6 Data Structures. 6.1 Quadtree. 6.2 Binary search tree

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1 6 Data Structures 6.1 Quadtree he basic principles of quadtrees have been outlined in the lecture. ollow these steps for the implementation in Java: 1. Download the quadtree.zip file from the course web page and unpack the archive. Copy the Java files into the src folder and the image in the root folder of your project. 2. Run QuadtreeDemoProgram in order to see how the Domain class works. 3. Implement the Quadree and QuadreeNode classes using the QuadtreeDemoProgram as test case. 4. Use a photograph of yourself as another test case. 6.2 Binary search tree A binary search tree (BS) is a data structure that is often used to store data in an ordered manner. Each node of a BS contains a left pointer, a right pointer and a data element. he nodes in a BS are arranged in order: or each node, all values in the left subtree are less than the value of the node. Correspondingly, all values in the right subtree are greater than the value of the node. he root node is the topmost node of the tree. igure 6.1 shows a binary search tree that contains integer values. he UML class diagram in igure 6.2 shows two classes that represent a binary search tree for integer values. he BinarySearchree class has an association with a BSNode that is the root of the tree. he insert method adds a new node to the tree. If the tree is empty the method creates the root node; otherwise it inserts the specified number in the root node. he contains method checks if the specified number is in the tree. If the tree is not empty, the method delegates the task to the root node. Similarly, the print method also delegates the work to the root node. he BSNode class holds the data values and is associated with a left BSNode and a right BSNode. he insert method inserts the specified number recursively either in the left or the right subtree of the node (see igure 6.3). he contains method searches either the left or the right subtree. In the print method, first the left node is printed (if there is one), then the value of this node is printed and finally the right node is printed (if there is one). 30

2 pointer to left node 5 data element pointer to right node complete notation compact notation igure 6.1: A binary search tree with six nodes BinarySearchree - root: BSNode + insert(n: int): void + contains(n: int): boolean + print(): void BSNode - value: int - left: BSNode - right: BSNode + BSNode(n: int) + insert(n: int): void + contains(n: int): boolean + print(): void igure 6.2: UML class diagram for binary search trees insert(n: int): void left = null left = left.insert(n) new BSNode(n) n < value n > value right = null right = right.insert(n) new BSNode(n) igure 6.3: Nassi-Shneidermann diagram for the insert method of the BSNode class

3 Assignment Implement in Java the classes BinarySearchree and BSNode as described above. In order to verify that your classes work, use the following demonstration class: public class BinarySearchreeDemoProgram { public static void main ( String [] args ) { BinarySearchree tree = new BinarySearchree (); // fill tree tree. insert (4); tree. insert (2); tree. insert (1); tree. insert (3); tree. insert (99); tree. insert ( -2); } } // print tree System. out. println (" ree "); tree. print (); System. out. println (" Contains "); System. out. println (" -2: " + tree. contains ( -2)); System. out. println (" 4: " + tree. contains (4)); System. out. println (" 99: " + tree. contains (99)); System. out. println (" -10: " + tree. contains ( -10)); he output of the test program should be as follows: ree [ ] Contains -2: true 4: true 99: true -10: false 6.3 Stack (optional) A stack is a data structure implementing last in and first out (LIO) access via two fundamental operations: push and pop.he push operation adds an item to the top of the list and the pop operation removes the top item from of the list. A stack can be easily created through a linked list implementation. he Java Collection framework provides a generic implementation for stacks with the following essential methods.

4 igure 6.4: Representation of a stack igure 6.5: UML class diagram java.util.stack Assignments Calculators employing reverse Polish notation (postfix notation) use a stack structure to hold values. he calculation: ((1 + 2) * 4) + 3 can be written down like this in postfix notation with the advantage of no precedence rules and parentheses needed (6.1) he expression is evaluated from the left to right using a stack: 1. push when encountering an operand and 2. pop two operands and evaluate the value when encountering an operation. 3. push the result he following stack operations are performed (the stack content is displayed after each operation):

5 input operation stack 1 push push 2 1, 2 + pop, pop, push push 4 3, 4 pop, pop, push push 3 12, 3 + pop, pop, push he final result, 15, lies on the top of the stack at the end of the calculation. Create a class for postfix calculators based on a stack for double objects (java.lang.double). Use the given UML class diagram to implement the calculator class. igure 6.6: UML class diagram PostfixCalculator Use the following demo program to test your implementation. public class PostfixCalculatorDemoProgram { public static void main ( String [] args ) { PostfixCalculator calc = new PostfixCalculator (); calc. push (1); calc. push (2); calc. performoperation ( + ); calc. push (4); calc. performoperation ( * ); calc. push (3); calc. performoperation ( + );

6 } }

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