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class=\"section-number\">2.11. </span>Discussion Questions", "<span class=\"section-number\">2.13. </span>Glossary", "<span class=\"section-number\">2.8. </span>Analysis of Hash Tables", "<span class=\"section-number\">2.1. </span>Objectives", "<span class=\"section-number\">2.5. </span>Performance of C++ Data Collections", "<span class=\"section-number\">2.12. </span>Programming Exercises", "<span class=\"section-number\">2.7. </span>Analysis of String Operators", "<span class=\"section-number\">2.6. </span>Analysis of Array and Vector Operators", "<span class=\"section-number\">2.2. </span>What Is Algorithm Analysis?", "<span class=\"section-number\">2. </span>Analysis", "<span class=\"section-number\">9.5. </span>An Adjacency List", "<span class=\"section-number\">9.4. </span>An Adjacency Matrix", "<span class=\"section-number\">9.21. </span>Analysis of Dijkstra\u2019s Algorithm", "<span class=\"section-number\">9.10. </span>Breadth First Search Analysis", "<span class=\"section-number\">9.12. </span>Building the Knight\u2019s Tour Graph", "<span class=\"section-number\">9.8. </span>Building the Word Ladder Graph", "<span class=\"section-number\">9.16. </span>Depth First Search Analysis", "<span class=\"section-number\">9.20. </span>Dijkstra\u2019s Algorithm", "<span class=\"section-number\">9.24. </span>Discussion Questions", "<span class=\"section-number\">9.15. </span>General Depth First Search", "<span class=\"section-number\">9.26. </span>Glossary", "<span class=\"section-number\">9.6. </span>Implementation", "<span class=\"section-number\">9.9. </span>Implementing Breadth First Search", "<span class=\"section-number\">9.13. </span>Implementing Knight\u2019s Tour", "<span class=\"section-number\">9.14. </span>Knight\u2019s Tour Analysis", "<span class=\"section-number\">9.1. </span>Objectives", "<span class=\"section-number\">9.22. </span>Prim\u2019s Spanning Tree Algorithm", "<span class=\"section-number\">9.25. </span>Programming Exercises", "<span class=\"section-number\">9.19. </span>Shortest Path Problems", "<span class=\"section-number\">9.18. </span>Strongly Connected Components", "<span class=\"section-number\">9.23. </span>Summary", "<span class=\"section-number\">9.3. </span>The Graph Abstract Data Type", "<span class=\"section-number\">9.11. </span>The Knight\u2019s Tour Problem", "<span class=\"section-number\">9.7. </span>The Word Ladder Problem", "<span class=\"section-number\">9.17. </span>Topological Sorting", "<span class=\"section-number\">9.2. </span>Vocabulary and Definitions", "<span class=\"section-number\">9. </span>Graphs and Graph Algorithms", "<span class=\"section-number\">1.10. </span>Collections", "<span class=\"section-number\">1.11. </span>Defining C++ Functions", "<span class=\"section-number\">1.16. </span>Discussion Questions", "<span class=\"section-number\">1.2. </span>Getting Started", "<span class=\"section-number\">1.8. </span>Getting Started with Data", "<span class=\"section-number\">1.18. </span>Glossary", "<span class=\"section-number\">1.14. </span><strong>Optional</strong>: Graphics in C++", "<span class=\"section-number\">1.12. </span>Object-Oriented Programming in C++: Defining Classes", "<span class=\"section-number\">1.13. </span>Inheritance in C++", "<span class=\"section-number\">1.1. </span>Objectives", "<span class=\"section-number\">1.17. </span>Programming Exercises", "<span class=\"section-number\">1.7. </span>Reviewing Basic C++", "<span class=\"section-number\">1.15. </span>Summary", "<span class=\"section-number\">1.3. </span>What Is Computer Science?", "<span class=\"section-number\">1.4. </span>What Is Programming?", "<span class=\"section-number\">1.6. </span>Why Study Algorithms?", "<span class=\"section-number\">1.5. </span>Why Study Data Structures and Abstract Data Types?", "<span class=\"section-number\">1. </span>Introduction", "<span class=\"section-number\">3.7. </span>Balanced Symbols - A General Case", "<span class=\"section-number\">3.8. </span>Converting Decimal Numbers to Binary Numbers", "<span class=\"section-number\">3.20. </span>Discussion Questions", "<span class=\"section-number\">3.22. </span>Glossary", "<span class=\"section-number\">3.17. </span>Using a Deque in C++", "<span class=\"section-number\">3.12. </span>Using a Queue in C++", "<span class=\"section-number\">3.5. </span>Using a Stack in C++", "<span class=\"section-number\">3.9. </span>Infix, Prefix and Postfix Expressions", "<span class=\"section-number\">3.1. </span>Objectives", "<span class=\"section-number\">3.18. </span>Palindrome-Checker", "<span class=\"section-number\">3.21. </span>Programming Exercises", "<span class=\"section-number\">3.6. </span>Simple Balanced Parentheses", "<span class=\"section-number\">3.13. </span>Simulation: Hot Potato", "<span class=\"section-number\">3.14. </span>Simulation: Printing Tasks", "<span class=\"section-number\">3.19. </span>Summary", "<span class=\"section-number\">3.16. </span>The Deque Abstract Data Type", "<span class=\"section-number\">3.11. </span>The Queue Abstract Data Type", "<span class=\"section-number\">3.4. </span>The Stack Abstract Data Type", "<span class=\"section-number\">3.2. </span>What Are Linear Structures?", "<span class=\"section-number\">3.15. </span>What Is a Deque?", "<span class=\"section-number\">3.10. </span>What Is a Queue?", "<span class=\"section-number\">3.3. </span>What is a Stack?", "<span class=\"section-number\">3. </span>Linear Structures", "What Is a Queue?", "<span class=\"section-number\">4.9. </span>Discussion Questions", "<span class=\"section-number\">4.11. </span>Glossary", "<span class=\"section-number\">4.6. </span>Implementing an Ordered Linked List", "<span class=\"section-number\">4.3. </span>Implementing an Unordered Linked List", "<span class=\"section-number\">4.1. </span>Objectives", "<span class=\"section-number\">4.10. </span>Programming Exercises", "<span class=\"section-number\">4.8. </span>Summary", "<span class=\"section-number\">4.7. </span>The Ordered List Abstract Data Type", "The Unordered Array Abstract Data Type", "<span class=\"section-number\">4.2. </span>What Are Linked Structures?", "<span class=\"section-number\">4. </span>Linear Linked Structures", "<span class=\"section-number\">5.9. </span>Complex Recursive Problems", "<span class=\"section-number\">5.15. </span>Discussion Questions", "<span class=\"section-number\">5.12. </span>Dynamic Programming", "<span class=\"section-number\">5.11. </span>Exploring a Maze", "<span class=\"section-number\">5.17. </span>Glossary", "<span class=\"section-number\">5.1. </span>Objectives", "<span class=\"section-number\">5.6. </span>Stack Frames: Implementing Recursion", "<span class=\"section-number\">5.4. </span>The Three Laws of Recursion", "<span class=\"section-number\">5.10. </span>Tower of Hanoi", "<span class=\"section-number\">5.2. </span>What Is Recursion?", "<span class=\"section-number\">5.3. </span>Calculating the Sum of a Vector of Numbers", "<span class=\"section-number\">5.5. </span>Converting an Integer to a String in Any Base", "<span class=\"section-number\">5.16. </span>Programming Exercises", "<span class=\"section-number\">5.8. </span>Sierpinski Triangle", "<span class=\"section-number\">5.7. </span>Introduction: Visualizing Recursion", "<span class=\"section-number\">5. </span>Recursion", "<span class=\"section-number\">6.8. </span>Discussion Questions", "<span class=\"section-number\">6.10. </span>Glossary", "<span class=\"section-number\">6.5. </span>Hashing", "<span class=\"section-number\">6.1. </span>Objectives", "<span class=\"section-number\">6.9. </span>Programming Exercises", "<span class=\"section-number\">6.7. </span>Summary", "<span class=\"section-number\">6.4. </span>The Binary Search", "<span class=\"section-number\">6.3. </span>The Sequential Search", "<span class=\"section-number\">6.2. </span>Searching", "<span class=\"section-number\">6. </span>Searching and Hashing", "<span class=\"section-number\">7.11. </span>Discussion Questions", "<span class=\"section-number\">7.13. </span>Glossary", "<span class=\"section-number\">7.1. </span>Objectives", "<span class=\"section-number\">7.12. </span>Programming Exercises", "<span class=\"section-number\">7.10. </span>Summary", "<span class=\"section-number\">7.3. </span>The Bubble Sort", "<span class=\"section-number\">7.5. </span>The Insertion Sort", "<span class=\"section-number\">7.7. </span>The Merge Sort", "<span class=\"section-number\">7.8. </span>The Quick Sort", "<span class=\"section-number\">7.4. </span>The Selection Sort", "<span class=\"section-number\">7.6. </span>The Shell Sort", "<span class=\"section-number\">7.2. </span>Sorting", "<span class=\"section-number\">7. </span>Sorting", "<span class=\"section-number\">8.17. </span>AVL Tree Implementation", "<span class=\"section-number\">8.16. </span>AVL Tree Performance", "<span class=\"section-number\">8.15. 