Data Structures. A Pseudocode Approach with С. Richard F. Gilberg De Anza College. Behrouz A. Forouzan De Anza College I(T)P. PWS Publishing Company

Transcription

1 Data Structures A Pseudocode Approach with С Richard F. Gilberg De Anza College Behrouz A. Forouzan De Anza College PWS Publishing Company I(T)P An International Thomson Publishing Company Boston 'Albany 'Bonn 'Cincinnati 'London 'Madrid Melbourne Mexico City New York Paris San Francisco Singapore «Tokyo -Toronto -Washington

2 Co ntents Preface хш. 1 Introduction Pseudocode 2 Algorithm Header 2 Purpose, Conditions, and Return 3 Statement Numbers 4 Variables 4 Algorithm Analysis 5 Statement Constructs 5 Sequence 5 Selection 6 Loop 6 Pseudocode Example The Abstract Data Type 7 Atomic and Composite Data 8 Data Structure 9 Abstract Data Type A Model For An Abstract Data Type 11 ADT Operations 12 ADT Data Structure Algorithm Efficiency 12 Linear Loops 14 Logarithmic Loops 14 Nested Loops 15 Linear Logarithmic 15 Dependent Quadratic 16 Quadratic 16 Big-O Notation 17 Standard Measures of Efficiency 18 Big-O Analysis Examples 19 Add Matrices 19 Multiply Matrices Summary 22 Practice Sets 23 Exercises 23 Problems 25 Projects 25 2 Searching Linear List Searches 28 Sequential Search 28 Sequential Search Algorithm 28 Variations on Sequential Searches 31 Sentinel Search 31 Probability Search 32 Ordered List Search 33 Binary Search 34 Target Found 34 Target Not Found 35 Binary Search Algorithm 37 Analyzing Linear Search Algorithms 38 Sequential Search 38 Binary Search 39 Linear Search С Algorithms 40 Sequential Search In С 40 Binary Search In С 41 Hashed List Searches 42 Basic Concepts 43 Hashing Methods 44 Direct Method 44 Subtraction Method 46 Modulo-Division Method 46 Digit-Extraction Method 47 Midsquare Method 47 V

3 vi Contents Folding Methods 48 Rotation Method 48 Pseudorandom Method 50 Hashing Algorithm Collision Resolution 51 Open Addressing 53 Linear Probe 54 Quadratic Probe 55 Pseudorandom Collision Resolution 55 Key Offset 56 Linked List Resolution 57 Bucket Hashing 58 Combination Approaches Summary Practice Sets 61 Exercises 61 Problems 62 Projects 63 3 Linear Lists Linear List Concepts 66 Insertion 67 Deletion 67 Retrieval 68 Traversal Linked Lists 69 Nodes 69 Linked List Data Structure 70 Head Node Structure 71 Data Node Structure 71 Pointers to Linked Lists Linked List Algorithms 72 Create List 74 Insert Node 76 Insert Into Empty List 76 Insert at Beginning 77 Insert in Middle 77 Insert at End 79 Insert Node Algorithm 79 Delete Node 79 Delete First Node 81 General Delete Case 82 Delete Node Algorithm 83 Search List 84 Retrieve Node 87 Empty List 87 Full List 88 List Count 88 Traverse List 89 Destroy List Processing A Linked List 91 Add Node 93 Remove Node 94 Print List 95 Testing Insert and Delete Logic Linear List Applications 97 Append Linked Lists 97 Array of Linked Lists Complex Linked List Structures 102 Header Nodes 102 Circularly-Linked Lists 103 Doubly-Linked Lists 104 Doubly-Linked List Insertion 105 Doubly-Linked List Deletion 109 Multilinked Lists 110 Multilinked List Insert 112 Multilinked List Delete Building A Linked List С Implementation 114 Data Structure 114 Application Functions 115 Main 115 Instructions 115 Build List 116 Compare Data 117 Process User Requests 118 Get User's Choice 119 Print List 120 Search List Linked List Abstract Data Type 122 List ADT Functions 123 Create List 124 Add Node 125 Insert Node 126 Remove Node 128 Delete Node 128 Search List 129 Internal Search Function 129 Retrieve Node 132 Empty List 133 Full List 133 List Count 134 Traverse 134 Destroy List 136

