Table Of Content

Data Structures & Algorithms About the Tutorial Data Structures are the programmatic way of storing data so that data can be used efficiently. Almost every enterprise application uses various types of data structures in one or the other way. This tutorial will give you a great understanding on Data Structures needed to understand the complexity of enterprise level applications and need of algorithms, and data structures. Audience This tutorial is designed for Computer Science graduates as well as Software Professionals who are willing to learn data structures and algorithm programming in simple and easy steps. After completing this tutorial you will be at intermediate level of expertise from where you can take yourself to higher level of expertise. Prerequisites Before proceeding with this tutorial, you should have a basic understanding of C programming language, text editor, and execution of programs, etc. Copyright and Disclaimer © Copyright 2016 by Tutorials Point (I) Pvt. Ltd. All the content and graphics published in this e-book are the property of Tutorials Point (I) Pvt. Ltd. The user of this e-book is prohibited to reuse, retain, copy, distribute or republish any contents or a part of contents of this e-book in any manner without written consent of the publisher. We strive to update the contents of our website and tutorials as timely and as precisely as possible, however, the contents may contain inaccuracies or errors. Tutorials Point (I) Pvt. Ltd. provides no guarantee regarding the accuracy, timeliness or completeness of our website or its contents including this tutorial. If you discover any errors on our website or in this tutorial, please notify us at [email protected] i Data Structures & Algorithms Compile & Execute Online For most of the examples given in this tutorial you will find Try it option, so just make use of this option to execute your programs on the spot and enjoy your learning. Try the following example using the Try it option available at the top right corner of the following sample code box − #include <stdio.h> int main(){ /* My first program in C */ printf("Hello, World! \n"); return 0; } ii Data Structures & Algorithms Table of Contents About the Tutorial ............................................................................................................................................ i Audience ........................................................................................................................................................... i Prerequisites ..................................................................................................................................................... i Copyright and Disclaimer ................................................................................................................................. i Compile & Execute Online ............................................................................................................................... ii Table of Contents ........................................................................................................................................... iii BASICS ......................................................................................................................................... 1 1. Overview .................................................................................................................................................. 2 Characteristics of a Data Structure .................................................................................................................. 2 Need for Data Structure .................................................................................................................................. 2 Execution Time Cases ...................................................................................................................................... 3 Basic Terminology ........................................................................................................................................... 3 2. Environment Setup ................................................................................................................................... 4 Try it Option Online ......................................................................................................................................... 4 Local Environment Setup ................................................................................................................................. 4 Installation on UNIX/Linux ............................................................................................................................... 5 Installation on Mac OS..................................................................................................................................... 5 Installation on Windows .................................................................................................................................. 6 ALGORITHM ................................................................................................................................ 7 3. Algorithms ─ Basics ................................................................................................................................... 8 Characteristics of an Algorithm ....................................................................................................................... 8 How to Write an Algorithm? ........................................................................................................................... 9 Algorithm Analysis ......................................................................................................................................... 10 Algorithm Complexity .................................................................................................................................... 11 Space Complexity .......................................................................................................................................... 11 Time Complexity ............................................................................................................................................ 11 4. Asymptotic Analysis ................................................................................................................................ 12 Asymptotic Notations .................................................................................................................................... 12 Common Asymptotic Notations .................................................................................................................... 15 5. Greedy Algorithms .................................................................................................................................. 16 Counting Coins ............................................................................................................................................... 16 6. Divide & Conquer .................................................................................................................................... 18 Divide/Break .................................................................................................................................................. 18 Conquer/Solve ............................................................................................................................................... 18 Merge/Combine ............................................................................................................................................ 19 7. Dynamic Programming ............................................................................................................................ 20 iii Data Structures & Algorithms DATA STRUCTURES ................................................................................................................... 21 8. Basic Concepts ........................................................................................................................................ 22 Data Definition .............................................................................................................................................. 22 Data Object .................................................................................................................................................... 22 Data Type ....................................................................................................................................................... 22 Basic Operations ............................................................................................................................................ 23 9. Arrays ..................................................................................................................................................... 24 Array Representation .................................................................................................................................... 24 Basic Operations ............................................................................................................................................ 25 Insertion Operation ....................................................................................................................................... 25 Array Insertions ............................................................................................................................................. 27 Insertion at the Beginning of an Array .......................................................................................................... 28 Insertion at the Given Index of an Array ....................................................................................................... 30 Insertion After the Given Index of an Array .................................................................................................. 32 Insertion Before the Given Index of an Array ................................................................................................ 34 Deletion Operation ........................................................................................................................................ 36 Search Operation ........................................................................................................................................... 37 Update Operation .......................................................................................................................................... 39 LINKED LIST ............................................................................................................................... 41 10. Linked List ─ Basics .................................................................................................................................. 42 Linked List Representation ............................................................................................................................ 42 Types of Linked List ....................................................................................................................................... 42 Basic Operations ............................................................................................................................................ 43 Insertion Operation ....................................................................................................................................... 