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36, 37, 39, 40, 42, 43, 44, 45, 46, 47, 49, 50, 51, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 72, 73, 74, 75, 79, 81, 82, 83, 84, 86, 87, 88, 89, 90, 92, 94, 95, 96, 97, 98, 99, 100, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 118, 119, 121, 122, 123, 124, 125, 126, 127, 128, 129, 131, 132, 133, 134, 135, 136, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 152, 153, 161, 162, 163, 166, 168], "classic": [0, 34, 66, 94, 145], "string": [0, 6, 11, 16, 24, 40, 43, 44, 46, 47, 51, 53, 56, 57, 58, 60, 64, 66, 68, 74, 77, 80, 89, 95, 96, 98, 104, 107, 108, 110, 131, 144, 148, 152, 155, 156, 157, 158, 160, 162, 168], "One": [0, 4, 10, 13, 17, 19, 24, 30, 31, 34, 39, 43, 46, 47, 54, 64, 69, 78, 84, 94, 104, 110, 112, 114, 121, 124, 141, 145, 148, 153], "anoth": [0, 1, 3, 4, 9, 10, 16, 17, 21, 22, 23, 27, 30, 31, 34, 35, 37, 39, 40, 41, 43, 44, 45, 46, 47, 52, 54, 58, 64, 67, 69, 75, 78, 83, 84, 88, 90, 100, 104, 105, 106, 110, 114, 115, 116, 123, 129, 131, 134, 137, 139, 140, 141, 142, 146, 148, 153], "second": [0, 1, 4, 9, 10, 16, 19, 24, 25, 26, 28, 31, 34, 39, 40, 42, 43, 45, 46, 64, 70, 84, 99, 100, 102, 103, 110, 112, 114, 121, 123, 125, 126, 127, 129, 131, 134, 139, 141, 142, 148, 153, 159, 160, 161, 163, 164, 165, 166], "simpli": [0, 1, 10, 21, 23, 28, 40, 43, 46, 47, 52, 54, 57, 58, 64, 68, 69, 70, 83, 84, 94, 98, 100, 103, 110, 114, 115, 116, 125, 126, 132, 134, 136, 141, 142, 144, 147, 148, 152, 160], "rearrang": [0, 132, 136], "first": [0, 1, 9, 10, 14, 16, 17, 19, 20, 22, 23, 25, 26, 28, 29, 30, 31, 32, 35, 36, 38, 39, 40, 42, 43, 45, 46, 47, 53, 58, 60, 64, 66, 67, 68, 69, 70, 71, 73, 77, 78, 80, 82, 83, 84, 86, 88, 89, 92, 94, 95, 99, 100, 102, 103, 105, 106, 110, 112, 114, 115, 119, 121, 123, 124, 125, 126, 127, 128, 129, 131, 134, 139, 141, 142, 144, 145, 147, 148, 152, 153, 159, 160, 161, 163, 164, 165, 166, 168], "For": [0, 1, 4, 9, 17, 19, 24, 25, 26, 28, 31, 35, 37, 39, 40, 45, 46, 47, 53, 57, 58, 67, 70, 74, 75, 78, 83, 84, 88, 94, 95, 96, 103, 104, 106, 110, 115, 116, 118, 126, 128, 129, 133, 134, 139, 142, 153, 160, 167], "heart": 0, "earth": 0, "ar": [0, 1, 3, 4, 6, 7, 8, 9, 10, 12, 13, 14, 16, 17, 18, 19, 21, 22, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 37, 39, 40, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 57, 58, 60, 61, 62, 63, 64, 65, 67, 68, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86, 87, 88, 89, 91, 92, 94, 95, 96, 97, 98, 99, 100, 102, 103, 104, 105, 106, 108, 109, 110, 112, 114, 115, 116, 119, 121, 122, 123, 124, 125, 126, 128, 129, 131, 132, 134, 135, 136, 137, 139, 140, 141, 142, 144, 145, 147, 148, 152, 153, 162, 167, 168], "The": [0, 1, 4, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 28, 30, 31, 36, 37, 38, 39, 40, 42, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 63, 64, 66, 67, 68, 69, 70, 71, 75, 77, 78, 79, 80, 81, 83, 86, 91, 94, 95, 96, 97, 98, 100, 102, 103, 104, 105, 106, 107, 109, 110, 112, 117, 121, 129, 130, 131, 135, 137, 139, 141, 142, 144, 145, 147, 148, 150, 152, 153, 154, 168], "python": [0, 1, 23, 28, 31, 33, 40, 45, 46, 57, 68, 76, 77, 78, 89, 98, 100, 103, 105, 106, 114, 115, 116, 123, 125, 134, 141, 142, 148, 152, 168], "typhon": 0, "well": [0, 1, 21, 33, 39, 40, 43, 46, 47, 51, 52, 57, 62, 63, 77, 80, 83, 84, 86, 88, 90, 99, 106, 110, 114, 128, 131, 141, 142, 144, 147], "sake": 0, "simplic": [0, 100], "we": [0, 1, 4, 6, 8, 9, 10, 12, 13, 14, 15, 16, 17, 19, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 37, 39, 40, 42, 43, 45, 46, 47, 49, 50, 52, 53, 54, 55, 57, 58, 61, 62, 63, 64, 66, 68, 69, 70, 72, 73, 75, 77, 78, 80, 83, 84, 86, 88, 90, 92, 94, 95, 98, 99, 100, 102, 103, 105, 106, 108, 110, 114, 115, 116, 123, 124, 125, 126, 127, 128, 129, 131, 132, 133, 134, 135, 136, 137, 138, 139, 141, 142, 144, 145, 147, 148, 149, 150, 151, 152, 153, 160, 168], "assum": [0, 25, 28, 49, 52, 58, 61, 63, 64, 68, 69, 72, 73, 76, 78, 83, 84, 88, 93, 95, 105, 110, 114, 115, 124, 125, 152, 162], "two": [0, 1, 4, 9, 10, 13, 15, 16, 17, 21, 22, 23, 24, 25, 26, 28, 29, 31, 33, 34, 37, 39, 40, 42, 43, 44, 45, 46, 47, 49, 54, 55, 57, 58, 60, 64, 67, 70, 75, 76, 83, 84, 86, 94, 95, 100, 102, 103, 104, 105, 109, 110, 112, 116, 119, 121, 123, 125, 126, 129, 131, 132, 134, 137, 138, 139, 140, 141, 142, 144, 145, 147, 148, 151, 152, 153], "question": [0, 10, 11, 17, 19, 38, 39, 43, 45, 46, 49, 56, 67, 70, 71, 79, 83, 84, 91, 107, 116, 117, 125, 130, 131, 139, 147, 154, 168], "equal": [0, 22, 28, 30, 39, 40, 43, 46, 64, 70, 84, 94, 109, 110, 115, 125, 126, 132, 134, 140, 153], "length": [0, 17, 24, 25, 34, 37, 39, 40, 66, 70, 78, 86, 95, 99, 102, 106, 112, 121, 125, 126, 129, 148, 149, 162], "thei": [0, 1, 6, 8, 9, 10, 13, 18, 19, 22, 24, 27, 28, 36, 39, 40, 41, 45, 46, 47, 52, 54, 55, 58, 60, 64, 66, 67, 68, 69, 70, 75, 77, 78, 80, 83, 84, 88, 89, 94, 95, 99, 100, 110, 115, 116, 123, 125, 128, 129, 144], "made": [0, 25, 47, 94, 99, 105, 123, 139], "up": [0, 1, 4, 10, 25, 26, 36, 39, 40, 45, 46, 51, 52, 67, 69, 70, 76, 83, 84, 86, 90, 92, 94, 95, 96, 99, 100, 103, 106, 110, 112, 114, 121, 123, 124, 125, 126, 131, 134, 136, 144, 146, 152, 160], "symbol": [0, 10, 39, 40, 43, 60, 64, 68, 79, 84, 168], "from": [0, 1, 4, 7, 8, 9, 10, 13, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 35, 36, 37, 39, 40, 41, 42, 44, 45, 46, 47, 49, 50, 52, 54, 55, 57, 58, 61, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 80, 83, 84, 86, 88, 90, 94, 95, 96, 98, 100, 102, 103, 104, 105, 106, 110, 112, 114, 115, 118, 119, 121, 125, 129, 131, 134, 135, 136, 137, 138, 139, 140, 141, 144, 145, 146, 147, 148, 149, 152, 153, 160, 162, 163, 167], "set": [0, 1, 3, 4, 9, 17, 19, 21, 22, 24, 28, 37, 40, 43, 44, 45, 46, 47, 50, 51, 53, 56, 57, 58, 61, 70, 82, 83, 84, 89, 90, 94, 102, 105, 110, 112, 118, 121, 125, 127, 128, 131, 134, 138, 141, 142, 144, 146, 152, 153, 159, 164, 165, 168], "26": [0, 17, 21, 36, 40, 58, 83, 84, 88, 94, 110, 124, 125, 144], "lowercas": 0, "alphabet": [0, 21, 25, 40, 58, 129], "charact": [0, 8, 39, 40, 44, 51, 56, 58, 64, 66, 67, 77, 80, 95, 98, 103, 108, 110, 118, 144, 146, 168], "our": [0, 1, 4, 6, 9, 12, 16, 17, 19, 21, 23, 24, 25, 27, 28, 31, 35, 36, 37, 40, 45, 46, 47, 50, 53, 54, 55, 58, 61, 62, 63, 68, 69, 70, 75, 77, 83, 84, 94, 95, 98, 99, 100, 102, 103, 106, 110, 114, 115, 116, 125, 126, 127, 128, 131, 132, 133, 134, 135, 136, 139, 142, 144, 146, 148, 152, 168], "goal": [0, 1, 6, 9, 10, 15, 21, 22, 25, 40, 50, 52, 94, 97, 100, 110, 126, 136], "write": [0, 1, 7, 10, 15, 29, 31, 40, 42, 45, 46, 47, 48, 49, 50, 52, 64, 67, 68, 70, 71, 85, 94, 99, 101, 103, 104, 116, 131, 134, 141, 142, 144, 146, 148, 150, 152, 160, 167], "boolean": [0, 39, 44, 47, 51, 56, 57, 68, 70, 72, 73, 74, 83, 84, 88, 89, 115, 146, 168], "function": [0, 3, 4, 6, 9, 10, 15, 16, 17, 20, 21, 23, 24, 25, 26, 29, 39, 44, 45, 46, 47, 48, 49, 51, 52, 54, 55, 56, 57, 58, 64, 66, 67, 68, 69, 70, 84, 94, 95, 96, 98, 99, 100, 101, 102, 103, 104, 105, 106, 108, 109, 112, 114, 115, 116, 117, 123, 125, 126, 127, 128, 131, 134, 138, 141, 142, 144, 145, 146, 147, 148, 152, 165, 168], "take": [0, 1, 4, 8, 9, 10, 14, 16, 22, 24, 25, 27, 36, 37, 39, 40, 42, 43, 45, 46, 47, 52, 53, 54, 58, 59, 60, 64, 66, 67, 78, 83, 84, 86, 88, 90, 94, 95, 98, 99, 102, 103, 105, 106, 110, 114, 119, 123, 125, 129, 131, 132, 134, 139, 144, 146, 148, 152], "return": [0, 1, 4, 10, 16, 21, 23, 24, 25, 26, 33, 36, 39, 40, 43, 44, 45, 46, 47, 49, 51, 52, 54, 58, 64, 68, 69, 70, 72, 73, 74, 83, 84, 86, 88, 89, 95, 98, 99, 100, 102, 103, 105, 110, 115, 116, 131, 134, 135, 141, 142, 144, 148, 149, 152, 159, 160, 161, 162, 163, 164, 165, 166], "whether": [0, 4, 9, 10, 43, 45, 54, 58, 64, 66, 68, 70, 72, 73, 74, 83, 84, 88, 89, 95, 99, 110, 114, 115, 116, 131], "see": [0, 1, 4, 6, 8, 9, 10, 13, 15, 16, 17, 19, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 33, 36, 37, 39, 40, 43, 45, 46, 47, 52, 54, 57, 58, 61, 64, 66, 68, 69, 70, 72, 73, 74, 83, 84, 88, 90, 94, 95, 96, 98, 99, 100, 102, 104, 105, 106, 110, 114, 123, 125, 126, 127, 129, 131, 132, 134, 139, 141, 142, 143, 144, 145, 148, 151, 152], "each": [0, 1, 4, 6, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 35, 36, 37, 39, 40, 43, 44, 45, 46, 47, 48, 57, 59, 60, 64, 66, 67, 68, 70, 78, 82, 83, 84, 86, 87, 88, 89, 90, 94, 95, 98, 99, 100, 102, 104, 105, 106, 109, 110, 112, 114, 115, 124, 125, 126, 127, 128, 131, 133, 134, 135, 139, 140, 144, 146, 147, 148, 151, 152, 153, 160], "actual": [0, 1, 10, 21, 39, 40, 43, 45, 46, 47, 55, 58, 64, 70, 78, 83, 84, 90, 115, 126, 128], "occur": [0, 35, 42, 47, 57, 60, 62, 63, 64, 70, 75, 77, 78, 80, 84, 95, 96, 110, 115, 126], "If": [0, 1, 4, 10, 16, 17, 21, 24, 25, 27, 31, 37, 40, 43, 44, 46, 47, 49, 50, 52, 57, 64, 66, 68, 70, 77, 78, 80, 83, 84, 90, 94, 95, 100, 102, 103, 104, 106, 110, 112, 114, 115, 123, 125, 126, 127, 128, 131, 132, 133, 134, 136, 139, 141, 144, 146, 147, 148, 149, 152, 153], "possibl": [0, 3, 6, 9, 16, 21, 23, 25, 26, 34, 35, 39, 43, 44, 46, 54, 57, 64, 67, 68, 70, 77, 80, 83, 84, 86, 89, 94, 106, 110, 114, 115, 125, 126, 129, 132, 134, 147, 159, 164, 165], "checkoff": 0, "must": [0, 1, 9, 13, 15, 16, 17, 19, 23, 24, 25, 27, 28, 29, 30, 31, 35, 36, 37, 39, 40, 42, 43, 44, 45, 46, 47, 51, 52, 53, 57, 64, 66, 67, 68, 77, 80, 83, 84, 94, 95, 96, 99, 100, 104, 106, 110, 112, 114, 115, 116, 123, 127, 131, 134, 138, 141, 142, 144, 148, 152, 153], "accomplish": [0, 35, 40, 46, 69, 84, 90, 152], "replac": [0, 17, 40, 45, 58, 84, 110, 131, 132, 136, 140, 144, 146, 148, 149, 152], "special": [0, 21, 27, 43, 44, 46, 66, 84, 87, 102, 112, 133, 148, 157, 158], "c": [0, 1, 3, 5, 10, 11, 13, 16, 17, 21, 22, 23, 24, 25, 26, 28, 30, 31, 42, 44, 48, 51, 52, 56, 57, 59, 64, 65, 68, 79, 84, 85, 86, 95, 98, 100, 102, 103, 105, 106, 110, 114, 115, 116, 131, 134, 139, 141, 142, 144, 148, 149, 152, 153, 159, 160, 164, 165], "0": [0, 1, 2, 4, 9, 10, 16, 17, 19, 22, 23, 24, 25, 26, 28, 30, 39, 40, 43, 45, 46, 47, 58, 61, 67, 70, 74, 84, 94, 95, 100, 102, 105, 110, 115, 116, 124, 126, 131, 132, 133, 134, 141, 144, 148, 152, 159, 160, 161, 162, 163, 164, 165, 166, 168], "step": [0, 1, 3, 10, 19, 20, 21, 24, 25, 28, 31, 34, 35, 36, 40, 45, 52, 53, 60, 64, 66, 79, 81, 83, 84, 94, 95, 100, 103, 106, 110, 115, 123, 124, 125, 126, 127, 128, 131, 134, 