4 Contents vii 3-9 Summary Ю Practice Sets 137 Exercises 137 Problems 140 Projects Stacks Basic Stack Operations 150 Push 150 Pop 150 Stack Top Stack Linked-List Implementation 153 Data Structure 153 Stack Head 153 Stack Data Node 153 Stack Algorithms 153 Create Stack 157 Push Stack 158 Pop Stack 159 Stack Top 160 Empty Stack 161 Full Stack 161 Stack Count 162 Destroy Stack Stack Applications 163 Reversing Data 163 Reverse a List 164 Convert Decimal to Binary 164 Parsing 165 Postponement 167 Infix To Postfix Transformation 167 Evaluating Postfix Expressions 1 73 Backtracking 175 Goal Seeking 175 Eight Queens Problem Eight Queens Problem С Implementation 181 Mainline Logic 182 Get Board Size 183 Fill Board 183 Guarded 185 Print Board ADT Linked-List Implementation 188 Data Structure 188 Stack ADT Implementation 188 Stack Structure 188 Create Stack 190 Push Stack 190 Pop Stack 192 Stack Top 193 Empty Stack 193 Full Stack 194 Stack Count 194 Destroy Stack Array Implementation of Stacks 196 Data Structures 196 Array Algorithms 197 Create Stack 197 Push Stack 198 Pop Stack 198 Stack Top 199 Empty Stack 200 Full Stack 200 Stack Count 201 Destroy Stack ADT Array Implementation 202 Create Stack Array 202 Push Stack Array 203 Pop Stack Array 204 Stack Top Array 205 Empty Stack Array 205 Full Stack Array 206 Stack Count Array 206 Destroy Stack Array Summary Practice Sets 208 Exercises 208 Problems 209 Projects Queues Queue Operations 216 Enqueue 216 Dequeue 216 Queue Front 217 Queue Rear 217 Queue Example Queue Linked-List Implementation 218 Data Structure 218 Queue Head 218 Queue Data Node 220 Queue Algorithms 220

5 viii Contents Create Queue 223 Enqueue 224 Dequeue 225 Retrieving Queue Data 226 Empty Queue 227 Full Queue 227 Queue Count 228 Destroy Queue Queuing Theory Queue Applications 230 Queue Simulation 231 Events 231 Data Structures 232 Output 233 Simulation Algorithm 233 Categorizing Data Categorizing Data С Implementation 240 Mainline Logic 240 FillQueues 241 Print Queues 242 Print One Queue Queue Linked-List Implementation 244 Queue Structure 244 Queue ADT Implementation 245 Create Queue 245 Enqueue 246 Dequeue 247 Queue Front 248 Queue Rear 249 Queue Empty 249 Full Queue 250 Queue Count 250 Destroy Queue Queues Array Implementation 252 Array Queues Implementation 253 Create Queue Array 255 Enqueue: Array Implementation 256 Dequeue: Array Implementation 257 Queue Front: Array Implementation 258 Queue Rear: Array Implementation 259 Full Queue: Array Implementation 259 Destroy Queue: Array Implementation Summary Practice Sets 261 Exercises 261 Problems 263 Projects Recursion Factorial A Case Study 270 Recursion Defined 270 Iterative Solution 271 Recursive Solution How Recursion Works Designing Recursive Algorithms 275 The Design Methodology 276 Limitations of Recursion 277 Design Implementation Reverse A Linked List Another Case Study Fibonacci Numbers The Towers Of Hanoi 282 Recursive Towers Of Hanoi С Implementations of Recursion 288 Fibonacci Numbers 288 Towers of Hanoi Summary Practice Sets 292 Exercises 292 Problems 294 Projects Introduction to Trees Basic Tree Concepts 298 Terminology 298 Tree Representation Binary Trees 302 Properties 304 Height of Binary Trees 304 Balance 304 Complete Binary Trees 305 Binary Tree Structure Binary Tree Traversais 306 Depth-First Traversals 306