43 Deletion Operation ........................................................................................................................................ 44 Reverse Operation ......................................................................................................................................... 45 Linked List Program in C ................................................................................................................................ 46 11. Doubly Linked List ................................................................................................................................... 55 Doubly Linked List Representation ................................................................................................................ 55 Basic Operations ............................................................................................................................................ 55 Insertion Operation ....................................................................................................................................... 56 Deletion Operation ........................................................................................................................................ 57 Insertion at the End of an Operation ............................................................................................................. 57 Doubly Linked List Program in C .................................................................................................................... 58 12. Circular Linked List .................................................................................................................................. 67 Singly Linked List as Circular .......................................................................................................................... 67 Doubly Linked List as Circular ........................................................................................................................ 67 Basic Operations ............................................................................................................................................ 67 Insertion Operation ....................................................................................................................................... 68 Deletion Operation ........................................................................................................................................ 68 Display List Operation .................................................................................................................................... 69 Circular Linked List Program in C ................................................................................................................... 69 iv Data Structures & Algorithms STACK & QUEUE ........................................................................................................................ 74 13. Stack ....................................................................................................................................................... 75 Stack Representation..................................................................................................................................... 75 Basic Operations ............................................................................................................................................ 76 peek() ............................................................................................................................................................. 76 isfull() ............................................................................................................................................................. 77 isempty() ........................................................................................................................................................ 77 Push Operation .............................................................................................................................................. 78 Pop Operation ............................................................................................................................................... 79 Stack Program in C ......................................................................................................................................... 81 14. Expression Parsing .................................................................................................................................. 85 Infix Notation ................................................................................................................................................. 85 Prefix Notation .............................................................................................................................................. 85 Postfix Notation ............................................................................................................................................. 85 Parsing Expressions ....................................................................................................................................... 86 Postfix Evaluation Algorithm ......................................................................................................................... 87 Expression Parsing Using Stack ...................................................................................................................... 87 15. Queue ..................................................................................................................................................... 93 Queue Representation .................................................................................................................................. 93 Basic Operations ............................................................................................................................................ 93 peek() ............................................................................................................................................................. 94 isfull() ............................................................................................................................................................. 94 isempty() ........................................................................................................................................................ 95 Enqueue Operation ....................................................................................................................................... 96 Dequeue Operation ....................................................................................................................................... 97 Queue Program in C ...................................................................................................................................... 99 SEARCHING TECHNIQUES ........................................................................................................ 103 16. Linear Search ........................................................................................................................................ 104 Linear Search Program in C ......................................................................................................................... 105 17. Binary Search ........................................................................................................................................ 108 How Binary Search Works? ......................................................................................................................... 108 Binary Search Program in C ......................................................................................................................... 111 18. Interpolation Search ............................................................................................................................. 115 Positioning in Binary Search ........................................................................................................................ 115 Position Probing in Interpolation Search ..................................................................................................... 116 Interpolation Search Program in C .............................................................................................................. 118 19. Hash Table ............................................................................................................................................ 120 Hashing ........................................................................................................................................................ 120 Linear Probing.............................................................................................................................................. 121 Basic Operations .......................................................................................................................................... 122 Data Item ..................................................................................................................................................... 122 v Data Structures & Algorithms Hash Method ............................................................................................................................................... 122 Search Operation ......................................................................................................................................... 122 Insert Operation .......................................................................................................................................... 123 Delete Operation ......................................................................................................................................... 124 Hash Table Program in C ............................................................................................................................. 125 SORTING TECHNIQUES ............................................................................................................ 130 20. Sorting Algorithm .................................................................................................................................. 131 In-place Sorting and Not-in-place Sorting ................................................................................................... 131 Stable and Not Stable Sorting ...................................................................................................................... 131 Adaptive and Non-Adaptive Sorting Algorithm ........................................................................................... 132 Important Terms.......................................................................................................................................... 132 21. Bubble Sort Algorithm .......................................................................................................................... 134 How Bubble Sort Works? ............................................................................................................................. 134 Bubble Sort Program in C ............................................................................................................................ 138 22. Insertion Sort ........................................................................................................................................ 142 How Insertion Sort Works? ......................................................................................................................... 