Assignment 4 - AVL Binary Search Trees

Transcription

1 Assignment 4 - AVL Binary Search Trees MTE Data Structures and Algorithms DUE: July 22-11:59 PM 1 Introduction For this assignment, you will be implementing a basic AVL tree. AVL trees are an important sub-class of binary search trees (BSTs) since they guarantee search times of O(log n) for any arrangement of input data (normal BSTs can do as poorly as O(n) if sorted data is put into the tree). 2 Data Structures The data structures we will be using to build our AVL tree are specified below: // An AVL Node typedef struct AVLNode_t char *data; // C strings are the data (dynamic arrays of chars) int NodeCnt; // How many nodes we have that contain the same value enum L_UNB, L_HVY, BAL, R_HVY, R_UNB} BF; // balance factor struct AVLNode_t *leftchild, *rightchild, *parent; } AVLNode; // The overall structure for a tree typedef struct AVLTree_t AVLNode *root; int size; } AVLTree; You may notice the use of an enum type in the above data structures. Enums are a very limited data type that allows the definition and use of various constants. An enum is actually an integer, however each of the enum constants are given a different integer value 1

2 (L UNB = 0, L HVY = 1, etc.). This allows one to use the enum in if statements with much greater legibility: if (node->bf == BAL) \\the node is balanced They can also be used in switch statements: switch (node->bf) case BAL: \\Balanced case case R_HVY: \\Node is left heavy case L_HVY: \\Node is right heavy... } 3 Functions This lab is much shorter than the previous two, however get a start on it early as some of the insertion sub-cases are tricky. As usual, you ARE NOT limited to the functions below, so feel free to add functions if they make the assignment easier (but don t modify AVL.h, prototype in AVL.c). The functions you are required to program are listed below: void DeleteAVLTree(AVLTree *tree) Frees an AVL tree and all it s nodes. AVLTree *NewAVLTree() Creates a new AVLTree and initializes the root to NULL and the number of nodes to 0. AVLTree *BuildAVLTree(FILE *infile) Takes a file pointer as input and builds an AVL tree from the information in the file. The first number in the file (n) will represent the number of data points to be put into the tree. 2

3 The following n strings are data for the tree. The next integer will be the number of data points to be used for the subsequent tree, followed by it s data. For example: 2 //a tree with 2 nodes Jane //data 1 Bob //data 2 3 //a tree with 3 nodes Anne //data 1 Luke //data 2 Julie //data 3 However, you only need to input one tree at a time (but leave the file open so that future trees can be read). Each string has a max length of 14 characters, however don t simply allocate 15 byte chunks of memory to store the strings. Instead, read each string into a temporary buffer (char array 15 chars long), and allocate memory based on the length of the string (determined using strlen( ) - look it up on void InsertNodeAVL(AVLTree *tree, char *element) This function should insert a node according to the AVL insertion rules. Use the function strcmp( ) to compare strings (look it up on For simplicity, the rules of AVL insertion have been summarized for you here: When inserting a node, ensure that data of every node is strictly greater than the data of the nodes in its left subtree, and strictly less than those in its right subtree. If a node with equal data is found, its NodeCnt should be incremented by one After insertion you have to re-calculate balance factors of all the nodes from the new node to the root. So, follow parent pointers back toward the root, calculating each nodes new balance factor based on i) its previous balance factor, ii) whether you have arrived there from a left or right child. Calculation stops under one of 3 conditions: 1. You re-calculate a node s balance factor as balanced 2. You reach the root, and no node s re-calculated balance factor is unbalanced. 3. You re-calculate a node s balance factor as unbalanced. If you reach the third condition then you have to rebalance the tree around the earliest unbalanced ancestor (EUA). In order to rebalance, you have to consider 4 separate cases (we will only show 2 cases, as the others are symmetrical). For this, we will call the left child of the EUA the EUAC (child): 1. If the newly-inserted node is in the left subtree of EUAC, perform a single right rotation around the EUA. After the rotation both EUA and EUAC should have balance factors set to balanced, and no other balance factors are changed. 3

4 2. If the newly-inserted node is in the right subtree of EUAC, call EUAC s right child EUAGC (grandchild) and perform a double right rotation around the EUA. Now you must consider 3 subcases: (a) EUAGC s balance factor is left heavy: set the EUA s balance factor to right heavy. Set EUAC s and EUAGC s balance factors to balanced. (b) EUAGC s balance factor is balanced: set the EUA s, EUAC s, and EUAGC s balance factors to balanced. (c) EUAGC s balance factor is right heavy: set EUAC s balance factor to left heavy. Set EUA s and EUAGC s balance factors to balanced. void PrintInOrder(AVLTree *tree) This function should begin by printing a small header containing the size of the tree. Then it should perform an InOrder traversal of the tree, printing out each element as it traverses the tree. The format should match the sample output (ie: print the element, along with the NodeCnt, the level on which it was found and the node s balance factor). 4 BONUS!!! - Don t waste your time here For some bonus marks, implement a function, void FancyPrint(AVLTree *tree) that prints out a tree in a fancy graphical format (ie: like you would draw a tree by hand - see below for an example). The root should be displayed at the center of the console, with subsequent children on the left and right side of their parent. Node data and the NodeCnt should be printed for each node, but the exact format is up to you. It should be able to print a tree of depth 4. LH 100 / \ LU LH / \ / \ RH B RH B / \ \ B LH B / B 36 4

5 Of course, your example will be printing strings instead of integers, and will have to print a NodeCnt somewhere :-) 5 Submission - Code The only file to be handed in is the completed version of AVL.c. The files AVL.h and AVL main.c have been provided for you along with some sample input (data.txt) and output (sampout.txt), the output that should be generated when tsp main.c is run. A template for AVL.c has also been provided for you to complete. Remember to hand in both an electronic copy and a hard copy of your assignment. Again, a different copy of AVL main.c may be used to test your electronic copy of the program, so don t forget to test every function you write. 6 Grading This assignment is due on July 22-11:59 PM. This is the marking scheme Correctness of Output 50% Algorithm Descriptions (comments at top of functions) 20% Style (other comments, indentation, variable names, etc.) 30% Bonus 10% 5