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"ProgrammingLanguages/LittleComputer2.rst", "ProgrammingLanguages/LittleComputer3.rst", "ProgrammingLanguages/MachineLanguages.rst", "ProgrammingLanguages/SyntaxAndVariety.rst", "ProgrammingLanguages/index.rst", "SQLGroupJoin/aggregating.rst", "SQLGroupJoin/exercises.rst", "SQLGroupJoin/grouping.rst", "SQLGroupJoin/having.rst", "SQLGroupJoin/joining.rst", "SQLGroupJoin/summary.rst", "SQLGroupJoin/toctree.rst", "SQLIntro/data.rst", "SQLIntro/exercises.rst", "SQLIntro/filtering.rst", "SQLIntro/introduction.rst", "SQLIntro/like.rst", "SQLIntro/selecting.rst", "SQLIntro/sorting.rst", "SQLIntro/summary.rst", "SQLIntro/toctree.rst", "global.rst", "index.rst"], "titles": ["<span class=\"section-number\">8.1. </span>Algorithms Introduction", "<span class=\"section-number\">8.10. </span>Big-O", "<span class=\"section-number\">8.14. </span>Estimating With Big-O", "<span class=\"section-number\">8.3. </span>Binary Search", "<span class=\"section-number\">8.9. </span>Algorithm Efficiency", "<span class=\"section-number\">8.11. </span>Efficiency Testing", "<span class=\"section-number\">8.7. </span>Insertion Sort", "<span class=\"section-number\">8.8. </span>Insertion Sort Code", "<span class=\"section-number\">8.2. </span>Linear Search", "<span class=\"section-number\">8.15. </span>Merging", "<span class=\"section-number\">8.16. </span>Merge Sort", "<span class=\"section-number\">8.17. </span>Merge Sort Efficiency", "<span class=\"section-number\">8.18. </span>Merge Sort Compared", "<span class=\"section-number\">8.12. </span>Search Efficiencies", "<span class=\"section-number\">8.5. </span>Selection Sort", "<span class=\"section-number\">8.6. </span>Selection Sort Code", "<span class=\"section-number\">8.13. </span>Sorting Efficiency", "<span class=\"section-number\">8.4. </span>Sorting", "<span class=\"section-number\">8. </span>Algorithms", "<span class=\"section-number\">3.1. </span>Analog and Digital", "<span class=\"section-number\">3.2. </span>Analog To Digital", "<span class=\"section-number\">3.3. </span>Binary and Its Advantages", "<span class=\"section-number\">3.5. </span>Bit Patterns", "<span class=\"section-number\">3.4. </span>Bits", "<span class=\"section-number\">3.6. </span>Bytes", "<span class=\"section-number\">3. </span>Binary and Bits", "&lt;no title&gt;", "<span class=\"section-number\">16.7. </span>Chapter Exercises", "<span class=\"section-number\">16.3. </span>Making a MadLib Story", "<span class=\"section-number\">16.2. </span>Iterating Parts of a List", "<span class=\"section-number\">16.1. </span>Iterating with Indexes", "<span class=\"section-number\">16.5. </span>Shuffle A List", "<span class=\"section-number\">16.4. </span>Slicing a List", "<span class=\"section-number\">16.6. </span>Chapter Concept Summary", "<span class=\"section-number\">16. </span>Changing and Chopping up Lists", "<span class=\"section-number\">15.10. </span>Chapter Exercises", "<span class=\"section-number\">15.5. </span>Adding and Removing Items", "<span class=\"section-number\">15.2. </span>What is a List?", "<span class=\"section-number\">15.6. </span>List Accumulation", "<span class=\"section-number\">15.3. </span>In and Not In", "<span class=\"section-number\">15.4. </span>Working with Indexes", "<span class=\"section-number\">15.7. </span>Finding the Largest or Smallest Value", "<span class=\"section-number\">15.8. </span>Rainfall Problem", "<span class=\"section-number\">15.9. </span>Chapter Concept Summary", "<span class=\"section-number\">15. </span>Working with Lists", "<span class=\"section-number\">15.1. </span>The Need for Lists", "<span class=\"section-number\">14.6. </span>Chapter Exercises", "<span class=\"section-number\">14.2. </span>A Pixel Selection Function", "<span class=\"section-number\">14.3. </span>Combining Pictures", "<span class=\"section-number\">14.1. </span>Using Decisions with Images", "<span class=\"section-number\">14.5. </span>Location based Conditions", "<span class=\"section-number\">14.4. </span>Posterizing", "<span class=\"section-number\">14. </span>Using Decisions with Images", "<span class=\"section-number\">11.9. </span>Chapter Exercises", "<span class=\"section-number\">11.1. </span>Making Decisions", "<span class=\"section-number\">11.6. </span>Using elif for more options", "<span class=\"section-number\">11.7. </span>Using elif correctly", "<span class=\"section-number\">11.2. </span>The if Statement", "<span class=\"section-number\">11.5. </span>Using if and else", "<span class=\"section-number\">11.3. </span>Functions that make Decisions", "<span class=\"section-number\">11.4. </span>Using Multiple if statements", "<span class=\"section-number\">11.8. </span>Chapter Summary", "<span class=\"section-number\">11. </span>Making Decisions", "<span class=\"section-number\">12.9. </span>Chapter Exercises", "<span class=\"section-number\">12.2. </span>Random Numbers", "<span class=\"section-number\">12.7. </span>Random Walks", "<span class=\"section-number\">12.4. </span>Building a Simulation", "<span class=\"section-number\">12.5. </span>Building a Simulation - 2", "<span class=\"section-number\">12.1. </span>Simulations", "<span class=\"section-number\">12.8. </span>Chapter Summary", "<span class=\"section-number\">12. </span>Decisions, Randomness, and Simulations", "<span class=\"section-number\">12.6. </span>Turtles And Randomness", "<span class=\"section-number\">12.3. </span>Using Random Numbers", "<span class=\"section-number\">13.10. </span>Chapter Exercises", "<span class=\"section-number\">13.4. </span>And, Or, and Not", "<span class=\"section-number\">13.8. </span>Making a Chatbot", "<span class=\"section-number\">13.3. </span>Complex Conditionals", "<span class=\"section-number\">13.6. </span>Complex Conditional Dangers", "<span class=\"section-number\">13.5. </span>When to use And and Or", "<span class=\"section-number\">13.1. </span>Using Decisions with Strings", "<span class=\"section-number\">13.7. </span>Testing parts of strings and length", "<span class=\"section-number\">13.2. </span>Comparing