144, 148, 168], "process": [0, 4, 17, 24, 26, 36, 39, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 55, 57, 58, 59, 60, 64, 66, 67, 68, 69, 70, 77, 80, 82, 83, 84, 94, 96, 103, 106, 109, 110, 114, 115, 116, 119, 122, 123, 124, 125, 126, 127, 128, 129, 134, 136, 144, 148], "convert": [0, 16, 43, 44, 59, 64, 65, 79, 81, 94, 107, 144, 152, 168], "local": [0, 30, 40, 43, 49, 98], "can": [0, 1, 3, 4, 7, 8, 9, 10, 15, 16, 17, 19, 21, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 39, 40, 42, 43, 44, 45, 46, 47, 51, 52, 53, 54, 55, 57, 58, 60, 61, 64, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 80, 83, 84, 86, 90, 92, 93, 94, 95, 96, 98, 99, 100, 101, 102, 103, 104, 105, 106, 109, 110, 112, 113, 114, 115, 116, 121, 123, 124, 125, 126, 128, 129, 131, 132, 133, 134, 136, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 151, 152, 153, 160, 167], "against": [0, 23, 64, 69, 83, 114, 115, 124, 126], "found": [0, 4, 17, 19, 23, 25, 45, 49, 83, 84, 89, 95, 105, 109, 110, 115, 116, 131, 134, 140, 147, 148, 162], "activecod": [0, 10, 17, 24, 46, 57, 58, 62, 63, 64, 66, 68, 69, 70, 83, 84, 94, 95, 98, 99, 100, 102, 103, 105, 106, 110, 115, 123, 124, 125, 126, 127, 128, 134, 135, 141, 142, 144], "thi": [0, 1, 4, 6, 8, 9, 10, 13, 15, 16, 17, 19, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 39, 40, 42, 43, 44, 45, 46, 47, 49, 50, 52, 53, 55, 57, 58, 59, 61, 64, 66, 67, 68, 69, 70, 76, 77, 78, 80, 81, 83, 84, 86, 88, 90, 92, 94, 95, 96, 97, 98, 99, 100, 102, 103, 104, 105, 106, 110, 112, 114, 115, 116, 118, 121, 123, 124, 125, 126, 127, 128, 129, 131, 132, 133, 134, 135, 136, 137, 139, 141, 142, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 159, 160, 164, 165, 167, 168], "To": [0, 5, 9, 10, 16, 17, 19, 24, 27, 28, 31, 35, 36, 39, 40, 43, 44, 45, 46, 47, 48, 51, 53, 55, 58, 64, 65, 68, 69, 70, 78, 83, 84, 85, 86, 94, 95, 96, 97, 99, 102, 106, 110, 111, 114, 115, 120, 123, 126, 131, 133, 134, 141, 142, 143, 144, 148, 151], "analyz": [0, 1, 4, 10, 15, 48, 83, 110, 114, 115, 123, 125, 126, 129], "need": [0, 1, 9, 11, 13, 17, 20, 21, 25, 28, 35, 39, 40, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 58, 64, 68, 70, 72, 73, 74, 78, 83, 84, 88, 94, 95, 99, 100, 102, 103, 106, 110, 112, 114, 115, 123, 124, 125, 126, 128, 131, 133, 134, 136, 138, 141, 142, 144, 147, 148, 152, 160, 168], "note": [0, 1, 2, 4, 9, 10, 14, 19, 21, 26, 28, 30, 39, 40, 43, 45, 46, 47, 52, 64, 68, 69, 70, 72, 76, 78, 83, 84, 94, 95, 99, 110, 114, 115, 123, 124, 125, 126, 128, 131, 134, 141, 152], "n": [0, 1, 2, 3, 4, 7, 8, 9, 10, 16, 17, 23, 24, 25, 26, 30, 37, 39, 40, 45, 46, 47, 61, 67, 68, 83, 84, 86, 95, 99, 103, 104, 113, 114, 115, 118, 122, 123, 124, 125, 126, 127, 128, 131, 132, 133, 134, 145, 146, 147, 151, 153, 168], "s1": 0, "caus": [0, 49, 64, 83, 96, 110, 123, 124, 148], "iter": [0, 1, 4, 8, 9, 10, 16, 19, 21, 23, 24, 39, 40, 43, 45, 46, 53, 58, 64, 83, 84, 88, 92, 94, 95, 97, 102, 104, 110, 112, 124, 148], "through": [0, 4, 9, 10, 15, 19, 21, 22, 23, 24, 28, 30, 39, 42, 45, 49, 53, 58, 78, 83, 88, 94, 95, 100, 102, 103, 110, 114, 115, 119, 123, 124, 125, 126, 127, 131, 134, 144, 152, 159], "arrai": [0, 1, 3, 4, 5, 6, 7, 8, 11, 24, 37, 43, 44, 45, 47, 51, 56, 57, 61, 63, 69, 85, 88, 94, 102, 114, 115, 116, 123, 138, 142, 146, 151, 168], "s2": 0, "posit": [0, 4, 8, 9, 16, 19, 26, 28, 45, 46, 49, 58, 60, 61, 64, 75, 76, 78, 83, 84, 86, 87, 88, 89, 94, 95, 108, 109, 110, 115, 119, 123, 124, 126, 129, 131, 134, 139, 141, 148, 152], "visit": [0, 21, 25, 26, 34, 82, 84, 95, 109, 110, 115, 140, 148, 152, 160], "onc": [0, 10, 14, 15, 16, 17, 18, 19, 24, 25, 26, 27, 31, 34, 39, 43, 45, 47, 52, 57, 64, 67, 68, 70, 75, 83, 84, 94, 95, 105, 106, 110, 114, 123, 125, 126, 131, 133, 134, 141, 144, 148], "match": [0, 11, 17, 19, 38, 45, 46, 56, 57, 64, 66, 67, 68, 79, 84, 91, 94, 107, 117, 130, 148, 154, 168], "number": [0, 1, 3, 4, 7, 9, 10, 13, 16, 17, 19, 21, 22, 23, 25, 26, 28, 30, 34, 35, 37, 39, 40, 42, 43, 44, 45, 46, 47, 51, 54, 57, 64, 67, 69, 70, 71, 72, 73, 74, 77, 78, 79, 80, 83, 84, 86, 88, 89, 93, 94, 95, 99, 100, 103, 104, 105, 107, 108, 109, 110, 112, 114, 115, 121, 123, 124, 125, 126, 127, 128, 129, 131, 132, 134, 135, 140, 144, 146, 147, 149, 152, 153, 155, 156, 157, 158, 168], "becom": [0, 1, 42, 43, 47, 48, 53, 58, 64, 83, 84, 109, 110, 115, 123, 126, 127, 131, 132, 133, 142, 144, 148], "sum": [0, 1, 10, 28, 37, 40, 46, 98, 99, 107, 123, 124, 168], "integ": [0, 1, 2, 10, 23, 39, 40, 43, 44, 45, 46, 49, 51, 53, 58, 64, 67, 70, 72, 73, 74, 83, 84, 88, 89, 107, 110, 112, 114, 115, 118, 121, 123, 124, 134, 138, 144, 168], "state": [0, 10, 19, 21, 24, 30, 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27, 30, 31, 34, 36, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 53, 54, 55, 56, 57, 58, 64, 68, 70, 75, 77, 78, 80, 90, 94, 97, 99, 102, 104, 106, 108, 110, 115, 116, 125, 129, 134, 139, 168], "scientist": [0, 1, 34, 36, 42, 52, 53, 54, 55, 94, 104], "given": [0, 1, 3, 7, 9, 10, 24, 30, 33, 35, 39, 40, 43, 44, 45, 46, 47, 49, 52, 53, 54, 57, 61, 63, 70, 72, 73, 74, 75, 83, 84, 86, 89, 100, 106, 108, 109, 110, 112, 125, 126, 128, 131, 132, 133, 134, 138, 141, 144, 148, 149], "choic": [0, 39, 45, 46, 62, 63, 64, 114], "determin": [0, 1, 4, 9, 19, 21, 29, 39, 64, 82, 84, 95, 109, 140, 145], "best": [0, 1, 3, 39, 40, 46, 94, 110, 114, 115, 123, 124, 126, 152], "resourc": [0, 4, 10, 45, 50, 54, 90, 129], "q": [0, 1, 4, 10, 19, 25, 26, 28, 39, 40, 43, 45, 46, 47, 58, 62, 63, 64, 66, 73, 74, 83, 84, 94, 99, 100, 103, 110, 114, 115, 123, 124, 125, 126, 127, 128, 131, 134, 139, 141, 142, 144, 147, 148, 152, 153], "7": [0, 1, 4, 10, 19, 20, 25, 30, 37, 43, 46, 58, 64, 67, 68, 69, 70, 84, 94, 95, 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30, 43, 44, 45, 46, 47, 51, 64, 66, 75, 95, 99, 105, 131, 147], "how": [1, 5, 6, 8, 9, 10, 13, 16, 17, 24, 26, 27, 28, 29, 30, 40, 42, 43, 44, 45, 46, 47, 49, 52, 54, 55, 58, 64, 70, 75, 81, 83, 84, 85, 94, 95, 97, 98, 99, 100, 102, 103, 104, 105, 106, 109, 110, 112, 114, 115, 116, 118, 123, 125, 126, 131, 132, 133, 139, 143, 144, 147, 148], "implement": [1, 4, 5, 6, 8, 9, 10, 12, 13, 16, 17, 19, 21, 22, 26, 27, 28, 32, 33, 38, 39, 40, 43, 44, 46, 47, 48, 49, 51, 52, 54, 55, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 69, 79, 81, 85, 86, 87, 88, 91, 95, 97, 99, 100, 103, 104, 107, 111, 112, 114, 115, 117, 118, 120, 121, 124, 125, 126, 133, 135, 136, 137, 138, 141, 142, 143, 144, 145, 146, 147, 149, 150, 152, 154, 168], "compar": [1, 4, 7, 10, 11, 17, 21, 39, 40, 45, 46, 54, 57, 64, 66, 68, 83, 84, 86, 104, 112, 114, 115, 116, 119, 121, 123, 124, 127, 128, 129, 134, 148, 168], "summat": [1, 10], "shown": [1, 4, 10, 16, 19, 20, 21, 23, 24, 25, 26, 28, 31, 36, 37, 39, 43, 45, 46, 47, 49, 57, 58, 64, 68, 69, 73, 83, 84, 88, 94, 95, 98, 100, 102, 104, 105, 106, 110, 114, 115, 123, 125, 126, 127, 128, 131, 134, 136, 139, 141, 142, 144, 147, 148, 152], "might": [1, 9, 17, 26, 27, 31, 35, 36, 37, 39, 45, 52, 54, 58, 64, 70, 75, 84, 100, 102, 103, 106, 110, 112, 115, 121, 131, 134, 139, 142, 147, 148], "count": [1, 2, 10, 11, 16, 18, 26, 39, 40, 67, 69, 84, 86, 110, 115, 160, 167, 168], "assign": [1, 4, 8, 9, 10, 39, 43, 46, 61, 70, 84, 96, 100, 112, 115, 121, 123, 124, 136, 161, 163, 166, 168], "statement": [1, 9, 10, 21, 33, 40, 42, 43, 45, 47, 52, 53, 68, 84, 95, 96, 98, 100, 106, 110, 125, 131, 141, 142, 144, 146, 149, 152], "sumofn": [1, 10], "thesum": [1, 10, 43, 102], "plu": [1, 40, 51, 94, 95, 103, 110, 146], "valu": [1, 3, 4, 10, 12, 13, 17, 19, 22, 24, 25, 28, 39, 44, 46, 47, 49, 51, 56, 58, 59, 64, 67, 68, 69, 70, 72, 73, 74, 81, 83, 84, 88, 89, 94, 95, 96, 98, 104, 106, 108, 109, 110, 112, 114, 115, 116, 118, 119, 121, 123, 124, 126, 127, 128, 129, 135, 137, 140, 141, 142, 144, 145, 148, 149, 152, 162, 168], "denot": [1, 43, 51, 64, 83, 84, 110, 131], "where": [1, 12, 21, 22, 25, 26, 30, 31, 34, 35, 37, 39, 40, 43, 44, 47, 54, 57, 60, 61, 64, 65, 67, 68, 69, 72, 74, 75, 77, 78, 80, 83, 84, 86, 87, 88, 89, 94, 95, 99, 100, 102, 103, 110, 114, 115, 116, 123, 125, 126, 128, 131, 134, 139, 141, 144, 147, 148, 152, 153, 167], "paramet": [1, 10, 23, 25, 29, 39, 44, 46, 47, 51, 52, 56, 58, 70, 72, 73, 74, 86, 88, 94, 95, 102, 103, 104, 106, 115, 123, 138, 144, 148, 152, 168], "often": [1, 10, 26, 39, 40, 42, 43, 45, 47, 53, 54, 55, 75, 84, 94, 96, 110, 123, 153], "refer": [1, 3, 10, 25, 42, 43, 44, 46, 47, 50, 51, 52, 55, 56, 63, 64, 75, 78, 81, 82, 83, 84, 89, 90, 95, 109, 110, 123, 131, 132, 134, 143, 144, 146, 148, 154, 168], "size": [1, 3, 4, 8, 9, 16, 23, 24, 26, 29, 39, 44, 45, 64, 66, 69, 70, 72, 73, 74, 83, 84, 88, 89, 103, 104, 109, 110, 112, 115, 116, 121, 123, 125, 126, 128, 134, 135, 146, 148, 161, 163, 166], "read": [1, 10, 19, 43, 44, 60, 64, 66, 67, 68, 83, 90, 95, 105, 144, 147, 152], "name": [1, 10, 21, 22, 23, 26, 33, 37, 39, 40, 43, 44, 45, 46, 47, 51, 52, 69, 75, 84, 95, 99, 108, 110, 133, 139, 142, 144, 152, 153], "abov": [1, 9, 10, 20, 21, 24, 26, 29, 31, 33, 35, 37, 39, 40, 43, 45, 46, 57, 59, 64, 70, 72, 73, 74, 83, 84, 86, 88, 89, 94, 95, 100, 103, 104, 105, 106, 110, 114, 123, 124, 125, 126, 128, 131, 133, 139, 141, 142, 144, 148, 153, 165], "sens": [1, 53, 64, 76, 84, 112, 115, 121, 136], "100": [1, 17, 39, 40, 43, 45, 89, 99, 110, 126, 159, 164, 165], "bigger": [1, 4, 126], "instanc": [1, 10, 21, 23, 24, 33, 43, 44, 46, 47, 52, 53, 70, 84, 94, 95, 142, 148], "becaus": [1, 4, 6, 8, 9, 10, 13, 15, 19, 24, 26, 28, 30, 39, 40, 43, 45, 46, 58, 64, 70, 86, 88, 90, 94, 95, 99, 103, 105, 106, 109, 123, 132, 134, 141, 144, 145, 147, 148, 152, 160], "seem": [1, 9, 10, 27, 64, 99, 101, 134, 147], "reason": [1, 