and algorithms CONTENTS Process for Design and Analysis of Algorithms Understanding the Problem

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1 Contents i advanced anced data structures and algorithms FOR m.tech (jntu - hyderabad) i year i semester (COMMON TO CSE, CS,, IT,, WT AND SE) CONTENTS UNIT - I [CH. H. - 1] ] [INTRODUCTION INTRODUCTION] INTRODUCTION TO O ALGORITHM Definition of Algorithm Notation of Algorithm Properties of Algorithm A Typical Example Process for Design and Analysis of Algorithms Understanding the Problem Desire Problem Solving Technique echnique Design of an Algorithm Validation of an Algorithm Analyze the Algorithm Coding of an Algorithm Testing of an Algorithm PSEUDO Code for Expressing Algorithms PERFORMANCE ANALYSIS Space Complexity

2 ii Contents Time Complexity The Unit of Algorithm s Runun-Time The Order of Growth Best Case, Average Case and Worst Case Efficiencies Solved Problems Comparison Between Priori Analysis and Posteriori Analysis ASYMPTOTIC TIC NOTATION TION Big-Oh (O) Notation Big-Oh Ratio Theorem Big-oh Notation Theorem Basic Efficiency Classes Omega (Ω) ) Notation Big Omega Ratio Theorem Little-Omega Notation (w) Theta (θ) ) Notation Theta Ratio Theorem Theta Notation Theorem Small-oh (o) Notation Order of Growth using Limits (Alternative Definitions for Asymptotic Notations) COMPLEXITY ANALYSIS EXAMPLES

3 Contents iii UNIT - I [CH. H. - 2] ] [DATA STRUCTURES] INTRODUCTION TO DATA A STRUCTURES LINEAR AND NON LINEAR DATA A STRUCTURES Linear Data Structure Non-Linear Data Structure ABSTRACT DATA TYPE (ADT) CONCEPT Linear List ADT Array Implementation Linked Implementation ARRAY Y REPRESENTATION TION Representation Changing the Length of a One-Dimensional Array The Class ArrayLinearList Constructors for ArrayLinearList Elementary Methods of ArrayLinearList An Interator for ArrayLinear List Using a Top op-l -Level Class Using a Member Class VECTOR OR REPRESENTATION TION LINKED REPRESENTATION TION Singly Linked List The Representation Operations Insertion Deletion Search

4 iv Contents Doubly Linked List Operations Inserting a Node in Doubly Linked List at the Beginning Doubly Linked List Deletion CIRCULAR LIST Counting Nodes in a Circular List Printing the Contents of a Circular List Operations Insertion Deletion REPRESENTATION TION OF SINGLE AND TWO DIMENSIONAL ARRAYS YS One-Dimensional Arrays Two wo Dimensional Arrays SPARSE MATRICES TRICES Array Representation Representation using a Single Linear List UNIT - II [CH. - 3] ] [STACKS AND QUEUES] INTRODUCTION TO O STACKS Stack ADT Array Representation Implementation as a Subclass Performance Measurement Linked Representation Performance Measurement

5 Contents v 3.2 QUEUES Queue ADT Array Representation The Class ArrayQueue Linked Representation INFIX TO POSTFIX CONVERSION USING STACK IMPLEMENTATION TION OF RECURSION CIRCULAR QUEUE Operations Insert Delete DEQUE ADT Array Implementation of Deque Linked Implementation of Deque PRIORITY QUEUE ADT Main Priority Queues Operations Auxiliary Priority Queues Operations IMPLEMENTATION TION USING HEAPS Insertion into Max Heap Deletion from Max Heap Example Problem JAVA.UTIL A.UTIL PACKA CKAGES Array List Obtaining an Array from a ArrayList Linked List Vector Classes Stacks in Java.util Queues Interface Interators in Java.util

6 vi Contents UNIT - III [CH. H. - 4] ] [SEARCHING SEARCHING] SEARCHING LINEAR AND BINARY SEARCH METHODS Linear Search Binary Search HASHING Hash Functions Division Method Mid-Square Method Folding Method Multiplicative Method COLLISION RESOLUTION METHODS Open Addressing Linear Probing Quadratic Probing Double Hashing Chaining Rehashing Extendible Hashing HASHING IN JAVA.UTIL Hash Map Hash Set Hash Table able UNIT - III [CH. - 5] ] [SORTING SORTING] SORTING BUBBLE SORT INSERTION SORT

7 Contents vii 5.4 QUICK SORT MERGE SORT HEAP SORT RADIX SORT COMPARISON OF SORTING METHODS UNIT - IV [CH. H. - 6] ] [TREES TREES] INTRODUCTION TO TREES ORDINARY (OR) BASIC TREE TERMINOLOGY BINARY TREE TERMINOLOGY PROPERTIES OF BINARY TREES BINARY TREE ADT REPRESENTATION TION OF BINARY Y TREE ADT Array Representation Linked Representation RECURSIVE AND NON-RECURSIVE TRAVERSALS Pre re-oder Traversal raversal In-Order Traversal raversal Post ost-order Traversal Levelevel-Order Traversal raversal JAVA CODE FOR TRAVERSALS THREADED BINARY TREE UNIT - IV [CH. - 7] ] [GRAPHS GRAPHS] INTRODUCTION TO GRAPHS GRAPH TERMINOLOGY PROPERTIES OF GRAPHS GRAPH ADT

8 viii Contents 7.5 REPRESENTATION TION OF GRAPH ADT Representation of Unweighted Graphs Representation of Weighted Graphs GRAPH TRAVERSALS/SEARCH METHODS Depth First Search (DFS) Breadth First Search (BFS) JAVA CODE FOR GRAPH TRAVERSALS Java Program to Traverse a Graph using DFS Java Program to Traverse a Graph using BFS APPLICATIONS OF GRAPHS Finding a Path ath Connected Graphs and Components Component Labelling Spanning Trees MINIMUM COST SPANNING TREE USING KRUSKAL S S ALGORITHM DIJKSTAR AR S S ALGORITHM FOR SINGLE SOURCE SHORTEST PATH TH PROBLEM UNIT - V [CH. - 8] ] [BINARY SEARCH TREES AND BALANCED SEARCH TREES] BINARY SEARCH TREE Indexed Binary Search Trees BINARY SEARCH TREE ADT Insertion DELETION Searching Ascend( ) Height of Binary Search Tree Implementation of Binary Search Tree ree

9 Contents ix 8.3 BALANCED SEARCH TREES AVL Trees Height of an AVL Tree ree Representation of an AVL Tree Insertion into an AVL Search Tree Deletion from an AVL Search Tree ree Red Black Trees rees Representation of a Red-Black Tree Searching a Red-Black Tree Insertion into a Red-Black Tree ree Deletion from Red-Black Tree ree B-Trees Indexed Sequential Access Method (ISAM) Representation of B-Trees rees B-Tree ree of Order m Height of B-tree Searching a B-tree Insertion into a B-Tree ree Deletion from B-tree Trees in Java.util Treeset Tree Map Classes Tries Standard Tries Compressed Tries Suffix Tries Comparisons of Search Trees

10 x Contents 8.4 TEXT COMPRESSION Huffman Coding and Decoding PATTERN MATCHING KMP Algorithm