6 Contents ix Preorder Traversal (NbR) 307 Inorder Traversal (LNR) 309 Postorder Traversal (LRN) 310 Breadth Traversal Expression Trees 313 Infix Traversal 313 Postfix Traversal 316 Prefix Traversal General Trees 316 Changing General Tree To Binary Tree 317 Insertions Into General Trees 318 FIFO Insertion 318 LIFO Insertion 318 Key Sequenced Insertion 318 General Tree Deletions Summary Practice Sets 321 Exercises 321 Problems 325 Projects Search Trees Binary Search Trees 334 Definition 334 Operations On Binary Search Trees 336 Binary Search Tree Traversals 336 Binary Search Tree Search Algorithms 337 Insert Node AVL Trees 348 AVL Balance Factor 349 Balancing Trees 350 Case 1: Left Of Left 352 Case 2: Right Of Right 353 Case 3: Right Of Left 354 Case 4: Left Of Right 354 AVL Node Structure 354 AVL Insert 355 AVL Insert Algorithm 358 AVL Left Balance Algorithm 359 Rotate Algorithms 360 AVL Delete Algorithm 361 Delete Right Balance 363 Adjusting The Balance Factors AVL Abstract Data Type 366 AVL Data Structure 368 AVL Algorithms 369 Create AVL Tree 369 AVL Tree Insert 370 AVL Tree Delete 376 AVL Tree Data Processing 382 Retrieve AVL Tree Node 382 Traverse AVL Tree 384 AVL Tree Utility Functions 384 AVL Empty Tree 385 AVL Full Tree 385 AVL Count 385 Destroy AVL Tree Summary Practice Sets 388 Exercises 388 Problems 390 Projects Heaps Heap Definition Heap Structure Basic Heap Algorithms 397 ReheapUp 398 ReheapDown Heap Data Structure Heap Algorithms 403 ReheapUp 403 ReheapDown 404 Build Heap 405 Insert Heap 406 Delete Heap Heap Applications 410 Selection Algorithms 410 Priority Queues A Heap Program 413 Heap Program Design 413 Heap Functions 419 ReheapUp 419 ReheapDown 420 Insert Heap 421 Delete Heap Node Summary Practice Sets 423 Exercises 423 Problems 425 Projects 425

7 X Contents 10 Multiway Trees 429 lo-l М-Way Search Trees B-Trees 431 B-Tree Insertion 433 B-Tree Insert Design 434 B-Tree Insert Node 436 Search Node 438 Split Node 439 Insert Entry 442 Insertion Summary 442 B-Tree Deletion 442 B-Tree Delete 445 Node Delete 445 Delete Entry 447 Delete Mid 447 ReFlow 448 Balance 451 Combine 453 Traverse B-Tree 455 B-Tree Search Simplified B-Trees Tree Tree B-tree Variations 461 B*Tree 461 В + Tree Lexical Search Tree 461 Tries 463 Trie Structure 464 Trie Search B-Tree Abstract Data Type 466 Header File 466 Utility Functions 468 Search 468 Traversal 470 Insert Algorithms 472 ADT Interface Function 472 Internal Insert Processing 474 Delete Algorithms 478 ADT Delete Interface 478 Delete Internal Function 479 Delete Middle 481 Reflow Function 482 Borrow Left or Right 484 Combine Summary Practice Sets 487 Exercises 487 Problems 487 Projects Advanced Sorting Concepts General Sort Concepts 492 Sort Order 492 Sort Stability 493 Sort Efficiency 494 Passes Insertion Sorts 494 Straight Insertion Sort 494 Straight Insertion Sort Example 494 Insertion Sort Algorithm 495 Shell Sort 497 Shell Sort Algorithm 497 Selecting the Increment Size 501 Insertion Sort Algorithmics 501 Straight Insertion Sort 501 Shell Sort 502 Summary 503 Insertion Sort Implementation 503 Straight Insertion Sort 503 Shell Sort Selection Sorts 506 Straight Selection Sort 506 Selection Sort Algorithm 506 Heap Sort 508 Heap Sort Algorithm 509 Selection Sort Algorithmics 510 Straight Selection Sort 510 Heap Sort 510 Summary 512 Selection Sort Implementation 513 Selection Sort С Code 513 Heap Sort С Code Exchange Sorts 514 Bubble Sort 515 Bubble Sort Algorithm 515 Quicksort 517 Quick Sort Algorithm 519 Exchange Sort Algorithmics 524 Bubble Sort 524 Quick Sort 525 Summary 526