Strings", "<span class=\"section-number\">13.9. </span>Chapter Summary", "<span class=\"section-number\">13. </span>Decisions with Strings and Complex Conditions", "<span class=\"section-number\">6.9. </span>Chapter Exercises", "<span class=\"section-number\">6.1. </span>Procedures that Call Procedures", "<span class=\"section-number\">6.2. </span>Program Design", "<span class=\"section-number\">6.7. </span>Program Implementation - Final", "<span class=\"section-number\">6.3. </span>Program Implementation - 1", "<span class=\"section-number\">6.4. </span>Program Implementation - 2", "<span class=\"section-number\">6.5. </span>Program Implementation - 3", "<span class=\"section-number\">6.6. </span>Program Implementation - 4", "<span class=\"section-number\">6.8. </span>Chapter Summary", "<span class=\"section-number\">6. </span>Designing with Procedures", "<span class=\"section-number\">7.9. </span>Chapter Exercises", "<span class=\"section-number\">7.4. </span>Common Function Issues", "<span class=\"section-number\">7.2. </span>Defining Functions - How", "<span class=\"section-number\">7.3. </span>Defining Functions - Why", "<span class=\"section-number\">7.5. </span>Functions Calling Functions - 1", "<span class=\"section-number\">7.6. </span>Functions Calling Functions - 2", "<span class=\"section-number\">7.7. </span>Functions Calling Functions - 3", "<span class=\"section-number\">7.1. </span>Functions and Composition", "<span class=\"section-number\">7.8. </span>Chapter Summary", "<span class=\"section-number\">7. </span>Names for Functions", "<span class=\"section-number\">2.13. </span>Chapter Exercises", "<span class=\"section-number\">2.12. </span>Mixed Up Code Practice", "<span class=\"section-number\">2.1. </span>Assigning a Name", "<span class=\"section-number\">2.6. </span>Driving from Chicago to Dallas", "<span class=\"section-number\">2.3. </span>Expressions", "<span class=\"section-number\">2.4. </span>Summary of Expression Types", "&lt;no title&gt;", "<span class=\"section-number\">2.9. </span>Figuring out an Invoice", "<span class=\"section-number\">2.7. </span>Following the Ketchup Ooze", "<span class=\"section-number\">2.10. </span>Math Library Functions", "<span class=\"section-number\">2.5. </span>How Expressions are Evaluated", "<span class=\"section-number\">2.2. </span>Rules for Names", "<span class=\"section-number\">2.11. </span>Chapter Summary", "<span class=\"section-number\">2. </span>Names for Numbers", "<span class=\"section-number\">2.8. </span>Walking through Assignment more Generally", "<span class=\"section-number\">5.9. </span>Chapter Exercises", "<span class=\"section-number\">5.3. </span>Defining Procedures - How", "<span class=\"section-number\">5.2. </span>Defining Procedures - Why", "<span class=\"section-number\">5.4. </span>Order and Indentation", "<span class=\"section-number\">5.6. </span>Multiple Parameters", "<span class=\"section-number\">5.1. </span>Stand Alone Procedures and Functions", "<span class=\"section-number\">5.5. </span>Parameters", "<span class=\"section-number\">5.7. </span>Practice - Write a Procedure", "<span class=\"section-number\">5.8. </span>Chapter Summary", "<span class=\"section-number\">5. </span>Names for Procedures", "<span class=\"section-number\">3.7. </span>Chapter 3 Exercises", "<span class=\"section-number\">3.6. </span>Mixed Up Code Practice", "<span class=\"section-number\">3.1. </span>Assign a Name to a String", "<span class=\"section-number\">3.3. </span>Strings are Immutable", "<span class=\"section-number\">3.4. </span>Making a MadLib story", "<span class=\"section-number\">3.2. </span>Strings are Objects", "<span class=\"section-number\">3.5. </span>Chapter Summary", "<span class=\"section-number\">3. </span>Names for Strings", "<span class=\"section-number\">4.10. </span>Chapter Exercises", "<span class=\"section-number\">4.2. </span>Procedures and Functions", "<span class=\"section-number\">4.3. </span>Errors in Programs", "<span class=\"section-number\">4.9. </span>Mixed Up Code Practice", "<span class=\"section-number\">4.5. </span>Single and Multiple Turtles", "<span class=\"section-number\">4.1. </span>Turtles as Objects", "<span class=\"section-number\">4.8. </span>Chapter Summary", "<span class=\"section-number\">4. </span>Names for Turtles", "<span class=\"section-number\">4.7. </span>Turtle Art", "<span class=\"section-number\">4.6. </span>Turtle Coordinates", "<span class=\"section-number\">4.4. </span>Turtle Procedures", "<span class=\"section-number\">19.10. </span>Chapter Exercises", "<span class=\"section-number\">19.5. </span>What\u2019s the average pollution?", "<span class=\"section-number\">19.8. </span>Comparing States", "<span class=\"section-number\">19.6. </span>Most Populated and Least Populated States", "<span class=\"section-number\">19.7. </span>Finding the Pollution for a State", "<span class=\"section-number\">19.4. </span>What\u2019s the largest pollution values?", "<span class=\"section-number\">19.2. </span>Our first data set: Air pollution in the United States", "<span class=\"section-number\">19.1. </span>Data and Python", "<span class=\"section-number\">19.3. </span>Reading the data", "<span class=\"section-number\">19.9. </span>Chapter Concept Summary", "<span class=\"section-number\">19. </span>Working with Data in Python", "&lt;no title&gt;", "<span class=\"section-number\">9.9. </span>Chapter Exercises", "<span class=\"section-number\">9.5. </span>Increasing and decreasing brightness", "<span class=\"section-number\">9.6. </span>Thinking About Pixel Locations", "<span class=\"section-number\">9.7. </span>Changing which data we use", "<span class=\"section-number\">9.1. </span>Understanding Image Representation", "<span class=\"section-number\">9.4. </span>A Pattern for Image Processing", "<span class=\"section-number\">9.2. </span>Using Repetition with Images", "<span class=\"section-number\">9.8. </span>Chapter Summary", "<span class=\"section-number\">9. </span>Repeating Steps with Images", "<span class=\"section-number\">10.10. </span>Chapter Exercises", "<span class=\"section-number\">10.7. </span>The