9, 10, 15, 21, 26, 36, 39, 42, 43, 45, 47, 52, 54, 64, 68, 70, 84, 88, 102, 106, 110, 148, 152], "larger": [1, 4, 8, 9, 19, 26, 29, 31, 39, 70, 83, 100, 104, 119, 124, 125, 127, 129, 132, 136], "greater": [1, 22, 28, 39, 43, 46, 58, 69, 83, 114, 119, 124, 125, 126, 133, 140, 147, 148], "smaller": [1, 19, 94, 96, 99, 100, 101, 102, 103, 104, 105, 106, 114, 119, 123, 124, 125, 126, 127, 128, 129, 134, 136, 140], "chang": [1, 3, 4, 8, 9, 19, 24, 25, 26, 28, 35, 39, 40, 42, 43, 44, 45, 46, 55, 58, 64, 70, 84, 86, 93, 94, 95, 99, 100, 103, 106, 110, 128, 131, 132, 139, 147, 148, 152, 159, 164, 165, 168], "respect": [1, 4, 10, 19, 24, 39, 43, 47, 53, 55, 58, 64, 84, 89, 103, 110, 114, 115, 126, 129, 136, 144, 146, 148, 152, 161, 166], "prefer": [1, 43, 67, 136], "analysi": [1, 5, 38, 48, 52, 54, 70, 91, 112, 117, 121, 125, 128, 154, 168], "further": [1, 9, 10, 24, 40, 47, 83, 95, 96, 110, 114, 123, 131, 132, 134, 144], "exact": [1, 10, 46, 90, 94, 105, 137, 148], "most": [1, 4, 9, 10, 13, 15, 22, 26, 28, 39, 43, 45, 46, 47, 49, 52, 53, 58, 64, 67, 68, 70, 75, 77, 78, 80, 83, 84, 86, 90, 94, 99, 103, 110, 114, 116, 123, 125, 129, 131, 132, 134, 136, 146, 147, 148, 152], "part": [1, 3, 4, 8, 9, 14, 15, 22, 26, 28, 31, 37, 39, 45, 46, 47, 53, 67, 68, 84, 95, 110, 114, 119, 123, 127, 131, 134, 139, 140, 144, 153], "portion": [1, 43, 96, 109, 110, 123, 125], "tend": [1, 26, 42, 45, 70, 128], "overpow": 1, "rest": [1, 28, 42, 84, 100, 102, 105, 125, 134, 139, 144, 152], "comparison": [1, 4, 17, 43, 45, 46, 67, 86, 88, 108, 114, 124, 127, 128, 129, 147], "describ": [1, 3, 5, 17, 26, 31, 33, 39, 44, 46, 47, 52, 53, 55, 62, 63, 67, 69, 70, 72, 73, 74, 84, 89, 93, 94, 95, 105, 106, 110, 112, 121, 123, 126, 128, 131, 144, 148], "increas": [1, 3, 9, 10, 70, 100, 106, 110, 112, 131], "fastest": [1, 3, 45], "f": [1, 3, 16, 21, 23, 24, 25, 28, 59, 64, 96, 141, 159, 160, 164, 165], "provid": [1, 4, 9, 10, 19, 21, 23, 28, 31, 32, 41, 42, 44, 45, 46, 47, 50, 52, 53, 55, 61, 64, 67, 70, 71, 76, 78, 83, 84, 96, 98, 100, 104, 110, 113, 115, 116, 131, 137, 141, 144, 148, 149, 153], "approxim": [1, 40, 46, 110, 114, 115, 124, 132, 134], "represent": [1, 12, 13, 19, 24, 27, 33, 45, 46, 47, 53, 58, 70, 84, 86, 95, 103, 134, 142, 145], "exampl": [1, 9, 10, 11, 17, 21, 25, 26, 28, 30, 31, 35, 36, 37, 39, 40, 42, 43, 45, 46, 47, 50, 52, 53, 54, 57, 58, 66, 67, 68, 69, 70, 74, 75, 77, 78, 80, 83, 84, 88, 90, 94, 95, 98, 99, 100, 103, 104, 105, 106, 110, 114, 116, 118, 123, 125, 126, 128, 129, 131, 133, 134, 141, 142, 144, 147, 152, 153, 154, 167, 168], "constant": [1, 4, 9, 26, 42, 43, 44, 69, 88, 110, 113, 114, 132, 147], "less": [1, 26, 28, 43, 46, 54, 94, 103, 106, 114, 119, 125, 126, 133, 134, 140, 147, 148], "result": [1, 4, 10, 19, 21, 22, 26, 36, 39, 40, 43, 46, 47, 49, 52, 53, 54, 58, 64, 68, 70, 72, 73, 74, 81, 84, 94, 95, 96, 98, 103, 109, 110, 112, 114, 115, 125, 126, 132, 134, 138, 141, 144, 148, 152], "look": [1, 4, 8, 9, 10, 13, 14, 17, 19, 21, 22, 24, 25, 26, 27, 28, 31, 32, 37, 39, 40, 43, 44, 45, 46, 47, 51, 64, 70, 78, 83, 84, 92, 94, 95, 98, 99, 102, 103, 104, 105, 106, 110, 114, 115, 123, 124, 125, 126, 127, 131, 132, 133, 134, 139, 141, 142, 144, 145, 147, 148, 149, 150, 151, 152, 153], "drop": [1, 95, 146], "certainli": [1, 10, 53], "just": [1, 8, 9, 10, 17, 19, 23, 26, 28, 30, 36, 39, 40, 45, 46, 52, 64, 83, 84, 85, 90, 94, 95, 102, 103, 105, 106, 114, 123, 131, 133, 141, 142, 144, 147, 148, 152], "accur": [1, 9, 134], "suppos": [1, 17, 40, 51, 62, 70, 94, 95, 98, 99, 100, 102, 103, 104, 110, 114, 115, 123, 124, 127, 148, 152], "5n": 1, "2": [1, 2, 3, 4, 10, 11, 12, 13, 16, 17, 19, 20, 21, 23, 24, 26, 28, 30, 37, 39, 40, 43, 46, 47, 55, 58, 59, 66, 67, 69, 70, 73, 74, 78, 81, 82, 83, 84, 94, 95, 98, 99, 100, 102, 103, 104, 106, 110, 114, 116, 118, 122, 123, 124, 125, 126, 127, 128, 131, 132, 134, 136, 138, 139, 140, 141, 142, 144, 147, 148, 152, 153, 155, 156, 158, 160, 161, 162, 163, 166, 168], "27n": 1, "1005": 1, "small": [1, 13, 17, 21, 26, 28, 30, 31, 94, 99, 101, 102, 106, 108, 110, 112, 114, 121, 129, 134, 139, 141], "realli": [1, 10, 26, 36, 40, 84, 90, 92, 106, 134, 144, 148], "insignific": [1, 115], "role": [1, 48, 52, 84, 126], "plai": [1, 34, 48, 49, 52, 69, 84, 90, 104, 106], "focu": [1, 46, 55, 99], "coeffici": [1, 104, 115], "5": [1, 10, 17, 19, 20, 21, 23, 24, 25, 26, 30, 37, 43, 45, 46, 58, 59, 63, 64, 68, 70, 83, 84, 94, 95, 98, 99, 100, 102, 104, 106, 114, 115, 116, 118, 123, 124, 125, 126, 127, 128, 131, 132, 134, 136, 138, 142, 144, 148, 152, 160, 161, 162, 163, 166], "3n": 1, "sometim": [1, 10, 39, 43, 47, 52, 53, 55, 75, 77, 78, 80, 84, 87, 94, 105, 110, 128, 148], "data": [1, 3, 4, 5, 11, 13, 23, 27, 28, 32, 38, 39, 40, 42, 44, 46, 47, 48, 50, 51, 53, 56, 57, 58, 60, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 75, 76, 77, 79, 82, 83, 84, 85, 86, 90, 91, 95, 96, 99, 100, 109, 111, 115, 117, 118, 125, 133, 137, 139, 140, 141, 142, 143, 144, 145, 148, 150, 151, 152], "rather": [1, 4, 12, 21, 30, 39, 40, 45, 46, 47, 69, 70, 84, 94, 96, 106, 146], "kind": [1, 26, 27, 39, 45, 47, 57, 81, 106, 119, 129, 133, 142, 144, 148, 152], "averag": [1, 3, 4, 26, 40, 67, 70, 83, 86, 99, 108, 110, 115, 123], "extrem": [1, 31, 39, 47, 94], "poorli": [1, 3], "outstand": 1, "somewher": [1, 64, 84, 95, 128], "understand": [1, 5, 6, 10, 27, 28, 30, 34, 39, 42, 43, 44, 46, 47, 48, 52, 54, 64, 65, 84, 85, 94, 97, 106, 110, 111, 131, 134, 143, 144, 147], "distinct": [1, 39, 47, 125, 142], "misl": 1, "veri": [1, 10, 13, 17, 19, 26, 27, 28, 30, 31, 39, 40, 43, 45, 46, 47, 51, 52, 53, 55, 57, 58, 61, 64, 66, 67, 68, 71, 72, 75, 77, 80, 84, 92, 94, 95, 99, 100, 101, 103, 104, 106, 110, 115, 116, 123, 124, 126, 128, 131, 132, 134, 139, 141, 148, 149, 152, 153, 168], "come": [1, 10, 22, 29, 36, 39, 45, 47, 52, 53, 58, 60, 64, 67, 70, 77, 78, 80, 84, 88, 94, 95, 99, 104, 105, 106], "over": [1, 16, 19, 21, 24, 26, 30, 36, 40, 45, 54, 64, 83, 98, 99, 104, 134, 148, 151], "studi": [1, 24, 27, 30, 31, 34, 35, 42, 51, 52, 53, 56, 58, 70, 75, 116, 124, 125, 127, 129, 131, 137, 139, 145, 168], "These": [1, 40, 47, 52, 53, 55, 57, 64, 70, 75, 88, 94, 95, 110, 123, 131, 152], "logarithm": [1, 3, 110, 114, 134], "quadrat": [1, 3, 109, 110, 112], "3": [1, 4, 9, 10, 11, 13, 19, 20, 21, 24, 25, 26, 28, 29, 30, 31, 36, 37, 39, 40, 43, 45, 46, 47, 58, 59, 62, 63, 68, 69, 70, 73, 74, 78, 83, 84, 90, 94, 95, 99, 100, 102, 103, 104, 105, 110, 115, 116, 118, 123, 125, 126, 128, 131, 132, 134, 136, 138, 139, 141, 142, 144, 148, 152, 153, 158, 160, 161, 162, 163, 166, 168], "cubic": 1, "exponenti": [1, 3, 26, 43], "figur": [1, 4, 10, 12, 13, 16, 17, 19, 21, 23, 24, 25, 26, 27, 28, 30, 31, 35, 36, 37, 43, 45, 46, 47, 52, 55, 58, 64, 66, 68, 69, 70, 76, 77, 78, 80, 83, 84, 94, 95, 98, 100, 102, 103, 105, 106, 110, 114, 115, 123, 124, 125, 126, 128, 131, 132, 133, 134, 136, 139, 141, 142, 144, 147, 148, 152, 153], "graph": [1, 12, 13, 14, 15, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 94, 145, 160, 168], "notic": [1, 4, 9, 10, 13, 16, 17, 21, 23, 31, 40, 45, 49, 69, 70, 90, 94, 95, 98, 100, 102, 103, 106, 110, 115, 125, 131, 134, 135, 139, 141, 142, 147, 148, 149, 152], "defin": [1, 23, 28, 31, 33, 37, 43, 44, 45, 51, 52, 55, 56, 63, 64, 68, 72, 73, 74, 86, 88, 89, 95, 96, 99, 102, 106, 110, 132, 133, 134, 141, 142, 144, 148, 151, 152, 153, 159, 160, 161, 162, 163, 164, 165, 166, 168], "hard": [1, 26, 42, 95, 134], "tell": [1, 6, 10, 45, 84, 94, 100, 104], "definit": [1, 23, 31, 33, 38, 39, 40, 44, 45, 46, 49, 51, 52, 96, 99, 106, 125, 131, 133, 141, 142, 148, 154, 168], "relationship": [1, 3, 21, 22, 27, 35, 37, 44, 47, 57, 86, 110, 115, 134, 140, 147, 148, 153], "easi": [1, 10, 13, 23, 26, 27, 28, 45, 83, 92, 94, 95, 100, 103, 106, 109, 110, 116, 125, 131, 134, 141, 145, 148], "top": [1, 45, 46, 47, 57, 63, 64, 74, 75, 78, 94, 95, 98, 100, 105, 134, 139, 144, 160], "bottom": [1, 10, 36, 45, 46, 64, 75, 94, 95, 100, 105, 125, 134, 139, 140, 147, 160], "least": [1, 4, 15, 22, 28, 64, 66, 84, 88, 94, 146, 153], "list": [1, 3, 4, 9, 10, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 33, 36, 38, 40, 46, 47, 48, 52, 57, 58, 60, 61, 64, 67, 70, 72, 74, 81, 82, 85, 86, 87, 89, 90, 91, 94, 95, 96, 98, 99, 100, 102, 104, 106, 108, 110, 112, 113, 114, 116, 118, 121, 122, 123, 124, 125, 126, 128, 129, 131, 134, 139, 140, 142, 143, 144, 148, 151, 152, 153, 160, 161, 163, 166, 168], "doe": [1, 10, 19, 24, 26, 40, 43, 45, 46, 47, 52, 53, 57, 64, 70, 74, 76, 84, 92, 94, 95, 96, 100, 104, 105, 106, 110, 112, 115, 116, 118, 121, 122, 125, 126, 128, 131, 144, 146, 147, 148], "anyth": [1, 24, 36, 40, 45, 84, 144], "instruct": [1, 3, 10, 42, 43, 44, 52, 60, 106, 152], "includ": [1, 4, 9, 16, 24, 27, 29, 36, 39, 40, 41, 43, 45, 46, 47, 48, 52, 57, 58, 64, 67, 84, 85, 86, 89, 90, 96, 103, 104, 116, 139, 142, 146, 159, 160, 161, 162, 163, 164, 165, 166, 167], "iostream": [1, 4, 9, 16, 24, 40, 46, 84, 142, 159, 164, 165], "namespac": [1, 4, 9, 16, 24, 40, 45, 46, 84, 142, 159, 160, 161, 162, 163, 164, 165, 166], "std": [1, 4, 9, 16, 24, 40, 46, 84, 116, 142, 159, 160, 161, 162, 163, 164, 165, 166], "6": [1, 4, 10, 19, 20, 24, 25, 28, 30, 43, 45, 46, 58, 64, 66, 68, 70, 84, 94, 95, 98, 99, 100, 102, 103, 104, 110, 114, 115, 118, 125, 126, 127, 128, 131, 134, 138, 142, 144, 147, 148, 152, 159, 160, 161, 163, 164, 165, 166], "x": [1, 3, 4, 16, 19, 24, 26, 43, 131, 134, 140, 141, 144, 148, 152, 160], "y": [1, 4, 16, 19, 24, 26, 45, 118, 144, 152, 160], "k": [1, 2, 24, 26, 39, 125, 128, 134, 135, 163], "w": [1, 13, 16, 19, 22, 24, 26, 31, 36, 37, 104, 159, 164, 165], "45": [1, 59, 81, 83, 104, 106, 125], "v": [1, 