8 Contents xi Exchange Sort Implementation 526 Bubble Sort Code 526 Quick Sort Code External Sorts 530 Merging Ordered Files 530 Merging Unordered Files 532 The Sorting Process 533 Natural Merge 535 Balanced Merge 535 Polyphase Merge 535 Sort Phase Revisited Summary Practice Sets 542 Exercises 542 Problems 544 Projects Graphs Terminology Operations 552 Add Vertex 552 Delete Vertex 552 Add Edge 553 Delete Edge 553 Find Vertex 553 Traverse Graph 553 Depth-First Traversal 554 Breadth-First Graph Storage Structures 557 Adjacency Matrix 557 Adjacency List Graph Algorithms 559 Create Graph 563 Insert Vertex 563 Delete Vertex 565 Insert Arc 566 Delete Arc 567 Retrieve Vertex 569 First Arc 569 Depth-First Traversal 570 Breadth-First Traversal Networks 574 Minimum Spanning Tree 575 Minimum Spanning Tree Example 576 Minimum Spanning Tree Data Structure 577 Minimum Spanning Tree Pseudocode 578 Shortest Path Algorithm 580 Shortest Path Manual Example 580 Shortest Path Data Structure 582 Shortest Path Pseudocode Abstract Data Type 584 Insert Vertex 586 Delete Vertex 587 Insert Arc 589 Delete Arc 590 Depth-First Traversal 592 Breadth-First Traversal Summary Practice Sets 597 Exercises 597 Problems 598 Projects 599 Appendix A ASCII Tables 603 A-l ASCII Codes (Long Form) 603 A-2 ASCII Table (Short Form) 607 Appendix В Structure Charts 609 B-l Structure Chart Symbols 610 Modules 610 Reading Structure Charts 612 Common Modules 612 Conditional Calls 613 Exclusive Or 613 Loops 613 Conditional Loops 614 Recursion 614 Data Flows and Flags 615 B-2 Structure Chart Rules 615 Appendix С Program Standards and Styles 617 C-l Global Area 618 C-2 Program Main Line 619 C-3 General Coding Standards 619

9 xii Contents C-4 Variables and Structures 620 C-5 Function Definition 621 Appendix D Random Numbers 623 D-l Random Numbers In С 624 Srand 624 Rand 624 D-2 Custom Random Number Generator 624 D-3 Scaling a Random Number 625 Appendix E Standard С Libraries 629 Б-l Limits.H 629 E-2 Float.H 630 Appendix F С Function Prototypes 631 F-l Function Index 632 F-2 Character Library 633 F-3 Math Library 633 F-4 Standard I/O Library 634 General I/O 634 Formatted I/O 634 Character I/O 634 File I/O 635 System Communication 635 String I/O 635 System File Control 635 F-5 Standard Library 635 Math Functions 635 Memory Functions 635 Program Control 636 System Communication 636 Conversion Functions 636 F-6 String Library 636 Copying Data 636 Comparing Data 636 String Lengths 636 F-7 Time 637 Solutions to Selected Exercises 639 Glossary 655 Index 665