Accumulator Pattern", "<span class=\"section-number\">10.8. </span>Debugging Loops", "<span class=\"section-number\">10.2. </span>Introducing the While Loop", "<span class=\"section-number\">10.6. </span>Infinite Loops", "<span class=\"section-number\">10.3. </span>Booleans and Logical Expressions", "<span class=\"section-number\">10.1. </span>Repeating Calculations", "<span class=\"section-number\">10.9. </span>Chapter Summary", "<span class=\"section-number\">10. </span>Repeating Steps with Numbers", "<span class=\"section-number\">10.5. </span>Counting with a While Loop", "<span class=\"section-number\">10.4. </span>While Loops - While vs Until", "<span class=\"section-number\">8.8. </span>Chapter Exercises", "<span class=\"section-number\">8.6. </span>More Turtle Repetition Practice", "<span class=\"section-number\">8.5. </span>Using the Loop Variable", "<span class=\"section-number\">8.4. </span>Nesting Loops", "<span class=\"section-number\">8.2. </span>Using Repetition with Turtles", "<span class=\"section-number\">8.1. </span>Repeating Steps &amp; Range", "<span class=\"section-number\">8.7. </span>Chapter Summary", "<span class=\"section-number\">8. </span>Repeating Steps with Turtles", "<span class=\"section-number\">8.3. </span>A Regular Polygon Recipe", "<span class=\"section-number\">1.6. </span>Chapter Summary", "<span class=\"section-number\">1.5. </span>Compute with Images", "<span class=\"section-number\">1.2. </span>Compute with Numbers", "<span class=\"section-number\">1.4. </span>Compute with Turtles", "<span class=\"section-number\">1.3. </span>Compute with Words", "&lt;no title&gt;", "<span class=\"section-number\">1.1. </span>About This Section of the Book", "<span class=\"section-number\">1. </span>An introduction to programming", "<span class=\"section-number\">20. </span>What\u2019s Next?", "<span class=\"section-number\">6.1. </span>Computer Components", "<span class=\"section-number\">6.6. </span>The Machine Cycle", "<span class=\"section-number\">6.4. </span>Main Memory", "<span class=\"section-number\">6.5. </span>Memory Hierarchy", "<span class=\"section-number\">6.2. </span>The Processor", "<span class=\"section-number\">6.3. </span>The Processor, cont.", "<span class=\"section-number\">6. </span>Computer Architecture &amp; The Machine Cycle", "<span class=\"section-number\">1.1. </span>Computer Engineering", "<span class=\"section-number\">1.2. </span>Computer Science", "<span class=\"section-number\">1.6. </span>Cybersecurity", "<span class=\"section-number\">1.7. </span>Data Science", "<span class=\"section-number\">1.5. </span>Information Systems", "<span class=\"section-number\">1.4. </span>Information Technology", "<span class=\"section-number\">1.3. </span>Software Engineering", "<span class=\"section-number\">1. </span>Computing Related Fields", "<span class=\"section-number\">4.9. </span>Representing Letters with ASCII", "<span class=\"section-number\">4.2. </span>Binary Conversions - Table Method", "<span class=\"section-number\">4.3. </span>Binary Conversions - Multiplication/Division Method", "<span class=\"section-number\">4.4. </span>Binary Addition", "<span class=\"section-number\">4.5. </span>Other Operations", "<span class=\"section-number\">4.8. </span>Floating Point Numbers", "<span class=\"section-number\">4.7. </span>Fractional Values", "<span class=\"section-number\">4.12. </span>Hex Data &amp; Colors", "<span class=\"section-number\">4.11. </span>Hexadecimal", "<span class=\"section-number\">4.10. </span>Representing Images", "<span class=\"section-number\">4.1. </span>Number Systems &amp; Binary", "<span class=\"section-number\">4.6. </span>Negative Values - Two\u2019s Complement", "<span class=\"section-number\">4. </span>Data Representation", "<span class=\"section-number\">2.2. </span>Dawn of Computers", "<span class=\"section-number\">2.3. </span>The First Generation", "<span class=\"section-number\">2.4. </span>The Second Generation", "<span class=\"section-number\">2.5. </span>The Third Generation", "<span class=\"section-number\">2.6. </span>The Fourth Generation", "<span class=\"section-number\">2.7. </span>Modern Computers", "<span class=\"section-number\">2.1. </span>Prehistory", "<span class=\"section-number\">2. </span>History of computers", "<span class=\"section-number\">12.2. </span>Analyzing Impacts", "<span class=\"section-number\">12.1. </span>Blown To Bits", "<span class=\"section-number\">12.3. </span>Example: Smart Locks", "<span class=\"section-number\">12.4. </span>Example: Street Maps", "<span class=\"section-number\">12. </span>Impacts of Computing", "<span class=\"section-number\">11.1. </span>Computability", "<span class=\"section-number\">11.2. </span>End of Moore\u2019s Law?", "<span class=\"section-number\">11.3. </span>Quantum Computing", "<span class=\"section-number\">11. </span>Limits and Future of Computing", "<span class=\"section-number\">5.8. </span>Adding Numbers with Logic", "<span class=\"section-number\">5.2. </span>The AND Gate", "<span class=\"section-number\">5.3. </span>Applying Logic Rules", "<span class=\"section-number\">5.9. </span>Circuit Playground", "<span class=\"section-number\">5.5. </span>Circuits", "<span class=\"section-number\">5.6. </span>Complex Circuits", "<span class=\"section-number\">5.7. </span>Remembering Things", "<span class=\"section-number\">5.4. </span>XOR and NOT Gates", "<span class=\"section-number\">5.1. </span>The OR Gate", "<span class=\"section-number\">5. </span>Logic Gates &amp; Circuits", "<span class=\"section-number\">9.2. </span>Operating Systems Goals", "<span class=\"section-number\">9.1. </span>Operating Systems", "<span class=\"section-number\">9.3. </span>Process Management", "<span class=\"section-number\">9.4. </span>Memory Management", "<span class=\"section-number\">9. </span>Operating Systems", "<span class=\"section-number\">10.3. </span>Parallel vs Serial Performance", "<span class=\"section-number\">10.1. </span>Moore\u2019s Law", "<span class=\"section-number\">10.2. </span>Multi Processing", "<span class=\"section-number\">10.4. </span>Synchronization", "<span