item) //unsorted list _________ enqueue(item) _________ getNextItem() _________ push(item) _________ isThere(item) 4. Fill in the blanks to implement a recursive binary search algorithm. Assume there is a public helper function that calls the recursive function: public int binarySearch(Comparable key){ return binarySearch(key, 0, vec.length – 1); } [10 pts] private int binarySearch(Comparable key, int lo, int hi){ if( ____ > ____ ) { return -1; //not found } else { int mid = ____________; int comp = vec[mid].compareTo(key); if(comp > 0){ return binarySearch(key, ________,________); } else if(comp ____ 0){ return binarySearch(key, ________,________); } else { // found it return ________ ; } } } 5. A recursive definition for determining the greatest common denominator is credited to Euclid. For example, the GCD of 16 and 12 is 4. If b==0 then the GCD(a,b) = a, otherwise the GCD (a,b) = GCD (b, a%b) //% is modulus [10 pts] Write this recursive Java function to implement the calculation of the greatest common denomionator. public static int GCD(int a, int b){ } CS 240 Computer Science II Exam 3 Page 3 6. Trees. [10 pts] a) Assume the root is at level 0. What is the level of node F? ____ b) Circle the largest subtree that is a binary tree. c) How many leaves are there in the whole tree? _____ d) If each node could have at most three children, how many nodes total could be stored in this tree without adding any more levels? ______ e) List the ancestors of node H ______________________ A / \ B C / \ \ D E F / \ /|\ G H I J K f) List the descendants of node C. _______________________ g) Draw the conversion of this general tree as a binary tree (left child as first child of the general tree and right child as a sibling in the general tree) 7. Assume nodes in a binary tree are defined in an inner class having the following instance variables. Comparable info; BSTNode left; BSTNode right; a) Finish the recursive Java function to count the number of nodes in a binary tree. The algorithm works as follows. If the root (of tree or subtree) is null then return 0; otherwise return the sum of the nodes on the left and the nodes on the right, plus one for the root. [7 pts] public int Counter( _________ curNode) { if(curNode _____________ ) return ____ ; return Counter ( _________________ ) + __________ ( _________________ ) + ____ ; } b) Finish the recursive Java function to return if the item exists in the binary search tree. [8 pts] public boolean isThere( BSTNode root, Comparable item) { if (_______ == null) return false; int comp = item.compareTo( _________ . ___________) if(comp == 0) return ___________ ; if(comp < 0) return isThere ( ______ . ______ , item ) else } return isThere (_______ . _______, item); CS 240 Computer Science II Exam 3 Page 4 8. Create a binary search tree from the following character data entered into the bst left to right. [4 pts] DTWABQMN a) List the nodes of your tree above from an inorder traversal. [3 pts] b) List the nodes of your tree above from a preorder traversal. [3 pts] 9. Draw the following infix arithmetic expression as an expression tree. Represent precedence properly. [4 pts] (a+b)-c*(d+e) a) Show a postorder traversal of your expression tree. [3 pts] 10. True/False [6 pts] ______ A doubly linked list permits traversal in both forward and backward directions ______ A doubly linked list doubles the algorithm complexity of the operations over a singly linked list. ______ Most operations on a binary tree depends on the depth of the tree which is logarithmic to its capacity. ______ A binary search tree always generates the same inorder traversal regardless of the sequence the nodes were entered into the tree. ______ A postorder traversal is the same as a reversed preorder travsersal. ______ The maximum number of nodes in a binary tree at level N is 2N