13, 14, 15, 18, 19, 22, 26, 28, 31, 36, 37], "d": [1, 4, 21, 24, 25, 28, 46, 58, 59, 64, 72, 131, 138, 141, 147, 159, 160, 164, 165], "33": [1, 31, 70, 93], "def": [1, 19, 24, 25, 26, 28, 46, 47, 95, 106, 110, 141, 142, 144, 148, 152, 158], "rang": [1, 4, 45, 70, 88, 104, 106, 110, 133], "four": [1, 17, 24, 25, 28, 45, 46, 47, 75, 94, 95, 100, 128, 144, 147, 153], "repres": [1, 3, 10, 12, 13, 16, 21, 22, 23, 26, 27, 30, 32, 34, 35, 37, 43, 44, 45, 46, 47, 49, 51, 53, 55, 58, 68, 70, 78, 83, 84, 95, 99, 109, 123, 124, 125, 126, 127, 134, 141, 142, 144, 147, 148, 152, 153], "start": [1, 9, 10, 15, 16, 17, 19, 21, 22, 24, 25, 26, 28, 31, 35, 36, 37, 39, 45, 46, 47, 49, 52, 56, 58, 64, 68, 70, 74, 77, 78, 80, 83, 84, 86, 93, 94, 95, 100, 102, 104, 105, 106, 110, 112, 114, 115, 123, 124, 125, 127, 131, 132, 134, 136, 138, 139, 140, 142, 144, 148, 152, 168], "due": [1, 8, 16, 23, 45, 52, 64, 70, 77, 80, 83, 90, 110, 127], "fourth": [1, 98, 100], "4": [1, 9, 10, 11, 12, 16, 19, 20, 21, 23, 24, 25, 26, 28, 29, 30, 36, 37, 40, 43, 46, 58, 59, 63, 67, 68, 70, 72, 73, 78, 83, 84, 94, 95, 98, 99, 103, 104, 105, 114, 116, 118, 124, 128, 131, 132, 134, 138, 142, 144, 148, 152, 153, 160, 161, 162, 163, 166, 168], "By": [1, 10, 30, 45, 46, 47, 54, 55, 64, 70, 94, 95, 110, 128, 131, 132, 139, 144, 153, 168], "expon": [1, 20], "easili": [1, 12, 26, 47, 57, 58, 64, 66, 94, 95, 100, 102, 103, 134], "few": [1, 13, 45, 64, 102, 110, 123, 126, 134, 139, 144, 148], "discuss": [1, 4, 11, 25, 37, 38, 43, 46, 55, 56, 64, 79, 83, 84, 91, 103, 107, 110, 117, 129, 130, 131, 134, 137, 148, 154, 168], "initi": [1, 10, 14, 15, 16, 19, 23, 24, 28, 39, 40, 43, 44, 46, 47, 68, 70, 83, 84, 95, 100, 102, 105, 106, 110, 114, 115, 123, 124, 125, 126, 127, 128, 134, 144, 161, 163], "quickli": [1, 21, 45, 77, 80, 110, 114], "overtak": 1, "continu": [1, 9, 10, 15, 21, 22, 24, 25, 28, 29, 49, 51, 57, 58, 66, 67, 69, 83, 84, 95, 104, 105, 112, 115, 121, 123, 125, 127, 131, 136, 142, 144, 148], "true": [1, 15, 16, 23, 24, 25, 33, 39, 43, 44, 46, 47, 51, 68, 70, 72, 73, 83, 84, 94, 95, 103, 110, 115, 116, 135, 139, 160, 161, 162, 166], "100n": 1, "find": [1, 4, 7, 8, 9, 10, 12, 16, 17, 19, 20, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 39, 43, 46, 49, 50, 54, 58, 69, 83, 84, 93, 94, 95, 104, 106, 109, 110, 114, 115, 116, 119, 123, 126, 134, 144, 147, 148, 160], "minimum": [1, 20, 28, 32, 53, 70, 94, 127, 134, 135, 148], "should": [1, 4, 19, 21, 23, 24, 30, 36, 39, 40, 43, 45, 46, 47, 49, 51, 52, 64, 67, 68, 70, 83, 84, 86, 95, 100, 102, 103, 104, 106, 110, 114, 123, 126, 129, 131, 141, 144, 146, 148, 152], "log_": 1, "complet": [1, 16, 19, 24, 25, 27, 39, 40, 44, 45, 46, 47, 63, 64, 66, 68, 70, 77, 80, 83, 84, 95, 99, 100, 106, 110, 114, 123, 124, 126, 127, 128, 131, 134, 136, 140, 144, 147], "1000": [1, 4, 9, 10, 40, 159, 160, 164, 165], "2000": 1, "1": [2, 4, 7, 8, 9, 10, 11, 16, 17, 19, 20, 21, 23, 24, 25, 26, 27, 28, 30, 34, 36, 37, 39, 40, 45, 46, 47, 52, 57, 58, 59, 61, 62, 63, 64, 66, 67, 68, 69, 70, 76, 77, 78, 80, 83, 84, 86, 94, 95, 98, 99, 100, 102, 103, 104, 105, 106, 114, 116, 118, 124, 125, 126, 127, 128, 131, 132, 133, 134, 135, 136, 138, 139, 141, 142, 144, 147, 148, 152, 153, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168], "divis": [2, 43, 44, 58, 64, 103, 126, 134], "certain": [3, 6, 45, 52, 61, 69, 70, 74, 94, 95], "circumst": [3, 67, 86, 112, 121, 148], "especi": [3, 10, 70, 114], "notat": [3, 4, 6, 11, 39, 46, 48, 53, 57, 60, 64, 168], "brute": [3, 11, 28, 168], "forc": [3, 11, 23, 28, 43, 64, 110, 168], "contain": [3, 4, 16, 19, 22, 23, 24, 25, 31, 36, 39, 44, 51, 67, 70, 74, 82, 83, 84, 86, 88, 89, 94, 95, 96, 110, 115, 116, 127, 148], "hash": [3, 6, 7, 11, 44, 51, 56, 64, 108, 109, 111, 112, 113, 137, 149, 151, 168], "check": [3, 11, 21, 23, 24, 39, 45, 49, 56, 57, 66, 67, 77, 80, 83, 102, 104, 107, 117, 130, 131, 134, 138, 139, 142, 144, 152, 168], "tabl": [3, 6, 7, 11, 44, 45, 47, 51, 56, 94, 108, 109, 112, 113, 137, 149], "specif": [3, 10, 23, 37, 39, 43, 45, 47, 57, 83, 84, 95, 103, 109, 129, 136, 139], "element": [3, 4, 8, 9, 39, 40, 44, 60, 63, 75, 77, 80, 82, 84, 88, 89, 94, 95, 96, 102, 115, 119, 123, 124, 125, 126, 127, 129, 134, 136, 139, 140, 141, 163], "contigu": [3, 4, 8, 9, 39, 51, 84, 85, 87, 128], "adjac": [3, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 33, 38, 115, 119, 123, 168], "next": [3, 16, 19, 21, 23, 24, 25, 26, 28, 30, 31, 39, 40, 46, 47, 54, 57, 64, 68, 70, 77, 78, 80, 83, 84, 86, 88, 94, 95, 96, 100, 103, 105, 106, 109, 110, 114, 116, 119, 123, 126, 127, 128, 131, 134, 139, 140, 142, 144, 145, 147, 148, 152], "dynam": [3, 8, 9, 39, 44, 51, 89, 93, 96, 104, 107, 168], "automat": [3, 8, 9, 39, 45, 112, 133, 140], "being": [3, 9, 10, 21, 24, 26, 39, 40, 43, 44, 45, 46, 52, 53, 58, 64, 67, 77, 80, 109, 110, 115, 123, 124, 125, 127, 128, 129, 142], "rais": [3, 10, 43, 45, 49, 96, 144, 148], "power": [3, 31, 34, 39, 43, 46, 47, 50, 51, 70, 75, 148], "like": [3, 8, 9, 10, 13, 17, 25, 30, 31, 39, 40, 43, 44, 45, 46, 47, 54, 58, 61, 64, 66, 67, 68, 69, 70, 71, 77, 78, 80, 84, 85, 88, 90, 92, 94, 95, 96, 98, 99, 100, 101, 102, 103, 104, 106, 110, 114, 129, 133, 134, 139, 141, 142, 144, 145, 147, 148, 152], "get_item": 3, "retriev": [3, 39, 66, 70, 144, 148], "inform": [3, 4, 22, 28, 30, 37, 40, 44, 50, 55, 58, 64, 84, 86, 88, 95, 110, 140, 144, 153], "associ": [3, 4, 22, 30, 39, 43, 44, 46, 51, 53, 64, 109, 110, 148], "kei": [3, 4, 12, 16, 17, 19, 22, 23, 24, 26, 37, 39, 40, 43, 44, 46, 48, 51, 52, 57, 94, 96, 100, 102, 109, 110, 114, 115, 128, 131, 132, 134, 135, 137, 138, 140, 142, 144, 145, 146, 147, 148, 149, 151, 152, 153, 161], "collect": [3, 11, 17, 43, 44, 45, 47, 51, 55, 56, 60, 67, 72, 73, 74, 75, 76, 77, 78, 80, 82, 84, 87, 88, 89, 109, 110, 115, 116, 119, 129, 137, 168], "pair": [3, 16, 19, 21, 22, 29, 30, 31, 39, 44, 51, 60, 64, 68, 102, 109, 110, 123, 137, 139, 148, 149, 153, 161, 163, 166], "map": [3, 4, 16, 17, 19, 23, 24, 27, 39, 44, 47, 64, 94, 109, 111, 112, 117, 133, 137, 143, 144, 148, 149, 154, 160, 168], "invers": [3, 147], "usual": [3, 44, 55, 84, 93, 94, 99, 144], "present": [3, 45, 50, 84, 88, 100, 110, 115, 116, 144], "logn": 3, "who": [3, 26, 28, 39, 43, 52, 69, 95, 104, 168], "highest": [3, 78, 145], "squar": [3, 10, 16, 25, 26, 34, 40, 45, 51, 52, 54, 57, 68, 86, 95, 109, 162], "complex": [3, 4, 42, 43, 45, 51, 52, 53, 55, 64, 83, 84, 96, 97, 107, 110, 115, 125, 129, 131, 168], "ax": 3, "bx": 3, "set_item": 3, "add": [3, 10, 14, 19, 21, 23, 24, 28, 33, 37, 39, 40, 46, 47, 49, 66, 70, 72, 73, 74, 81, 83, 84, 88, 94, 95, 100, 103, 110, 131, 134, 135, 141, 142, 144, 146, 148, 149, 152], "item": [3, 4, 8, 9, 39, 43, 44, 47, 53, 58, 60, 61, 62, 63, 66, 69, 72, 73, 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 86, 87, 88, 89, 94, 95, 104, 109, 110, 112, 114, 115, 116, 118, 119, 123, 124, 125, 126, 127, 128, 129, 134, 135, 136, 137, 139, 145, 146, 161, 163, 166], "your": [3, 10, 13, 20, 24, 26, 29, 30, 36, 39, 40, 42, 43, 44, 45, 46, 47, 52, 58, 64, 66, 67, 78, 84, 90, 94, 95, 104, 106, 112, 118, 146, 153, 167], "vector": [3, 4, 6, 7, 8, 11, 16, 17, 19, 23, 24, 43, 44, 47, 51, 56, 57, 59, 64, 67, 70, 75, 85, 86, 88, 99, 107, 112, 114, 115, 116, 121, 124, 125, 127, 128, 134, 135, 137, 144, 145, 161, 162, 163, 166, 168], "sequenc": [3, 19, 21, 22, 27, 28, 34, 35, 37, 39, 44, 47, 57, 58, 63, 68, 72, 73, 74, 82, 86, 88, 96, 102, 103, 104, 110, 114, 115, 132], "store": [3, 4, 8, 13, 17, 19, 23, 36, 39, 40, 43, 44, 47, 51, 52, 58, 66, 67, 77, 78, 80, 84, 85, 86, 88, 89, 94, 96, 109, 110, 115, 131, 134, 141, 142, 144, 148, 149, 152], "singl": [3, 9, 15, 17, 21, 26, 28, 31, 34, 39, 40, 43, 44, 45, 46, 47, 51, 64, 70, 76, 77, 80, 84, 86, 95, 96, 100, 103, 105, 110, 125, 128, 134, 145, 148], "type": [3, 21, 22, 23, 26, 27, 32, 38, 39, 40, 41, 44, 46, 47, 49, 50, 51, 52, 53, 56, 57, 62, 63, 64, 65, 70, 71, 77, 79, 80, 81, 85, 90, 91, 94, 95, 96, 100, 109, 111, 115, 117, 123, 124, 125, 126, 127, 128, 133, 137, 139, 141, 151, 168], "alloc": [3, 9, 39, 44, 45, 51, 98], "major": [4, 27, 45, 104], "structur": [4, 6, 13, 27, 31, 39, 40, 42, 44, 46, 47, 48, 56, 57, 58, 60, 62, 63, 64, 65, 66, 67, 68, 71, 72, 73, 74, 76, 82, 83, 84, 85, 88, 89, 96, 99, 100, 109, 110, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 150, 151, 152, 154], "recal": [4, 19, 47, 57, 63, 64, 70, 83, 84, 102, 110, 112, 114, 115, 123, 125, 129, 132, 137, 144, 147], "access": [4, 8, 9, 39, 44, 46, 47, 78, 83, 84, 88, 89, 95, 98, 110, 141, 152], "mostli": 4, "empti": [4, 13, 19, 33, 58, 63, 64, 68, 70, 71, 72, 73, 74, 83, 84, 88, 89, 110, 125, 131, 134, 135, 141, 144, 148, 149, 153], "index": [4, 7, 8, 9, 10, 24, 39, 44, 47, 58, 84, 86, 88, 95, 110, 112, 115, 134, 141, 161, 163, 166, 168], "bucket": [4, 17, 24], "locat": [4, 8, 9, 16, 24, 26, 28, 30, 39, 40, 43, 44, 51, 52, 75, 83, 84, 88, 95, 110, 115, 123, 126, 127, 161, 163, 166], "ideal": [4, 83], "distribut": [4, 110, 147], "uniformli": 4, "uniqu": [4, 39, 44, 47, 51, 88, 109, 110, 128, 139, 153], "design": [4, 9, 28, 39, 40, 44, 45, 46, 47, 49, 52, 54, 67, 69, 70, 71, 86, 99, 110, 136, 144, 153], "handl": [4, 28, 46, 57, 64, 66, 67, 70, 84, 90, 95, 96, 98, 100, 110, 112, 115, 134, 142, 146, 148], "collis": [4, 109, 112, 117, 168], "depth": [4, 16, 22, 25, 26, 29, 30, 31, 32, 36, 38, 147, 168], "book": [4, 6, 78, 90, 94, 100, 134, 152, 167], "wai": [4, 9, 10, 12, 13, 19, 21, 22, 24, 26, 27, 33, 37, 39, 40, 42, 43, 44, 45, 46, 47, 49, 52, 53, 54, 55, 58, 64, 70, 71, 75, 77, 80, 83, 84, 89, 90, 94, 95, 96, 98, 99, 100, 102, 105, 106, 110, 112, 114, 115, 116, 121, 124, 125, 126, 128, 129, 131, 134, 136, 