class=\"section-number\">10. </span>Parallel Processing", "<span class=\"section-number\">7.4. </span>Assembly Languages", "<span class=\"section-number\">7.6. </span>High Level Programming Languages", "<span class=\"section-number\">7.2. </span>The Little Computer", "<span class=\"section-number\">7.3. </span>The Little Computer - Branching", "<span class=\"section-number\">7.5. </span>The Little Computer - Assembly", "<span class=\"section-number\">7.1. </span>Machine Languages", "<span class=\"section-number\">7.7. </span>Variety and Syntax", "<span class=\"section-number\">7. </span>Programming Languages", "<span class=\"section-number\">18.1. </span>Aggregating Data", "<span class=\"section-number\">18.6. </span>Chapter Exercises", "<span class=\"section-number\">18.2. </span>Grouping", "<span class=\"section-number\">18.3. </span>Filtering with Aggregated Results", "<span class=\"section-number\">18.4. </span>Joining", "<span class=\"section-number\">18.5. </span>Chapter Summary", "<span class=\"section-number\">18. </span>SQL Grouping and Joining", "<span class=\"section-number\">17.2. </span>Tables of Records", "<span class=\"section-number\">17.8. </span>Chapter Exercises", "<span class=\"section-number\">17.4. </span>Filtering", "<span class=\"section-number\">17.1. </span>Introduction", "<span class=\"section-number\">17.5. </span>Filtering with Like", "<span class=\"section-number\">17.3. </span>Selecting", "<span class=\"section-number\">17.6. </span>Sorting", "<span class=\"section-number\">17.7. </span>Chapter Summary", "<span class=\"section-number\">17. </span>SQL Introduction", "&lt;no title&gt;", "Welcome To CS"], "terms": {"algorithmsintro": 0, "nbsp": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 86, 87, 88, 89, 90, 91, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 287, 288], "simpli": [0, 2, 42, 183, 203, 206, 221, 223, 234, 245, 249, 250, 262, 265, 271], "put": [0, 4, 14, 17, 22, 31, 36, 37, 38, 48, 56, 59, 63, 66, 73, 85, 86, 88, 90, 95, 99, 101, 105, 107, 111, 112, 116, 118, 129, 130, 131, 133, 138, 139, 140, 141, 142, 146, 147, 162, 169, 170, 178, 182, 210, 212, 235, 238, 253, 255, 258, 259, 273, 279, 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226, 227, 228, 229, 230, 232, 234, 263, 264, 265, 270, 288], "But": [0, 4, 12, 13, 21, 24, 25, 28, 30, 31, 32, 41, 42, 47, 49, 50, 55, 58, 60, 73, 75, 77, 78, 85, 86, 87, 88, 90, 95, 100, 104, 105, 108, 113, 118, 121, 122, 123, 130, 133, 150, 152, 156, 164, 165, 174, 175, 179, 182, 183, 185, 195, 198, 201, 206, 216, 218, 219, 220, 224, 226, 227, 235, 239, 240, 241, 245, 249, 254, 255, 258, 265, 271, 272, 275], "order": [0, 3, 7, 10, 17, 30, 31, 36, 37, 38, 40, 43, 44, 54, 55, 56, 58, 60, 65, 72, 73, 78, 79, 85, 86, 95, 97, 99, 105, 106, 111, 112, 114, 118, 128, 130, 131, 133, 137, 138, 139, 140, 141, 142, 144, 146, 148, 149, 161, 162, 169, 170, 178, 183, 188, 214, 236, 258, 261, 266, 272, 273, 274, 275, 279, 280, 283, 284], "must": [0, 3, 21, 27, 42, 55, 57, 61, 64, 74, 77, 78, 82, 84, 86, 88, 97, 98, 101, 113, 115, 120, 122, 123, 125, 131, 147, 148, 153, 156, 160, 166, 180, 182, 185, 191, 195, 201, 202, 203, 209, 213, 219, 224, 236, 239, 241, 244, 254, 258, 259, 261, 264, 268, 273, 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97, 115, 195, 199, 200, 202, 203, 205, 206, 207, 209, 210, 211, 226, 227, 229, 230, 231, 232, 235, 240, 241, 263, 264, 268], "page": [0, 1, 5, 6, 9, 14, 19, 20, 21, 22, 23, 24, 28, 31, 37, 48, 56, 58, 59, 63, 76, 78, 88, 97, 115, 120, 122, 124, 147, 166, 173, 182, 183, 189, 199, 200, 201, 202, 203, 205, 206, 207, 209, 210, 211, 214, 215, 218, 221, 226, 227, 229, 230, 231, 232, 234, 235, 253, 258, 260, 263, 264, 265, 268, 283, 284], "adapt": [0, 6, 14, 19, 20, 21, 22, 23, 24, 41, 115, 199, 200, 202, 203, 205, 206, 207, 209, 210, 211, 217, 226, 227, 229, 230, 231, 232, 235, 263, 264, 268], "permiss": [0, 6, 14, 16, 19, 20, 21, 22, 23, 24, 115, 195, 199, 200, 202, 203, 205, 206, 207, 209, 210, 211, 215, 216, 217, 226, 227, 229, 230, 231, 232, 235, 255, 263, 264, 268], "onlin": [0, 6, 14, 75, 197, 263, 264, 268], "interact": [0, 6, 14, 28, 75, 156, 204, 207, 229, 231, 241, 253, 254, 263, 264, 268], "modul": [0, 6, 14, 138, 141, 142, 146, 263, 264, 268], "teach": [0, 6, 14, 263, 264, 268], "scienc": [0, 6, 9, 14, 18, 19, 20, 21, 22, 23, 24, 65, 105, 164, 197, 200, 207, 211, 212, 226, 229, 239, 263, 264, 268], "osman": [0, 6, 14, 263, 264, 268], "balci": [0, 6, 14, 263, 264, 268], "et": [0, 6, 14, 263, 264, 268], "al": [0, 6, 14, 149, 150, 152, 153, 154, 156, 159, 199, 263, 264, 268], "bigo": 1, "saw": [1, 11, 37, 41, 58, 63, 131, 156, 160, 173, 179, 201, 226, 229], "last": [1, 3, 16, 27, 31, 32, 36, 37, 40, 43, 45, 48, 55, 58, 75, 78, 97, 119, 120, 130, 131, 139, 142, 148, 150, 162, 163, 173, 178, 185, 204, 214, 216, 223, 224, 245, 258, 268, 271, 273, 280, 284], "count": [1, 4, 13, 30, 32, 33, 35, 40, 42, 44, 49, 63, 67, 72, 75, 77, 149, 152, 162, 169, 170, 177, 180, 181, 182, 186, 200, 216, 232, 243, 259, 266, 272, 273, 274, 277], "unit": [1, 2, 4, 11, 12, 13, 16, 24, 158, 189, 192, 198, 199, 202, 203, 226, 239, 260, 268], "work": [1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 27, 28, 30, 31, 32, 35, 41, 42, 45, 47, 48, 51, 53, 55, 56, 59, 63, 65, 66, 67, 72, 76, 77, 79, 80, 81, 85, 86, 87, 88, 89, 90, 91, 94, 95, 96, 97, 98, 99, 100, 101, 106, 113, 115, 119, 121, 122, 124, 125, 132, 133, 137, 138, 139, 141, 142, 148, 150, 152, 153, 155, 156, 157, 160, 162, 163, 164, 166, 167, 169, 171, 173, 178, 183, 188, 189, 190, 191, 195, 197, 198, 199, 200, 202, 203, 205, 206, 208, 209, 210, 211, 213, 214, 215, 216, 217, 218, 219, 220, 221, 224, 226, 227, 229, 232, 234, 235, 236, 239, 240, 241, 242, 243, 245, 250, 251, 253, 254, 255, 256, 258, 260, 261, 262, 263, 264, 265, 266, 268, 269, 274, 275, 280, 281, 284, 288], "algorithm": [1, 2, 3, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 31, 37, 48, 54, 155, 171, 179, 206, 208, 214, 215, 216, 217, 226, 234, 239, 240, 241, 242, 258, 264, 285, 288], "degre": [1, 35, 56, 65, 96, 142, 180, 183, 192, 205, 206, 