142 Insertion Sort Program in C ......................................................................................................................... 145 23. Selection Sort ........................................................................................................................................ 149 How Selection Sort Works? ......................................................................................................................... 149 Selection Sort Program in C ......................................................................................................................... 152 24. Merge Sort Algorithm ........................................................................................................................... 155 How Merge Sort Works? ............................................................................................................................. 155 Merge Sort Program in C ............................................................................................................................. 158 25. Shell Sort .............................................................................................................................................. 160 How Shell Sort Works? ................................................................................................................................ 160 Shell Sort Program in C ................................................................................................................................ 164 26. Quick Sort ............................................................................................................................................. 168 Partition in Quick Sort ................................................................................................................................. 168 Quick Sort Pivot Algorithm .......................................................................................................................... 168 Quick Sort Pivot Pseudocode ...................................................................................................................... 169 Quick Sort Algorithm ................................................................................................................................... 169 Quick Sort Pseudocode ................................................................................................................................ 170 Quick Sort Program in C .............................................................................................................................. 170 GRAPH DATA STRUCTURE ....................................................................................................... 174 27. Graphs .................................................................................................................................................. 175 Graph Data Structure .................................................................................................................................. 175 Basic Operations .......................................................................................................................................... 177 vi Data Structures & Algorithms 28. Depth First Traversal ............................................................................................................................. 178 Depth First Traversal in C ............................................................................................................................ 181 29. Breadth First Traversal .......................................................................................................................... 186 Breadth First Traversal in C ......................................................................................................................... 188 TREE DATA STRUCTURE .......................................................................................................... 194 30. Tree ...................................................................................................................................................... 195 Important Terms.......................................................................................................................................... 195 Binary Search Tree Representation ............................................................................................................. 196 Tree Node .................................................................................................................................................... 196 BST Basic Operations ................................................................................................................................... 197 Insert Operation .......................................................................................................................................... 197 Search Operation ......................................................................................................................................... 199 Tree Traversal in C ....................................................................................................................................... 200 31. Tree Traversal ....................................................................................................................................... 206 In-order Traversal ........................................................................................................................................ 206 Pre-order Traversal ...................................................................................................................................... 207 Post-order Traversal .................................................................................................................................... 208 Tree Traversal in C ....................................................................................................................................... 209 32. Binary Search Tree ................................................................................................................................ 215 Representation ............................................................................................................................................ 215 Basic Operations .......................................................................................................................................... 216 Node ............................................................................................................................................................ 216 Search Operation ......................................................................................................................................... 216 Insert Operation .......................................................................................................................................... 217 33. AVL Trees .............................................................................................................................................. 219 AVL Rotations .............................................................................................................................................. 220 34. Spanning Tree ....................................................................................................................................... 224 General Properties of Spanning Tree .......................................................................................................... 224 Mathematical Properties of Spanning Tree ................................................................................................. 225 Application of Spanning Tree ...................................................................................................................... 225 Minimum Spanning Tree (MST) ................................................................................................................... 225 Minimum Spanning-Tree Algorithm ............................................................................................................ 225 Kruskal's Spanning Tree Algorithm .............................................................................................................. 226 Prim's Spanning Tree Algorithm .................................................................................................................. 229 35. Heaps .................................................................................................................................................... 233 Max Heap Construction Algorithm .............................................................................................................. 234 Max Heap Deletion Algorithm ..................................................................................................................... 235 RECURSION ............................................................................................................................. 236 vii Data Structures & Algorithms 36. Recursion ─ Basics ................................................................................................................................. 237 Properties .................................................................................................................................................... 237 Implementation ........................................................................................................................................... 238 Analysis of Recursion ................................................................................................................................... 238 Time Complexity .......................................................................................................................................... 238 Space Complexity ........................................................................................................................................ 239 37. Tower of Hanoi ..................................................................................................................................... 240 Rules ............................................................................................................................................................ 240 Algorithm ..................................................................................................................................................... 244 Tower of Hanoi in C ..................................................................................................................................... 247 38. Fibonacci Series .................................................................................................................................... 251 Fibonacci Iterative Algorithm ...................................................................................................................... 252 Fibonacci Interactive Program in C .............................................................................................................. 252 Fibonacci Recursive Algorithm .................................................................................................................... 254 Fibonacci Recursive Program in C ................................................................................................................ 254 viii Data Structures & Algorithms Basics 1

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