137, 139, 144, 145, 147, 148, 152], "thing": [4, 9, 10, 15, 21, 24, 26, 27, 28, 36, 39, 45, 46, 47, 52, 60, 61, 64, 69, 72, 90, 94, 95, 100, 105, 110, 131, 136, 139, 142, 144], "now": [4, 6, 8, 9, 10, 19, 21, 24, 28, 31, 36, 37, 43, 46, 47, 49, 55, 62, 63, 64, 66, 68, 70, 78, 83, 84, 88, 94, 95, 98, 100, 103, 106, 110, 123, 124, 125, 126, 128, 131, 134, 135, 136, 139, 142, 144, 147, 148, 152, 153], "also": [4, 6, 8, 9, 10, 12, 19, 21, 22, 23, 24, 25, 27, 28, 37, 39, 40, 42, 43, 44, 45, 46, 47, 50, 52, 53, 54, 58, 60, 61, 64, 68, 69, 70, 75, 76, 77, 80, 84, 86, 88, 94, 95, 98, 102, 103, 106, 110, 119, 123, 124, 125, 126, 127, 129, 131, 134, 136, 139, 144, 147, 148, 152, 153, 160], "summar": [4, 115, 151], "side": [4, 26, 29, 43, 62, 69, 103, 104, 105, 106, 119, 126, 131, 132], "below": [4, 16, 21, 23, 24, 25, 26, 30, 39, 40, 43, 45, 47, 64, 66, 70, 72, 73, 74, 84, 89, 95, 104, 106, 110, 114, 124, 148], "rare": [4, 152], "degener": 4, "talk": [4, 30, 90, 95, 99], "insert": [4, 7, 8, 9, 26, 39, 43, 52, 78, 84, 86, 88, 89, 104, 110, 112, 118, 119, 120, 121, 122, 128, 130, 131, 134, 135, 136, 138, 141, 142, 145, 147, 148, 168], "eras": [4, 7, 8, 9, 39, 89, 102], "speed": [4, 26, 39, 42, 45, 52, 70, 94, 112, 121, 159, 161, 162, 163, 164, 165, 166], "experi": [4, 6, 7, 9, 54, 67, 68, 86, 95, 112, 121, 139], "confirm": 4, "ll": [4, 9, 21, 40], "Then": [4, 17, 23, 64, 67, 94, 100, 105, 106, 114, 126, 144, 152], "pick": [4, 90, 118, 126], "random": [4, 7, 40, 69, 70, 71, 104, 106, 112, 118, 121, 126, 138, 147], "longer": [4, 9, 10, 49, 58, 64, 70, 83, 84, 106], "repeat": [4, 9, 10, 24, 49, 95, 114, 115, 126, 134], "much": [4, 8, 10, 17, 26, 39, 46, 47, 49, 54, 55, 66, 70, 84, 90, 95, 101, 106, 114, 116, 139, 148], "remain": [4, 9, 25, 28, 42, 46, 49, 55, 60, 64, 68, 69, 70, 76, 83, 84, 86, 100, 110, 114, 126, 127, 131, 133, 140, 163], "line": [4, 10, 21, 25, 26, 40, 43, 46, 47, 49, 57, 58, 64, 67, 68, 69, 70, 77, 78, 80, 83, 84, 94, 95, 98, 99, 100, 102, 103, 104, 106, 110, 123, 124, 125, 127, 131, 142, 144, 152, 155, 156, 157, 159, 160, 162, 164, 165], "ctime": [4, 9, 10], "unordered_map": [4, 39], "10000": [4, 166], "1000001": 4, "20000": [4, 39], "clock_t": 4, "clock": [4, 9, 10], "avector": [4, 125, 134], "push_back": [4, 8, 9, 16, 23, 24, 39, 70, 71, 72, 134, 160, 161, 162, 163, 166], "doubl": [4, 39, 40, 43, 44, 51, 70, 76, 147], "elapsed_sec": 4, "clocks_per_sec": 4, "begin_ht": 4, "null": [4, 16, 23, 24, 70, 83, 84, 131, 142, 148, 149, 152], "end_ht": 4, "elapsed_secs_ht": 4, "print": [4, 23, 24, 40, 45, 46, 77, 79, 80, 86, 94, 95, 100, 104, 125, 148, 152, 168], "output": [4, 10, 23, 30, 31, 39, 40, 43, 44, 46, 47, 49, 64, 70, 110, 159, 164, 165], "cout": [4, 16, 23, 24, 40, 43, 46, 47, 63, 70, 86, 95, 100, 110, 112, 116, 152], "endl": [4, 16, 23, 24, 40, 43, 46, 70, 100, 110, 116, 148, 152], "timeit": 4, "timer": [4, 9, 70], "randrang": [4, 70], "__main__": 4, "lst_time": 4, "d_time": 4, "3f": 4, "smallest": [4, 7, 19, 28, 30, 35, 88, 93, 94, 104, 105, 106, 119, 123, 125, 127, 134, 135, 136, 140, 145, 148], "89": [4, 138], "largest": [4, 22, 31, 88, 94, 100, 119, 123, 127, 134, 140, 145, 148], "990": 4, "11": [4, 8, 16, 21, 24, 25, 28, 30, 39, 40, 43, 47, 58, 64, 70, 84, 94, 100, 102, 110, 114, 115, 125, 126, 127, 138], "603": 4, "linearli": 4, "verifi": [4, 7, 9, 23, 110], "assert": [4, 134], "seen": [4, 8, 9, 10, 26, 32, 40, 46, 54, 64, 68, 83, 84, 100, 128, 129, 131, 134, 137, 152], "took": [4, 70], "004": 4, "millisecond": 4, "evolv": 4, "languag": [4, 10, 39, 40, 42, 43, 44, 45, 46, 47, 48, 50, 51, 53, 57, 62, 63, 67, 68, 70, 116], "behind": [4, 30, 45, 83, 84, 124], "scene": [4, 30], "latest": [4, 28], "websit": 4, "measur": [4, 8, 9, 10, 45, 129], "allow": [4, 9, 12, 19, 25, 34, 35, 39, 40, 44, 45, 46, 47, 49, 51, 52, 53, 54, 55, 64, 67, 69, 70, 71, 75, 83, 84, 86, 88, 95, 99, 100, 101, 105, 110, 123, 124, 125, 127, 131, 134, 136, 141, 142, 144, 145, 148, 152, 167, 168], "classifi": [4, 148], "factor": [4, 26, 30, 109, 110, 112, 125, 131, 132, 133, 134, 138, 140, 147], "mind": [4, 43, 84], "select": [4, 25, 26, 28, 45, 47, 53, 84, 94, 104, 106, 112, 118, 119, 120, 121, 122, 126, 130, 158, 165, 168], "appli": [4, 8, 9, 11, 20, 36, 39, 45, 46, 47, 51, 95, 97, 105, 106, 131, 144, 168], "descript": [4, 43, 45, 46, 53, 55, 95, 100, 110], "why": [5, 6, 9, 20, 21, 26, 39, 42, 43, 45, 56, 64, 90, 99, 100, 112, 121, 138, 148, 168], "dictionari": [5, 12, 23, 57, 96, 144, 148], "impact": [5, 10, 40, 86, 110], "benchmark": [5, 10, 67, 86, 112, 121, 124, 127], "idea": [6, 10, 16, 26, 28, 39, 42, 46, 47, 48, 50, 52, 55, 58, 69, 70, 78, 84, 95, 102, 104, 105, 106, 110, 111, 126, 131, 135], "section": [6, 25, 35, 39, 44, 46, 47, 50, 57, 61, 70, 84, 92, 94, 95, 103, 106, 110, 129, 133, 134, 136, 137, 139, 140, 144, 145, 147, 151, 152], "illustr": [6, 12, 13, 16, 20, 21, 28, 30, 34, 36, 37, 45, 85, 94, 98, 103, 105, 106, 125, 128, 131, 132, 134, 139, 141, 144, 148, 152, 153], "benefit": [6, 40, 45, 47, 110, 114, 129, 133], "build": [6, 14, 15, 24, 25, 38, 46, 53, 56, 58, 61, 70, 84, 86, 104, 105, 110, 133, 134, 135, 138, 142, 144, 148, 168], "block": [6, 10, 47, 53, 57, 84, 95, 96, 123], "remaind": [6, 31, 43, 46, 58, 59, 81, 83, 99, 103, 109, 142], "explain": [6, 7, 9, 10, 20, 33, 81, 83, 90, 108, 111, 112, 120], "devis": [7, 108, 118], "work": [7, 10, 17, 19, 21, 24, 28, 30, 39, 40, 43, 44, 45, 46, 47, 49, 52, 53, 54, 58, 60, 64, 70, 77, 80, 81, 83, 84, 86, 94, 95, 100, 102, 103, 105, 106, 110, 114, 115, 116, 123, 124, 125, 126, 131, 134, 141, 144, 147, 148, 152], "kth": 7, "improv": [7, 9, 40, 44, 46, 94, 110, 112, 115, 121, 122, 125, 127, 128, 129, 131, 136], "previou": [7, 10, 20, 25, 40, 50, 57, 61, 67, 83, 84, 88, 92, 94, 95, 98, 103, 106, 110, 124, 128, 131, 132, 133, 138, 147, 148], "prior": 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94, 98, 103, 105, 106, 110, 114, 118, 124, 125, 127, 131, 132, 134, 135, 136, 141, 142, 144, 145, 146, 147, 148, 149], "delet": [8, 9, 39, 45, 88, 89, 104, 110, 112, 131, 136, 147, 148, 149], "realloc": [8, 9, 39], "exist": [8, 9, 39, 44, 45, 47, 49, 51, 52, 53, 54, 57, 58, 60, 67, 70, 76, 77, 78, 80, 83, 84, 106, 108, 110, 124, 142, 144, 148, 152, 159, 160], "alreadi": [8, 9, 19, 21, 24, 26, 37, 46, 51, 61, 62, 63, 64, 84, 88, 94, 95, 96, 100, 102, 110, 123, 124, 125, 126, 129, 131, 134, 137, 141, 144, 146, 148, 149, 152], "matter": [8, 9, 10, 43, 46, 64, 106, 115, 125, 135, 139, 148], "concret": [8, 9, 103], "strike": 8, "resembl": [8, 142], "similar": [8, 9, 10, 16, 19, 28, 30, 31, 40, 46, 47, 54, 55, 61, 76, 84, 89, 103, 105, 114, 125, 131, 132, 141, 148, 149], "pop_back": [8, 9, 39, 71, 72, 134], "srt": [8, 9], "stp": [8, 9], "reserv": [8, 9, 39, 43, 51], "unless": [8, 9, 39, 110, 131, 153], "inadequ": [8, 9], "capac": [8, 9, 39, 42], "move": [8, 9, 16, 19, 25, 26, 28, 34, 39, 45, 47, 64, 69, 72, 78, 83, 84, 99, 100, 103, 105, 106, 110, 112, 114, 115, 119, 121, 123, 124, 126, 128, 131, 134, 139, 144, 145, 152, 153, 160], "nevertheless": [9, 39], "remov": [9, 14, 24, 28, 36, 39, 40, 43, 57, 58, 60, 61, 64, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 80, 81, 83, 84, 86, 88, 103, 125, 134, 135, 136, 145, 148, 152, 160], "resiz": [9, 112], "middl": [9, 16, 26, 64, 77, 80, 83, 84, 95, 100, 105, 110, 114, 118, 119, 122, 125, 126, 134, 160], "right": [9, 10, 26, 37, 43, 45, 46, 49, 58, 64, 66, 67, 68, 72, 73, 74, 75, 84, 88, 94, 95, 103, 105, 106, 110, 114, 124, 125, 126, 131, 132, 133, 134, 136, 140, 141, 142, 144, 147, 148, 152, 158, 162, 163], "shift": [9, 52, 124, 128, 134, 159, 164, 165], "creat": [9, 13, 16, 17, 19, 21, 22, 23, 25, 31, 33, 39, 40, 42, 43, 44, 45, 46, 47, 51, 53, 55, 58, 64, 70, 71, 72, 73, 74, 78, 82, 83, 84, 88, 89, 90, 94, 95, 98, 105, 106, 110, 112, 114, 116, 121, 128, 131, 134, 135, 138, 139, 141, 142, 144, 146, 148, 149, 159, 164, 165, 167], "method": [9, 10, 19, 21, 23, 25, 26, 29, 40, 44, 45, 46, 47, 48, 49, 51, 61, 62, 63, 64, 70, 81, 83, 84, 86, 94, 95, 101, 103, 105, 109, 112, 119, 121, 123, 126, 129, 131, 134, 135, 138, 142, 144, 146, 147, 148, 152], "adequ": 9, "void": [9, 16, 23, 24, 40, 44, 51, 70, 83, 84, 110, 131, 134, 142, 148, 152, 159, 160, 161, 162, 163, 164, 165, 166], "test1": 9, "num": [9, 40, 46, 69, 144, 152], "vect": 9, "captur": 9, "modul": [9, 52, 70, 104, 105, 106, 144, 168], "develop": [9, 10, 24, 25, 28, 42, 45, 47, 48, 52, 53, 54, 64, 104, 129], "cross": [9, 29, 46, 104], "platform": [9, 42], "environ": 9, "mechan": [9, 40, 52, 67], "across": [9, 10, 21, 26, 28, 29, 45, 64, 95, 104], "system": [9, 10, 27, 43, 44, 52, 58, 77, 80, 90, 97, 139], "object": [9, 11, 12, 19, 22, 23, 34, 38, 43, 44, 45, 47, 50, 51, 56, 62, 63, 70, 76, 77, 78, 79, 80, 84, 89, 91, 94, 95, 100, 107, 117, 126, 130, 142, 144, 148, 154, 168], "mark": [9, 29, 84, 95, 104], "current": [9, 10, 18, 19, 24, 25, 26, 47, 57, 64, 68, 70, 72, 73, 78, 83, 84, 88, 94, 95, 110, 124, 125, 126, 127, 128, 131, 134, 140, 141, 144, 148], "runtim": [9, 96], "subtract": [9, 46, 53, 64, 70, 94, 103, 104, 105, 106, 131, 144], "elaps": 9, "session": [9, 23, 39, 43, 47, 110], "within": [9, 14, 23, 40, 42, 44, 45, 47, 58, 64, 77, 80, 114, 152], "loop": [9, 10, 14, 15, 18, 19, 21, 23, 25, 31, 43, 64, 84, 94, 95, 102], "taken": [9, 14, 27], "Not": [9, 35, 40, 43, 47, 84, 115], "durat": 9, "bit": [9, 39, 49, 64, 72, 90, 94, 106, 131, 134, 141, 142, 148], "advanc": [9, 42, 56, 168], "memori": [9, 10, 39, 40, 42, 43, 44, 45, 51, 53, 54, 82, 84, 85, 110, 115, 123, 126, 168], "anywher": [9, 84], "li": [9, 28, 139], "choos": [9, 25, 28, 40, 45, 46, 47, 70, 94, 104, 106, 118, 119, 126, 128, 148], "front": [9, 16, 19, 24, 28, 40, 43, 60, 