207, 208, 209, 210, 211, 226, 240], "size": [1, 2, 4, 5, 10, 11, 12, 13, 24, 27, 31, 63, 71, 86, 123, 126, 164, 181, 182, 188, 213, 218, 228, 231, 239, 240, 258, 259, 260], "its": [1, 5, 6, 7, 8, 27, 31, 41, 46, 57, 60, 66, 75, 77, 80, 85, 86, 88, 90, 91, 94, 95, 96, 100, 101, 106, 115, 119, 120, 122, 123, 124, 125, 131, 139, 141, 142, 150, 152, 156, 157, 160, 161, 162, 164, 166, 170, 178, 180, 183, 195, 199, 201, 206, 207, 215, 219, 220, 227, 234, 235, 239, 241, 250, 251, 254, 266, 268, 269, 275, 280, 281, 283], "input": [1, 4, 5, 28, 73, 74, 75, 79, 80, 81, 82, 83, 98, 101, 107, 113, 120, 123, 124, 125, 127, 129, 134, 135, 136, 139, 147, 170, 172, 179, 198, 202, 204, 226, 234, 239, 243, 244, 245, 246, 247, 248, 249, 250, 251, 255, 265, 266], "alwai": [1, 4, 5, 6, 10, 12, 13, 27, 31, 32, 37, 38, 40, 46, 49, 55, 56, 58, 61, 63, 64, 78, 82, 85, 90, 94, 100, 101, 106, 108, 120, 132, 142, 148, 156, 162, 163, 165, 173, 174, 175, 178, 179, 180, 201, 214, 218, 224, 244, 250, 258, 266, 280], "involv": [1, 63, 65, 97, 99, 115, 165, 178, 179, 210, 224, 234, 239, 241, 248, 256, 281], "more": [1, 3, 4, 5, 7, 12, 13, 15, 18, 19, 21, 22, 24, 28, 30, 31, 40, 42, 45, 46, 47, 48, 49, 50, 53, 59, 60, 61, 62, 65, 71, 73, 75, 76, 78, 80, 82, 84, 85, 86, 87, 88, 92, 98, 101, 113, 117, 119, 121, 133, 137, 139, 140, 143, 144, 147, 148, 151, 154, 155, 156, 157, 161, 162, 164, 166, 172, 175, 178, 179, 183, 187, 188, 193, 195, 201, 202, 205, 206, 207, 209, 210, 211, 213, 214, 215, 216, 217, 218, 219, 221, 222, 223, 224, 226, 228, 229, 230, 231, 234, 235, 236, 237, 239, 240, 241, 242, 248, 249, 250, 251, 254, 255, 256, 257, 258, 259, 260, 261, 262, 264, 265, 266, 267, 269, 274, 275, 280, 283], "effici": [1, 3, 10, 18, 157, 206, 211, 217, 218, 219, 239, 242, 254, 257], "than": [1, 3, 4, 6, 7, 9, 10, 12, 13, 15, 17, 19, 24, 27, 30, 31, 32, 36, 37, 40, 41, 46, 47, 48, 51, 53, 55, 56, 57, 59, 60, 63, 65, 66, 73, 74, 76, 78, 81, 84, 86, 88, 97, 101, 107, 108, 113, 115, 124, 131, 139, 144, 147, 150, 153, 169, 172, 174, 175, 179, 183, 190, 191, 193, 195, 197, 200, 201, 206, 209, 213, 214, 215, 216, 217, 219, 222, 224, 226, 228, 229, 230, 231, 235, 236, 237, 239, 240, 241, 244, 248, 249, 250, 253, 255, 256, 258, 259, 262, 263, 264, 265, 266, 269, 271, 272, 274, 275, 279], "where": [1, 3, 15, 20, 21, 23, 28, 31, 33, 36, 38, 47, 49, 55, 58, 60, 63, 65, 71, 73, 75, 80, 81, 86, 90, 96, 97, 98, 101, 115, 118, 119, 129, 134, 146, 147, 148, 152, 162, 165, 178, 182, 183, 190, 192, 193, 199, 200, 203, 208, 211, 221, 222, 234, 235, 239, 241, 245, 246, 253, 254, 256, 258, 261, 268, 271, 272, 273, 274, 275, 278, 279, 280, 282, 284], "grow": [1, 4, 12, 13, 208, 239], "function": [1, 4, 10, 11, 13, 27, 28, 29, 30, 31, 35, 36, 40, 42, 44, 46, 48, 50, 51, 52, 53, 56, 58, 62, 63, 64, 66, 67, 70, 71, 73, 74, 78, 79, 80, 81, 83, 94, 102, 107, 117, 119, 120, 121, 122, 125, 126, 127, 128, 129, 131, 132, 136, 139, 142, 143, 144, 147, 148, 150, 156, 158, 163, 169, 172, 174, 177, 184, 185, 188, 189, 198, 204, 226, 228, 239, 243, 247, 248, 257, 265, 270, 271, 273, 274, 277, 288], "least": [1, 46, 47, 53, 66, 67, 73, 74, 75, 82, 84, 100, 129, 158, 169, 214, 256, 272, 280], "pass": [1, 27, 46, 53, 59, 71, 85, 95, 101, 102, 115, 125, 127, 148, 149, 150, 152, 153, 154, 156, 157, 159, 175, 241, 251], "further": [1, 84, 122, 203], "categori": [1, 2, 27, 139, 212, 272, 277], "kind": [1, 5, 9, 13, 17, 21, 76, 118, 138, 142, 154, 185, 201, 203, 207, 212, 216, 225, 236, 239, 240, 241, 252, 253, 254, 259, 263, 268, 280, 281], "determin": [1, 11, 47, 53, 63, 72, 74, 180, 185, 203, 220, 223, 244, 248], "growth": [1, 5, 12, 235, 239, 240, 259, 262], "idea": [1, 24, 25, 64, 65, 76, 84, 85, 88, 121, 139, 162, 192, 200, 206, 218, 223, 224, 226, 234, 238, 239, 244, 249, 256, 259, 269], "behind": [1, 192, 204, 234, 247, 249], "known": [1, 6, 8, 18, 32, 51, 57, 86, 88, 102, 108, 120, 125, 127, 138, 163, 164, 178, 183, 199, 202, 218, 220, 227, 232, 239, 243, 249, 250, 251, 256, 258, 268, 269, 283], "classif": [1, 12], "assign": [1, 24, 40, 57, 72, 105, 108, 116, 117, 127, 136, 144, 174, 178, 213, 222, 234, 250], "class": [1, 16, 17, 53, 76, 77, 81, 115, 206, 211, 229, 234, 239, 250, 282], "describ": [1, 3, 13, 24, 38, 74, 84, 115, 120, 143, 147, 164, 165, 179, 191, 193, 210, 215, 220, 227, 232, 235, 236, 239, 244, 248, 250, 266], "common": [1, 9, 13, 17, 18, 30, 41, 48, 57, 74, 77, 80, 86, 103, 115, 156, 164, 170, 171, 178, 179, 197, 198, 201, 213, 218, 222, 226, 227, 228, 229, 230, 231, 232, 235, 239, 253, 254, 258, 259, 269, 271, 273, 283], "constant": [1, 5, 12, 239], "linear": [1, 2, 3, 5, 9, 13, 18, 208], "logarithm": [1, 13, 259], "quadrat": [1, 5, 9, 16], "rel": [1, 3, 6, 18, 21, 24, 49, 142, 156, 198, 207, 215, 235, 239, 241, 254, 259, 261, 265], "shown": [1, 38, 40, 48, 55, 61, 64, 78, 114, 123, 131, 133, 134, 138, 141, 142, 146, 150, 165, 180, 181, 182, 183, 184, 199, 200, 214, 215, 220, 243, 245, 247, 251, 265, 278], "figur": [1, 11, 13, 16, 19, 24, 31, 35, 42, 46, 57, 60, 65, 66, 73, 99, 101, 107, 108, 112, 113, 115, 117, 118, 126, 153, 171, 182, 183, 188, 190, 192, 201, 218, 219, 224, 248, 250, 251, 257, 258, 260, 261, 268, 269, 280], "sai": [1, 2, 4, 5, 8, 11, 13, 16, 20, 30, 32, 38, 45, 46, 47, 53, 58, 59, 66, 73, 75, 77, 85, 86, 88, 98, 106, 111, 113, 115, 124, 125, 133, 141, 156, 162, 164, 172, 173, 175, 176, 178, 179, 182, 185, 190, 199, 200, 202, 215, 216, 218, 219, 221, 222, 224, 235, 236, 239, 241, 245, 248, 250, 251, 255, 256, 258, 260, 261, 263, 266, 267, 268, 269, 271, 275, 278, 282, 284], "n": [1, 2, 4, 5, 9, 11, 12, 13, 16, 22, 76, 94, 175, 191, 213, 239, 258], "log": [1, 2, 11, 13, 113, 191], "spoken": 1, "oh": [1, 75, 97, 122, 149, 150, 152, 153, 154, 156, 159], "ani": [1, 3, 4, 18, 19, 20, 21, 23, 27, 30, 31, 37, 40, 41, 42, 43, 46, 57, 60, 73, 77, 79, 80, 85, 101, 103, 104, 106, 114, 115, 123, 124, 125, 133, 135, 138, 139, 148, 152, 156, 169, 179, 188, 189, 195, 197, 199, 201, 202, 208, 210, 213, 214, 216, 217, 219, 224, 226, 227, 235, 238, 239, 240, 241, 244, 245, 251, 253, 255, 256, 258, 261, 264, 270, 272, 273, 280, 281, 282, 283], "take": [1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 19, 24, 30, 35, 40, 53, 54, 56, 57, 64, 65, 66, 72, 88, 89, 94, 98, 99, 101, 105, 106, 107, 112, 120, 123, 124, 129, 134, 135, 139, 148, 149, 150, 156, 166, 169, 172, 175, 183, 188, 190, 192, 202, 206, 211, 216, 222, 223, 224, 226, 229, 232, 235, 239, 243, 249, 251, 253, 256, 258, 264, 266], "It": [1, 5, 6, 10, 18, 19, 21, 27, 28, 29, 35, 36, 40, 41, 43, 47, 48, 50, 53, 55, 56, 57, 58, 59, 61, 63, 66, 67, 71, 73, 77, 78, 80, 81, 82, 85, 88, 96, 101, 104, 106, 107, 108, 111, 112, 113, 115, 118, 119, 120, 121, 122, 125, 126, 127, 129, 131, 133, 134, 138, 139, 142, 146, 148, 150, 152, 153, 154, 163, 166, 169, 172, 173, 178, 180, 182, 183, 185, 188, 189, 191, 195, 197, 199, 200, 201, 203, 207, 208, 211, 213, 218, 219, 224, 227, 238, 239, 243, 250, 254, 255, 256, 258, 260, 261, 264, 265, 266, 268, 271, 272, 275, 278, 279, 280, 281, 283, 284], "could": [1, 3, 4, 11, 16, 19, 20, 21, 30, 31, 32, 37, 41, 42, 49, 55, 60, 66, 72, 78, 82, 88, 90, 97, 101, 111, 121, 123, 140, 156, 161, 162, 163, 164, 165, 170, 171, 178, 183, 192, 202, 213, 215, 218, 219, 222, 226, 227, 228, 232, 236, 241, 244, 248, 253, 258, 260, 261, 263, 264, 275, 284], "100": [1, 3, 4, 11, 12, 13, 16, 24, 46, 49, 63, 65, 66, 67, 72, 89, 90, 113, 119, 123, 126, 139, 143, 165, 170, 171, 180, 181, 182, 183, 185, 192, 216, 223, 224, 239, 248, 259, 260, 265, 272, 279, 284], "thing": [1, 2, 3, 4, 10, 11, 16, 17, 19, 21, 24, 29, 31, 36, 37, 38, 40, 43, 72, 74, 77, 78, 80, 86, 88, 97, 100, 107, 113, 115, 120, 123, 127, 135, 142, 147, 149, 151, 153, 156, 162, 164, 171, 174, 183, 188, 191, 193, 195, 198, 200, 201, 204, 213, 215, 216, 218, 220, 223, 224, 226, 232, 234, 235, 239, 241, 250, 252, 253, 255, 258, 267, 268, 269, 282], "exampl": [1, 2, 5, 12, 17, 21, 24, 30, 41, 43, 47, 60, 63, 65, 73, 74, 78, 79, 93, 100, 106, 107, 113, 115, 116, 118, 127, 131, 132, 133, 135, 139, 142, 143, 147, 157, 163, 164, 165, 176, 179, 182, 183, 184, 185, 188, 189, 190, 191, 193, 195, 203, 210, 214, 215, 216, 218, 221, 222, 224, 227, 234, 238, 239, 243, 251, 254, 258, 261, 269, 271, 273, 275, 280, 283, 284], "drawsquar": [1, 4, 71, 98, 127], "look": [1, 3, 5, 8, 10, 11, 12, 13, 14, 16, 19, 21, 28, 29, 31, 33, 35, 41, 47, 48, 49, 53, 64, 65, 67, 75, 76, 77, 80, 86, 88, 97, 101, 107, 115, 122, 123, 124, 126, 139, 145, 147, 148, 152, 154, 155, 156, 161, 166, 172, 173, 174, 180, 188, 191, 197, 199, 213, 214, 215, 220, 221, 222, 235, 239, 241, 243, 245, 247, 250, 253, 255, 256, 258, 261, 262, 263, 264, 265, 266, 269, 271, 272, 275, 278, 279, 280, 282, 283], "roster": [1, 17], "decid": [1, 4, 21, 28, 63, 66, 73, 86, 97, 137, 178, 199, 200, 201, 212, 214, 221, 250, 251, 253, 256], "student": [1, 8, 13, 38, 45, 50, 73, 76, 82, 117, 171, 195, 205, 206, 211, 235, 244], "enrol": 1, "ye": [1, 53, 66, 73, 74, 78, 80, 214, 251], "No": [1, 76, 77, 191, 214, 261, 282], "whether": [1, 19, 24, 73, 138, 195, 235, 243, 244], "0": [1, 2, 3, 4, 5, 7, 8, 13, 15, 19, 20, 21, 22, 23, 24, 27, 29, 30, 31, 35, 37, 40, 41, 42, 43, 46, 47, 49, 50, 51, 53, 55, 58, 59, 60, 63, 65, 66, 71, 72, 73, 74, 76, 77, 81, 84, 90, 101, 105, 106, 108, 111, 129, 134, 135, 141, 146, 147, 152, 156, 160, 161, 162, 163, 164, 165, 166, 167, 169, 170, 171, 172, 178, 179, 182, 189, 190, 191, 198, 199, 200, 201, 203, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 229, 230, 231, 232, 239, 243, 244, 245, 248, 249, 250, 251, 252, 253, 258, 259, 263, 264, 266, 268, 272], "relationship": [1, 118, 239], "between": [1, 3, 4, 13, 19, 21, 24, 28, 31, 35, 51, 58, 63, 64, 65, 71, 72, 74, 76, 82, 98, 115, 118, 131, 134, 138, 142, 147, 164, 170, 183, 188, 189, 193, 200, 209, 212, 213, 219, 221, 234, 239, 244, 246, 253, 255, 258, 261, 262, 276, 279], "f": [1, 4, 13, 35, 55, 56, 81, 96, 146, 220, 221, 282], "given": [1, 16, 32, 33, 42, 45, 57, 74, 80, 81, 87, 100, 120, 129, 131, 132, 134, 135, 147, 162, 169, 174, 175, 200, 202, 219, 222, 224, 232, 234, 235, 238, 240, 253, 255, 256, 258, 268, 270, 278], "log_2": [1, 2, 11, 12, 13, 113], "cdot": [1, 2, 12, 16, 53, 170], "log_": [1, 113], "10": 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121, 122, 123, 124, 126, 129, 130, 131, 132, 133, 134, 135, 136, 138, 139, 140, 141, 142, 143, 144, 147, 148, 153, 156, 160, 162, 163, 165, 166, 171, 172, 173, 175, 178, 179, 180, 185, 188, 191, 195, 199, 200, 201, 209, 213, 214, 221, 223, 234, 238, 239, 240, 244, 250, 254, 256, 258, 262, 264, 271, 272, 273, 275, 278, 281, 282], "actual": [1, 5, 28, 30, 65, 76, 85, 88, 91, 95, 98, 106, 108, 114, 120, 121, 122, 125, 127, 135, 139, 141, 156, 162, 174, 178, 182, 191, 197, 199, 223, 227, 234, 250, 256, 261, 264, 268], "care": [1, 4, 7, 15, 16, 19, 88, 107, 108, 115, 147, 192, 216, 218, 253, 271, 282, 283], "see": [1, 3, 5, 6, 12, 13, 14, 15, 30, 31, 40, 41, 42, 46, 47, 49, 51, 54, 55, 56, 57, 58, 60, 63, 64, 66, 67, 71, 72, 74, 75, 80, 81, 88, 95, 97, 101, 106, 107, 108, 115, 118, 121, 122, 124, 133, 138, 139, 141, 142, 146, 147, 148, 149, 150, 152, 154, 156, 170, 172, 173, 174, 178, 181, 182, 183, 191, 192, 195, 197, 202, 203, 213, 215, 216, 219, 221, 223, 227, 236, 245, 248, 250, 255, 258, 261, 265, 268, 273, 284], "soon": [1, 178, 254], "frac": [1, 2, 13, 16, 113, 191, 258], "5n": 1, "drawshap": [1, 4], "side": [1, 4, 10, 40, 63, 71, 72, 77, 91, 96, 97, 98, 99, 101, 104, 106, 108, 112, 119, 122, 123, 126, 132, 162, 163, 178, 180, 181, 182, 185, 188, 215, 218, 234, 235, 238, 241, 247, 282, 284], "highest": [1, 3, 37, 41, 45, 56, 63, 86, 114, 148, 152, 153, 200, 272, 279], "score": [1, 37, 41, 45, 55, 56, 95, 106, 116, 189, 191, 241, 272, 279], "stack": [1, 13, 164, 183, 258], "test": [1, 13, 18, 27, 28, 31, 35, 42, 47, 51, 53, 55, 57, 58, 59, 60, 63, 68, 73, 75, 81, 83, 84, 86, 88, 90, 91, 98, 99, 100, 148, 151, 152, 156, 171, 178, 179, 192, 205, 211, 241, 248, 266, 267, 269], "get": [1, 4, 5, 6, 7, 10, 13, 14, 18, 20, 22, 24, 27, 28, 29, 30, 31, 32, 35, 38, 40, 41, 42, 44, 47, 48, 49, 53, 55, 63, 66, 67, 71, 72, 73, 74, 77, 78, 79, 80, 81, 88, 91, 94, 95, 96, 97, 100, 101, 104, 105, 106, 107, 108, 112, 115, 117, 119, 121, 122, 129, 131, 133, 135, 136, 