61, 62, 64, 66, 69, 70, 72, 73, 75, 76, 77, 80, 89, 140, 145, 152], "closer": [9, 43, 47, 64, 78, 128, 132], "silli": 9, "tradeoff": 9, "thought": [9, 52, 75, 110], "command": [9, 30, 45, 116, 159, 164, 165], "sort": [9, 11, 13, 20, 22, 26, 28, 29, 32, 38, 44, 48, 67, 88, 109, 112, 114, 115, 116, 118, 119, 120, 121, 122, 134, 145, 146, 147, 151, 159, 163, 164, 165, 168], "otherwis": [9, 27, 33, 39, 46, 68, 94, 95, 97, 101, 103, 110, 131, 135, 149], "demonstr": [9, 36, 43, 110, 131, 135, 139], "let": [9, 10, 14, 15, 17, 19, 24, 25, 26, 28, 31, 35, 36, 39, 40, 43, 46, 64, 69, 94, 95, 99, 100, 102, 103, 105, 106, 126, 131, 132, 136, 139, 141, 142, 144, 147, 149, 151, 152], "known": [9, 19, 33, 34, 35, 40, 46, 49, 52, 70, 76, 77, 78, 80, 84, 86, 88, 94, 110, 123], "pop": [9, 16, 17, 24, 25, 58, 62, 63, 64, 68, 70, 71, 73, 74, 77, 80, 84, 86, 88, 98, 141, 144], "want": [9, 10, 19, 28, 30, 36, 39, 40, 43, 46, 47, 58, 64, 70, 77, 80, 83, 84, 94, 95, 102, 103, 104, 105, 106, 110, 124, 129, 132, 144, 148, 152, 167, 168], "expect": [9, 28, 39, 43, 46, 53, 61, 64, 99, 106, 142], "stai": [9, 47, 64, 75, 126], "attempt": [9, 90, 95, 110, 126], "There": [9, 10, 13, 16, 19, 25, 26, 28, 29, 33, 35, 39, 43, 45, 46, 54, 64, 77, 80, 83, 94, 102, 104, 110, 114, 115, 123, 125, 128, 129, 132, 142, 144, 148, 152], "coupl": [9, 19, 46, 84, 95, 106, 141, 145], "point": [9, 10, 17, 21, 22, 24, 25, 26, 28, 39, 43, 44, 45, 46, 47, 49, 51, 52, 64, 66, 69, 83, 84, 94, 102, 103, 104, 105, 106, 108, 114, 115, 119, 122, 124, 126, 131, 134, 138, 140, 144, 148, 152, 159, 160, 164, 165], "decreas": [9, 22, 28, 31, 36, 70], "scienc": [10, 27, 31, 42, 45, 47, 48, 51, 53, 56, 57, 58, 68, 70, 75, 77, 80, 94, 129, 139, 168], "student": [10, 27, 41, 45, 70, 77, 80, 95, 110, 167], "ones": [10, 67, 78], "interest": [10, 21, 26, 27, 28, 31, 35, 66, 70, 77, 80, 92, 94, 100, 106, 110, 116, 128, 134, 137, 141, 145, 148, 150], "aris": [10, 52, 53, 54, 57, 70, 84, 116], "better": [10, 17, 28, 39, 40, 42, 45, 46, 47, 49, 54, 55, 70, 84, 88, 110, 114, 118, 126, 128, 132, 145, 148, 152, 159, 164, 165], "answer": [10, 46, 58, 64, 67, 70, 71, 83, 94, 99, 100, 114, 116, 125, 126, 128, 134, 139, 141, 147, 152], "rememb": [10, 21, 39, 46, 64, 70, 83, 84, 94, 95, 100, 103, 106, 110, 124, 131, 134, 142, 146, 147, 148], "produc": [10, 22, 26, 29, 31, 36, 40, 47, 49, 53, 64, 70, 115, 128], "desir": [10, 44, 45, 46, 51, 64], "hand": [10, 24, 26, 37, 43, 46, 52, 58, 64, 68, 83, 105, 125, 129, 131], "been": [10, 17, 21, 24, 25, 26, 31, 36, 44, 45, 55, 58, 64, 68, 69, 70, 72, 73, 74, 77, 78, 80, 83, 84, 95, 110, 115, 125, 128, 129, 131, 134, 148], "encod": [10, 53, 58], "programm": [10, 39, 43, 46, 51, 52, 55, 94, 99, 106], "explor": [10, 19, 21, 24, 25, 26, 31, 32, 47, 57, 77, 80, 106, 107, 148, 168], "familiar": [10, 30, 39, 52, 95, 110, 125, 132], "accumul": [10, 98, 102], "variabl": [10, 19, 21, 23, 24, 26, 39, 40, 43, 44, 46, 47, 51, 57, 64, 68, 83, 84, 95, 98, 102, 115, 131, 146, 155, 156, 157, 158], "solut": [10, 11, 17, 24, 26, 28, 29, 35, 42, 52, 53, 54, 58, 64, 66, 84, 92, 94, 97, 99, 100, 101, 102, 104, 114, 144, 168], "strang": [10, 64], "upon": [10, 39, 40, 43, 44, 47, 49, 54, 61, 64, 69, 70, 88, 105], "inspect": 10, "essenti": [10, 39, 44, 110, 131], "obviou": [10, 64], "poor": [10, 147], "did": [10, 43, 49, 52, 64, 84, 94, 103, 114], "identifi": [10, 31, 39, 43, 44, 54, 64, 94, 139, 144], "assist": [10, 53, 57, 64, 71, 126], "readabl": 10, "dure": [10, 45, 64, 70, 98, 119, 123, 124, 125, 127, 128, 148], "necessari": [10, 21, 26, 44, 45, 46, 49, 52, 53, 70, 77, 80, 83, 84, 108, 110, 112, 114, 121, 123, 125, 128, 129, 131], "ask": [10, 39, 40, 46, 47, 49, 84, 94, 116, 125, 139, 141, 152], "criteria": [10, 94, 118], "foo": 10, "introductori": 10, "cours": [10, 15, 26, 27, 31, 46, 58, 126, 134], "itself": [10, 21, 39, 40, 43, 45, 46, 52, 55, 84, 94, 96, 99, 101, 102, 105, 106, 112, 125, 141, 142, 148, 152], "hope": [10, 70], "strive": 10, "those": [10, 17, 21, 37, 39, 47, 52, 54, 57, 58, 68, 76, 78, 88, 94, 123, 124, 126, 136], "perhap": [10, 52, 54, 70, 78, 110], "fewer": [10, 16, 54, 110], "perspect": [10, 52, 55], "dictat": [10, 45, 64], "care": [10, 39, 84, 141], "variat": [10, 19, 35, 69, 70, 75, 109, 110, 112, 115, 121, 145], "altern": [10, 45, 52, 59, 81, 86, 94, 108, 110, 112, 118, 121], "track": [10, 19, 21, 23, 24, 25, 45, 58, 70, 72, 94, 100, 104, 114, 131, 133, 134, 141, 144, 146, 148], "librari": [10, 39, 40, 43, 45, 52, 61, 62, 63, 65, 70, 89, 105, 116, 159, 164, 165], "arbitrari": [10, 21, 45, 110], "twice": [10, 64, 70], "fraction": [10, 15, 26, 43, 49, 56, 94, 168], "embed": 10, "calcul": [10, 52, 67, 94, 96, 99, 107, 114, 146, 147, 168], "job": [10, 30, 94, 103], "No": [10, 21, 26, 28, 58, 95, 115, 123, 124, 125, 126, 127, 128], "carefulli": [10, 21, 64, 83, 147, 148, 152], "condit": [10, 25, 39, 43, 83, 84, 94, 95, 96, 99, 103, 132, 148], "incorrect": [10, 43, 49, 152], "pleas": [10, 43, 45, 100], "sigma": 10, "mathemat": [10, 39, 44, 45, 103, 106, 132, 134, 144, 146], "termin": [10, 96, 110], "ever": [10, 27, 29, 43, 83, 96, 104], "immedi": [10, 49, 64, 69, 94, 95, 103, 115, 125], "afterward": [10, 78], "plug": 10, "similarli": 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99, 100, 103, 131, 144, 147], "intuit": 10, "older": [10, 39, 70, 78], "machin": [10, 42, 43, 44, 45, 50, 52, 67, 94], "dai": [10, 26, 30, 69, 70, 100, 136, 139], "compil": [10, 24, 39, 40, 43, 44, 45, 50], "instead": [10, 23, 26, 39, 40, 43, 58, 64, 69, 84, 95, 98, 104, 106, 110, 114, 128, 152], "judg": 10, "alon": 10, "math": [11, 58, 132, 168], "anagram": [11, 110, 129, 168], "detect": [11, 39, 64, 100, 103, 168], "off": [11, 33, 39, 54, 67, 68, 95, 98, 100, 106, 126, 144, 148, 168], "summari": [11, 38, 39, 56, 79, 91, 107, 115, 117, 130, 154, 168], "self": [11, 21, 56, 105, 107, 117, 130, 142, 152, 168], "exercis": [11, 15, 21, 26, 31, 38, 46, 56, 64, 69, 79, 83, 84, 91, 106, 107, 110, 117, 125, 126, 130, 131, 134, 141, 145, 148, 152, 154, 168], "glossari": [11, 38, 56, 79, 91, 107, 117, 130, 154, 168], "spars": [12, 13, 16, 17], "connect": [12, 13, 16, 17, 20, 21, 22, 23, 24, 27, 28, 29, 30, 32, 33, 37, 38, 47, 88, 95, 105, 140, 153, 168], "master": [12, 22, 23], "vertic": [12, 13, 14, 15, 16, 17, 19, 21, 22, 23, 24, 25, 28, 31, 33, 36, 37, 128, 160], "vertex": [12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 28, 29, 31, 33, 34, 36, 37, 160], "maintain": [12, 22, 40, 45, 49, 57, 67, 71, 73, 84, 87, 119, 124, 134, 136, 146], "weight": [12, 13, 16, 19, 20, 22, 23, 24, 28, 30, 32, 33, 37, 70, 104, 108, 110, 157], "compactli": 12, "link": [12, 15, 19, 21, 24, 28, 31, 48, 81, 82, 85, 86, 87, 88, 148, 155, 156, 157, 158, 168], "directli": [12, 19, 25, 39, 43, 45, 46, 47, 66, 88, 94, 99, 141, 148], "easiest": [13, 24, 27, 28, 34, 46, 83, 84, 134], "dimension": 13, "row": [13, 16, 22, 34, 70, 94, 95, 104, 162], "column": [13, 16, 22, 34, 95, 162], "cell": [13, 17], "intersect": [13, 39], "indic": [13, 21, 24, 25, 26, 36, 39, 40, 43, 44, 45, 55, 94, 95, 114, 124, 125, 148, 153], "edg": [13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 30, 31, 33, 36, 37, 45, 95, 140, 147, 153], "node": [13, 15, 16, 19, 21, 22, 24, 25, 26, 28, 31, 37, 81, 82, 83, 85, 86, 90, 91, 94, 131, 132, 133, 134, 136, 138, 139, 140, 141, 144, 146, 147, 148, 152, 153, 154, 160, 168], "fill": [13, 17, 29, 45, 89, 94, 104, 105, 110, 134, 136, 148], "full": [13, 16, 26, 45, 49, 59, 108, 109, 110, 112, 128, 134, 148], "real": [13, 17, 19, 34, 39, 46, 67, 68, 69, 70, 71, 136, 144], "involv": [13, 40, 46, 94, 101, 103, 153], "prioriti": [14, 19, 28, 140, 143, 150, 154, 168], "queue": [14, 15, 16, 19, 21, 24, 25, 28, 45, 48, 59, 60, 61, 65, 66, 67, 69, 70, 71, 75, 76, 79, 81, 86, 103, 139, 140, 143, 150, 154, 168], "construct": [14, 17, 21, 24, 25, 28, 36, 41, 42, 45, 46, 47, 50, 53, 55, 57, 58, 66, 68, 70, 71, 78, 84, 88, 94, 96, 102, 103, 109, 110, 115, 134, 136, 141, 144, 147, 148], "delmin": [14, 19, 28, 134, 135], "togeth": [14, 23, 30, 31, 36, 39, 43, 44, 46, 47, 70, 82, 90, 102, 103, 109, 110, 125, 144], "decreasekei": [14, 19, 28], "e": [14, 15, 18, 21, 25, 28, 37, 43, 44, 53, 59, 64, 74, 95, 131, 133, 140, 141, 159, 160, 164, 165], "combin": [14, 15, 31, 43, 45, 47, 67, 94, 119, 125, 152], "observ": [15, 21, 31, 45, 61, 64, 68, 78, 90, 136], "white": [15, 16, 18, 21, 24, 25, 26, 43, 158, 159, 160, 164, 165], "examin": [15, 19, 24, 26, 28, 40, 95, 114, 124, 125, 131, 141, 144, 152], "insid": [15, 25, 30, 40, 45, 52, 57, 68, 138, 139, 145], "dequeu": [15, 24, 67, 69, 73, 86, 145, 146], "Of": [15, 26, 31, 46, 70, 134], "task": [15, 32, 39, 40, 44, 46, 54, 77, 79, 80, 90, 148, 168], "chain": [15, 109, 110, 112], "normal": [15, 21, 43, 159, 164, 165], "buildgraph": [15, 17, 20, 24], "chessboard": [16, 25, 34], "legal": [16, 25, 26, 34], "correspond": [16, 20, 24, 26, 40, 42, 57, 58, 60, 64, 67, 68, 94, 103, 106, 110, 131, 139, 141, 144], "12": [16, 21, 26, 28, 30, 45, 46, 47, 58, 63, 70, 73, 84, 110, 114, 115, 123, 124, 126, 127, 128, 144], "board": [16, 25, 26, 34], "knightgraph": 16, "pass": [16, 22, 23, 28, 44, 46, 49, 51, 56, 67, 69, 95, 112, 114, 115, 116, 119, 121, 124, 125, 127, 128, 144, 148, 159, 168], "helper": [16, 21, 46, 57, 64, 70, 131, 134, 148], "genlegalmov": 16, "coordtonum": 16, "bdsize": 16, "ktgraph": 16, "fals": [16, 23, 24, 25, 33, 39, 43, 44, 46, 47, 51, 57, 70, 72, 73, 83, 84, 94, 95, 103, 110, 115, 116, 135, 161, 162, 166], "col": 16, "nodeid": 16, "newposit": 16, "newid": 16, "addedg": [16, 23, 24, 33, 160], "eight": [16, 25, 26, 34], "legalcoord": 16, "sure": [16, 21, 40, 46, 49, 57, 64, 67, 84, 88, 94, 100, 106, 110, 131, 