138, 141, 142, 146, 148, 149, 152, 153, 154, 156, 160, 161, 162, 163, 164, 165, 166, 170, 172, 173, 174, 175, 178, 182, 183, 185, 188, 191, 197, 198, 199, 200, 201, 214, 216, 218, 219, 223, 224, 234, 236, 238, 241, 243, 250, 251, 253, 255, 256, 258, 260, 261, 264, 265, 266, 271, 272, 273, 275, 280, 281, 282, 283, 284], "twice": [1, 58, 86, 90, 150, 184, 214, 219, 223, 260, 273], "me": [1, 86, 118, 130, 140, 149, 150, 152, 153, 154, 156, 159, 202, 213, 214, 258], "lai": [1, 235], "grid": [1, 85, 164, 167, 180, 189, 190, 222], "cone": 1, "25": [1, 2, 21, 123, 148, 149, 150, 152, 153, 154, 156, 159, 180, 218, 219], "layout": 1, "place": [1, 7, 11, 58, 60, 72, 82, 86, 88, 95, 100, 104, 125, 139, 151, 199, 203, 215, 219, 220, 232, 239, 256, 278], "In": [1, 7, 9, 11, 13, 15, 17, 18, 19, 20, 24, 30, 31, 40, 41, 43, 44, 49, 55, 56, 57, 58, 59, 60, 64, 65, 66, 71, 77, 79, 81, 85, 86, 88, 101, 106, 108, 115, 116, 120, 122, 123, 124, 127, 131, 135, 138, 139, 142, 147, 150, 152, 155, 156, 162, 163, 164, 166, 170, 173, 178, 181, 182, 183, 185, 186, 188, 189, 190, 192, 193, 195, 199, 201, 202, 205, 207, 209, 216, 219, 221, 222, 224, 226, 227, 230, 232, 234, 235, 236, 240, 243, 245, 248, 249, 250, 251, 256, 258, 259, 260, 261, 266, 267, 273, 275, 278, 280, 282, 283, 284], "case": [1, 5, 9, 16, 28, 39, 41, 48, 59, 66, 78, 80, 85, 86, 88, 101, 106, 107, 108, 115, 116, 123, 124, 130, 131, 132, 138, 139, 156, 185, 188, 192, 193, 213, 230, 247, 250, 260, 268, 273, 275, 280, 283, 284], "doubl": [1, 22, 30, 67, 107, 131, 133, 135, 165, 178, 189, 193, 246, 259, 280], "increas": [1, 5, 29, 63, 65, 106, 154, 168, 169, 182, 183, 190, 191, 203, 240, 258, 259, 260, 262, 284], "4x": [1, 259], "Or": [1, 11, 16, 17, 29, 47, 80, 83, 86, 155, 173, 178, 182, 214, 223, 261, 273, 280], "sort": [1, 2, 3, 9, 18, 21, 226, 239, 272, 273, 286], "paper": [1, 13, 21, 216, 219, 227, 237], "alphabet": [1, 17, 19, 36, 153], "go": [1, 5, 9, 10, 11, 12, 13, 23, 27, 28, 37, 42, 47, 48, 49, 64, 66, 71, 73, 74, 75, 79, 84, 85, 86, 88, 97, 104, 105, 107, 108, 112, 118, 122, 124, 125, 129, 135, 139, 142, 143, 147, 154, 163, 165, 171, 173, 178, 179, 185, 189, 192, 195, 200, 201, 208, 211, 212, 214, 215, 234, 236, 245, 247, 248, 256, 258, 261, 264, 265, 266, 269, 281, 282, 284], "multipl": [1, 17, 31, 37, 38, 45, 51, 55, 59, 62, 74, 78, 84, 86, 97, 100, 107, 109, 114, 115, 116, 119, 120, 122, 128, 144, 148, 164, 166, 175, 183, 185, 200, 201, 202, 213, 214, 217, 222, 223, 225, 228, 229, 237, 241, 243, 249, 250, 255, 258, 260, 262, 272, 275, 276, 279, 280, 283, 286], "classifi": 1, "accord": [1, 10, 77, 154, 232, 234, 236, 237, 245, 252], "fastest": 1, "2n": [1, 4], "consid": [1, 4, 5, 13, 14, 16, 77, 148, 174, 195, 218, 226, 227, 234, 238, 239, 251, 269, 280], "valu": [1, 3, 4, 5, 6, 8, 12, 15, 19, 20, 21, 22, 23, 24, 27, 29, 30, 31, 32, 35, 36, 37, 38, 40, 42, 44, 45, 46, 47, 48, 49, 50, 51, 53, 54, 55, 59, 60, 63, 64, 65, 69, 71, 72, 73, 74, 76, 77, 79, 80, 81, 82, 85, 94, 95, 96, 100, 101, 102, 104, 105, 106, 107, 108, 111, 113, 115, 116, 117, 118, 123, 124, 125, 127, 128, 129, 131, 132, 133, 134, 135, 138, 143, 144, 147, 148, 149, 152, 156, 158, 160, 161, 162, 163, 164, 165, 166, 167, 169, 170, 171, 172, 174, 175, 176, 178, 179, 180, 182, 185, 186, 189, 191, 199, 200, 202, 203, 204, 213, 214, 215, 216, 218, 220, 221, 222, 223, 225, 226, 239, 241, 243, 249, 250, 252, 255, 261, 263, 264, 265, 266, 267, 268, 273, 274, 275, 277, 284], "domin": [1, 16, 226, 231, 237], "000": [1, 2, 3, 11, 12, 13, 24, 67, 166, 169, 171, 179, 183, 191, 222, 224, 235, 239, 248, 274, 284], "200": [1, 24, 36, 63, 71, 105, 164, 166, 190, 241, 243, 248, 256], "extra": [1, 27, 73, 74, 75, 105, 122, 130, 140, 142, 146, 148, 153, 156, 178, 201, 218, 222, 224, 247, 255, 258, 268, 282], "hardli": 1, "even": [1, 5, 13, 19, 20, 21, 24, 37, 40, 53, 58, 64, 85, 86, 103, 120, 121, 132, 139, 142, 154, 157, 163, 164, 171, 178, 183, 190, 195, 200, 207, 222, 227, 228, 229, 234, 238, 239, 241, 249, 258, 261, 264, 269], "matter": [1, 4, 5, 21, 115, 139, 161, 178, 203, 213, 235, 244, 258], "compar": [1, 4, 7, 13, 14, 17, 18, 37, 41, 58, 83, 108, 115, 121, 153, 158, 174, 176, 177, 183, 202, 229, 258], "bigoestim": 2, "how": [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 21, 22, 24, 30, 31, 32, 35, 41, 42, 50, 51, 57, 59, 60, 63, 64, 66, 72, 76, 77, 78, 79, 80, 85, 86, 93, 97, 100, 101, 103, 104, 105, 106, 107, 108, 111, 112, 116, 117, 121, 122, 123, 124, 125, 128, 131, 138, 139, 147, 149, 153, 154, 155, 156, 169, 171, 172, 174, 175, 179, 182, 183, 184, 185, 188, 189, 190, 191, 192, 195, 197, 199, 200, 201, 203, 206, 207, 209, 211, 212, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 225, 227, 231, 234, 236, 237, 238, 239, 241, 249, 250, 251, 253, 254, 256, 258, 259, 260, 261, 265, 266, 268, 269, 270, 271, 273, 275, 278, 280, 281, 283, 284], "smaller": [2, 3, 9, 31, 41, 86, 92, 108, 151, 153, 154, 171, 179, 201, 202, 218, 219, 222, 228, 229, 240, 254, 259, 260], "version": [2, 15, 28, 29, 30, 31, 55, 56, 66, 71, 76, 78, 90, 91, 95, 97, 100, 101, 108, 131, 148, 156, 160, 161, 178, 179, 182, 213, 221, 239, 246, 251, 254], "up": [2, 3, 4, 5, 6, 8, 13, 16, 19, 20, 24, 28, 31, 32, 33, 35, 36, 38, 42, 45, 48, 49, 50, 55, 56, 58, 59, 60, 63, 65, 67, 71, 72, 73, 75, 76, 80, 86, 88, 92, 93, 99, 101, 106, 112, 117, 118, 119, 122, 123, 124, 125, 136, 138, 141, 142, 144, 146, 147, 148, 149, 152, 156, 157, 160, 161, 163, 164, 169, 170, 171, 173, 174, 176, 178, 180, 181, 182, 184, 188, 190, 200, 201, 213, 219, 221, 222, 223, 225, 227, 228, 235, 241, 253, 256, 257, 258, 260, 261, 264, 268, 283, 288], "proport": 2, "textrm": [2, 11, 16, 221, 258], "job": [2, 6, 8, 41, 73, 81, 86, 88, 98, 101, 120, 121, 122, 127, 131, 139, 150, 170, 200, 202, 207, 209, 210, 228, 229, 235, 239, 253, 254, 258, 261, 263, 281], "kei": [2, 3, 8, 9, 16, 38, 120, 122, 152, 180, 198, 203, 213, 235, 236, 247, 262, 284], "rememb": [2, 9, 11, 13, 15, 21, 28, 32, 40, 45, 53, 58, 71, 72, 73, 80, 84, 88, 106, 115, 119, 120, 122, 123, 131, 153, 160, 169, 173, 174, 178, 180, 185, 200, 204, 218, 220, 221, 222, 224, 234, 243, 252, 267, 272, 