133, 136, 140, 144, 148], "id": [16, 23, 24, 31, 40, 45, 160], "numtocoord": 16, "make_pair": 16, "bool": [16, 23, 24, 43, 44, 46, 47, 51, 70, 83, 84, 110, 116, 148, 160, 162], "els": [16, 21, 23, 25, 47, 64, 83, 84, 95, 110, 131, 134, 136, 141, 142, 144, 148, 152, 160, 163], "coord": 16, "newmov": 16, "myvec": 16, "unsign": [16, 23, 24, 43, 116], "newx": 16, "newi": 16, "336": 16, "fulli": [16, 52, 60, 64, 102, 144, 152], "096": 16, "matrix": [16, 17, 20, 22, 33, 38, 168], "percent": 16, "ran": 16, "version": [16, 24, 25, 26, 28, 31, 39, 45, 69, 104, 106, 114, 144, 148, 152, 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"character-data"]], "Pointers": [[43, "pointers"]], "Pointer Syntax": [[43, "pointer-syntax"]], "The address-of operator, &": [[43, "the-address-of-operator"]], "Accessing Values from Pointers": [[43, "accessing-values-from-pointers"]], "The NULL pointer": [[43, "the-null-pointer"]], "Optional: Graphics in C++": [[45, "optional-graphics-in-c"]], "Introduction to Turtles": [[45, "introduction-to-turtles"]], "Turtle & TurtleScreen": [[45, "turtle-turtlescreen"]], "Geometry, Shapes, and Stamps": [[45, "geometry-shapes-and-stamps"]], "Advanced Features": [[45, "advanced-features"]], "Object-Oriented Programming in C++: Defining Classes": [[46, "object-oriented-programming-in-c-defining-classes"]], "A Fraction Class": [[46, "a-fraction-class"]], "Abstraction and Encapsulation": [[46, "abstraction-and-encapsulation"]], "Polymorphism": [[46, "polymorphism"]], "Inheritance in C++": [[47, "inheritance-in-c"]], "Logic Gates and Circuits": [[47, "logic-gates-and-circuits"]], "Building Circuits": [[47, "building-circuits"]], "Self  Check Challenge": [[47, null]], "Reviewing Basic C++": [[50, "reviewing-basic-c"]], "What Is Computer Science?": [[52, "what-is-computer-science"]], "What Is Programming?": [[53, "what-is-programming"]], "Why Study Algorithms?": [[54, "why-study-algorithms"]], "Why Study Data Structures and Abstract Data Types?": [[55, "why-study-data-structures-and-abstract-data-types"]], "Introduction": [[56, "introduction"]], "Balanced Symbols - A General Case": [[57, "balanced-symbols-a-general-case"]], "Converting Decimal Numbers to Binary Numbers": [[58, "converting-decimal-numbers-to-binary-numbers"]], "Using a Deque in C++": [[61, "using-a-deque-in-c"]], "Using a Queue in C++": [[62, "using-a-queue-in-c"]], "Using a Stack in C++": [[63, "using-a-stack-in-c"]], "Infix, Prefix and Postfix Expressions": [[64, "infix-prefix-and-postfix-expressions"]], "Table 2: Examples of Infix, Prefix, and Postfix": [[64, "id1"]], "Table 3: An Expression with Parentheses": [[64, "id2"]], "Table 4: Additional Examples of Infix, Prefix, and Postfix": [[64, "id3"]], "Conversion of Infix Expressions to Prefix and Postfix": [[64, "conversion-of-infix-expressions-to-prefix-and-postfix"]], "General Infix-to-Postfix Conversion": [[64, "general-infix-to-postfix-conversion"]], "Postfix Evaluation": [[64, "postfix-evaluation"]], "Palindrome-Checker": [[66, "palindrome-checker"]], "Simple Balanced Parentheses": [[68, "simple-balanced-parentheses"]], "Simulation: Hot Potato": [[69, "simulation-hot-potato"]], "Simulation: Printing Tasks": [[70, "simulation-printing-tasks"]], "Main Simulation Steps": [[70, "main-simulation-steps"]], "C++ Implementation": [[70, "c-implementation"]], "Discussion": [[70, "discussion"]], "The Deque Abstract Data Type": [[72, "the-deque-abstract-data-type"]], "Table 1: Examples of Deque Operations": [[72, "id1"]], "The Queue Abstract Data Type": [[73, "the-queue-abstract-data-type"]], "Table 1: Example Queue Operations": [[73, "id1"]], "The Stack Abstract Data Type": [[74, "the-stack-abstract-data-type"]], "Table 1: Sample Stack Operations": [[74, "id1"]], "What Are Linear Structures?": [[75, "what-are-linear-structures"]], "What Is a Deque?": [[76, "what-is-a-deque"]], "What Is a Queue?": [[77, "what-is-a-queue"], [80, "what-is-a-queue"]], "What is a Stack?": [[78, "what-is-a-stack"]], "Linear Structures": [[79, "linear-structures"], [79, null]], "Implementing an Ordered Linked List": [[83, "implementing-an-ordered-linked-list"]], "Analysis of Linked Lists": [[83, "analysis-of-linked-lists"]], "Implementing an Unordered Linked List": [[84, "implementing-an-unordered-linked-list"]], "The Node Class": [[84, "the-node-class"]], "The Unordered Linked List Class": [[84, "the-unordered-linked-list-class"]], "The Ordered List Abstract Data Type": [[88, "the-ordered-list-abstract-data-type"]], "Forward lists": [[88, "forward-lists"]], "Lists": [[88, "lists"]], "The Unordered Array Abstract Data Type": [[89, "the-unordered-array-abstract-data-type"]], "What Are Linked Structures?": [[90, "what-are-linked-structures"]], "Linear Linked Structures": [[91, "linear-linked-structures"], [91, null]], "Complex Recursive Problems": [[92, "complex-recursive-problems"]], "Dynamic Programming": [[94, "dynamic-programming"]], "Self-check": [[94, "self-check"]], "Exploring a Maze": [[95, "exploring-a-maze"]], "Stack Frames: Implementing Recursion": [[98, "stack-frames-implementing-recursion"]], "The Three Laws of Recursion": [[99, "the-three-laws-of-recursion"]], "Tower of Hanoi": [[100, "tower-of-hanoi"]], "What Is Recursion?": [[101, "what-is-recursion"]], "Calculating the Sum of a Vector of Numbers": [[102, "calculating-the-sum-of-a-vector-of-numbers"]], "Converting an Integer to a String in Any Base": [[103, "converting-an-integer-to-a-string-in-any-base"]], "Sierpinski Triangle": [[105, "sierpinski-triangle"]], "Introduction: Visualizing Recursion": [[106, "introduction-visualizing-recursion"]], "Recursion": [[107, "recursion"], [107, null]], "Hashing": [[110, "hashing"]], "Table 4: Simple Hash Function Using Remainders": [[110, "id2"]], "Hash Functions": [[110, "hash-functions"]], "Table 5: Comparison of Remainder and Mid-Square Methods": [[110, "id4"]], "Collision Resolution": [[110, "collision-resolution"]], "Implementing the Map Abstract Data Type": [[110, "implementing-the-map-abstract-data-type"]], "Table 1: Map  Operations": [[110, "id12"]], "Analysis of Hashing": [[110, "analysis-of-hashing"]], "The Binary Search": [[114, "the-binary-search"]], "Analysis of Binary Search": [[114, "analysis-of-binary-search"]], "Table 3: Tabular Analysis for a Binary Search": [[114, "id2"]], "The Sequential Search": [[115, "the-sequential-search"]], "Analysis of Sequential Search": [[115, "analysis-of-sequential-search"]], "Table 1: Comparisons Used in a Sequential Search of an Unordered List": [[115, "id2"]], "Table 2: Comparisons Used in Sequential Search of an Ordered List": [[115, "id4"]], "Searching": [[116, "searching"]], "Searching and Hashing": [[117, "searching-and-hashing"], [117, null]], "The Bubble Sort": [[123, "the-bubble-sort"]], "Table 1: Comparisons for Each Pass of Bubble Sort": [[123, "id3"]], "The Insertion Sort": [[124, "the-insertion-sort"]], "The Merge Sort": [[125, "the-merge-sort"]], "The Quick Sort": [[126, "the-quick-sort"]], "The Selection Sort": [[127, "the-selection-sort"]], "The Shell Sort": [[128, "the-shell-sort"]], "Sorting": [[129, "sorting"], [130, "sorting"], [130, null]], "AVL Tree Implementation": [[131, "avl-tree-implementation"]], "AVL Tree Performance": [[132, "avl-tree-performance"]], "Balanced Binary Search Trees": [[133, "balanced-binary-search-trees"]], "Binary Heap Implementation": [[134, "binary-heap-implementation"]], "The Structure Property": [[134, "the-structure-property"]], "The Heap Order Property": [[134, "the-heap-order-property"]], "Heap Operations": [[134, "heap-operations"]], "Binary Heap Operations": [[135, "binary-heap-operations"]], "Priority Queues with Binary Heaps Example": [[136, "priority-queues-with-binary-heaps-example"]], "Binary Search Trees": [[137, "binary-search-trees"]], "Examples of Trees": [[139, "examples-of-trees"]], "List of Lists Representation": [[141, "list-of-lists-representation"]], "Nodes and References": [[142, "nodes-and-references"]], "Parse Tree": [[144, "parse-tree"]], "Priority Queues with Binary Heaps": [[145, "priority-queues-with-binary-heaps"]], "Search Tree Analysis": [[147, "search-tree-analysis"]], "Search Tree Implementation": [[148, "search-tree-implementation"]], "Search Tree Operations": [[149, "search-tree-operations"]], "Summary of Map ADT Implementations": [[151, "summary-of-map-adt-implementations"]], "Table 1: Comparing the Performance of Different Map Implementations": [[151, "id1"]], "Tree Traversals": [[152, "tree-traversals"]], "Trees and Tree Algorithms": [[154, "trees-and-tree-algorithms"], [154, null]], "Class Assignments": [[167, "class-assignments"]], "Problem Solving with Algorithms and Data Structures using C++": [[168, "problem-solving-with-algorithms-and-data-structures-using-c"]], "Acknowledgements": [[168, "acknowledgements"]], "Indices and tables": [[168, "indices-and-tables"]]}, "indexentries": {"big-o notation": [[3, "term-Big-O-notation"]], "algorithm": [[3, "term-algorithm"], [44, "term-algorithm"], [60, "term-algorithm"]], "average case": [[3, "term-average-case"]], "best case": [[3, "term-best-case"]], "brute force": [[3, "term-brute-force"]], "contains": [[3, "term-contains"]], "contiguous": [[3, "term-contiguous"]], "dynamic size": [[3, "term-dynamic-size"]], "exponential": [[3, "term-exponential"]], "get_item": [[3, "term-get_item"]], "hash table": [[3, "term-hash-table"], [44, "term-hash-table"], [109, "term-hash-table"]], "linear": [[3, "term-linear"]], "logarithmic": [[3, "term-logarithmic"]], "order of magnitude": [[3, "term-order-of-magnitude"]], "quadratic": [[3, "term-quadratic"]], 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