280], "necessarili": [2, 63, 219, 234, 258], "equal": [2, 16, 27, 56, 57, 59, 61, 65, 76, 77, 104, 106, 113, 115, 118, 173, 174, 244, 258, 259, 266], "instead": [2, 4, 7, 13, 15, 27, 28, 36, 38, 40, 50, 59, 65, 66, 75, 80, 81, 88, 104, 127, 131, 139, 153, 156, 162, 163, 171, 173, 176, 182, 185, 198, 202, 205, 206, 209, 211, 218, 223, 229, 235, 236, 239, 240, 250, 253, 254, 258, 260, 263, 264, 265, 266, 267, 268, 271, 273, 283], "appli": [2, 13, 50, 52, 65, 175, 206, 208, 209, 212, 226, 250, 252, 259, 262, 280], "calcul": [2, 3, 4, 5, 11, 13, 24, 27, 29, 35, 36, 38, 41, 42, 53, 55, 58, 59, 60, 73, 81, 94, 96, 97, 98, 99, 100, 101, 104, 108, 111, 113, 115, 117, 118, 124, 131, 139, 149, 150, 151, 152, 162, 169, 170, 171, 177, 179, 191, 198, 200, 217, 218, 219, 226, 227, 232, 239, 264, 271, 273, 277], "approxim": [2, 5, 49, 94, 169, 175, 219, 222, 224, 226], "list": [2, 3, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 22, 23, 27, 28, 30, 33, 35, 36, 39, 40, 41, 42, 43, 86, 115, 120, 131, 132, 142, 147, 148, 150, 152, 156, 157, 162, 166, 172, 176, 178, 179, 182, 185, 186, 187, 195, 200, 212, 221, 234, 239, 254, 263, 268, 270, 272, 275, 279, 283, 284, 288], "1000": [2, 13, 24, 169, 173, 221, 274], "want": [2, 13, 17, 21, 27, 28, 29, 30, 31, 32, 35, 36, 37, 38, 40, 42, 45, 48, 50, 55, 56, 59, 61, 64, 65, 66, 71, 72, 73, 74, 76, 77, 78, 79, 80, 82, 85, 86, 88, 89, 90, 94, 97, 98, 108, 113, 122, 123, 124, 129, 131, 133, 139, 140, 145, 146, 147, 149, 150, 151, 152, 153, 154, 155, 156, 161, 162, 163, 164, 165, 166, 170, 171, 175, 176, 178, 179, 180, 181, 182, 183, 184, 185, 188, 189, 191, 192, 193, 197, 200, 202, 211, 212, 213, 214, 219, 221, 222, 234, 235, 236, 241, 248, 249, 250, 253, 254, 256, 258, 261, 271, 272, 273, 274, 275, 279, 280, 281, 282, 283, 284], "binari": [2, 11, 13, 17, 18, 23, 156, 157, 170, 179, 195, 199, 200, 213, 217, 218, 219, 220, 221, 222, 225, 232, 243, 251, 265, 268, 288], "That": [2, 5, 11, 19, 22, 24, 30, 31, 32, 37, 46, 58, 64, 71, 72, 75, 81, 86, 90, 95, 98, 101, 115, 152, 153, 156, 164, 166, 174, 175, 179, 182, 185, 190, 191, 201, 213, 214, 216, 222, 224, 227, 237, 245, 247, 250, 256, 258, 275, 282, 284], "9": [2, 3, 7, 9, 10, 12, 13, 15, 19, 24, 29, 32, 37, 40, 53, 63, 96, 97, 101, 113, 115, 118, 148, 149, 150, 152, 153, 154, 156, 159, 160, 162, 173, 181, 182, 191, 198, 216, 220, 221, 222, 239, 272], "9657": 2, "just": [2, 3, 4, 5, 6, 13, 17, 18, 21, 27, 28, 29, 30, 31, 32, 35, 37, 38, 39, 40, 41, 42, 45, 47, 48, 49, 50, 53, 55, 56, 63, 64, 65, 66, 73, 74, 75, 77, 78, 80, 84, 85, 86, 88, 95, 96, 97, 101, 104, 106, 107, 108, 112, 113, 115, 119, 120, 123, 124, 125, 131, 134, 138, 142, 148, 150, 152, 154, 156, 160, 161, 162, 164, 165, 166, 170, 171, 172, 173, 180, 183, 185, 190, 192, 193, 195, 197, 198, 199, 200, 201, 213, 214, 216, 219, 220, 221, 222, 224, 226, 234, 235, 240, 241, 245, 247, 250, 255, 260, 262, 263, 265, 266, 269, 271, 272, 273, 274, 275, 279, 280, 281, 282, 283, 284], "select": [2, 6, 7, 9, 12, 16, 18, 31, 33, 46, 49, 52, 122, 239, 271, 272, 273, 274, 275, 279, 280, 284, 286], "wolfram": 2, "alpha": 2, "websit": [2, 11, 13, 197, 220, 272, 279], "type": [2, 8, 11, 13, 30, 37, 38, 43, 57, 73, 78, 79, 81, 97, 100, 101, 104, 112, 117, 121, 129, 131, 139, 144, 173, 174, 182, 185, 189, 192, 193, 220, 243, 246, 247, 248, 249, 254, 258, 260, 264, 271, 273, 278], "log2": [2, 11, 13], "1024": [2, 11, 13, 24], "try": [2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 20, 21, 22, 30, 31, 36, 46, 47, 49, 50, 55, 56, 60, 63, 64, 65, 66, 67, 71, 72, 73, 74, 75, 77, 79, 80, 81, 84, 86, 88, 91, 97, 98, 100, 103, 105, 106, 107, 108, 111, 114, 115, 118, 120, 121, 122, 124, 125, 126, 129, 130, 131, 133, 138, 139, 140, 141, 147, 148, 151, 152, 156, 161, 162, 163, 165, 166, 170, 171, 173, 175, 178, 179, 181, 183, 190, 191, 192, 213, 214, 216, 219, 220, 221, 224, 234, 238, 239, 241, 243, 247, 248, 249, 258, 261, 265, 269, 273, 274, 275, 280, 282, 283, 284], "sampl": [2, 36, 40, 46, 55, 63, 75, 77, 88, 100, 101, 108, 120, 122, 124, 125, 131, 147, 152, 156, 162, 163, 172, 174, 183, 264, 282], "item": [2, 3, 8, 9, 10, 11, 12, 13, 14, 16, 27, 28, 29, 30, 31, 32, 33, 35, 37, 38, 39, 40, 41, 42, 43, 44, 60, 77, 79, 105, 131, 156, 178, 179, 185, 213, 239], "243": 2, "second": [2, 4, 5, 8, 10, 12, 16, 21, 22, 29, 30, 31, 32, 37, 40, 43, 55, 58, 60, 72, 88, 97, 101, 105, 106, 108, 112, 123, 131, 135, 152, 162, 163, 169, 170, 182, 183, 190, 203, 221, 223, 229, 233, 235, 239, 242, 243, 244, 245, 248, 250, 255, 256, 258, 259, 260, 261, 268, 275, 278, 280, 283, 284], "50": [2, 36, 51, 53, 58, 59, 63, 71, 72, 88, 89, 101, 105, 119, 120, 121, 123, 127, 161, 169, 183, 185, 189, 240, 258, 260], "10000": [2, 63, 66, 67, 78, 274], "50000": [2, 169], "100000000": 2, "2500000000": 2, "cross": [2, 20, 86, 149, 150, 152, 153, 154, 156, 159, 207, 208], "multipli": [2, 16, 30, 38, 53, 65, 114, 169, 191, 202, 215, 218, 223, 241, 264], "075": 2, "12": [2, 3, 4, 5, 7, 15, 24, 32, 35, 59, 64, 65, 73, 78, 97, 104, 107, 108, 109, 118, 148, 149, 150, 152, 153, 154, 156, 159, 160, 172, 174, 188, 215, 218, 221, 222], "call": [2, 8, 9, 10, 11, 18, 20, 21, 24, 28, 29, 30, 31, 36, 43, 54, 57, 59, 61, 64, 66, 71, 72, 75, 79, 82, 84, 87, 90, 92, 93, 95, 96, 97, 101, 102, 103, 106, 115, 116, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 131, 132, 133, 135, 138, 139, 141, 147, 148, 150, 152, 156, 157, 162, 166, 173, 180, 181, 182, 183, 184, 185, 188, 189, 190, 192, 193, 198, 199, 203, 219, 222, 224, 232, 239, 251, 252, 259, 260, 261, 265, 271, 275, 278, 285], "both": [2, 9, 13, 24, 31, 42, 46, 47, 48, 55, 58, 60, 63, 74, 76, 77, 78, 80, 82, 85, 86, 87, 97, 120, 124, 131, 138, 142, 161, 163, 167, 169, 173, 184, 185, 189, 191, 200, 202, 207, 209, 211, 213, 220, 224, 226, 236, 237, 238, 239, 241, 243, 244, 245, 247, 249, 250, 251, 256, 261, 265, 266, 272, 275, 282, 284], "howev": [2, 24, 31, 42, 45, 46, 65, 75, 85, 107, 121, 124, 126, 138, 161, 170, 172, 178, 179, 195, 197, 203, 207, 209, 210, 211, 222, 228, 234, 248, 254, 256, 262, 263, 270, 274, 275, 283], "differ": [2, 4, 5, 10, 12, 13, 17, 18, 22, 23, 24, 31, 37, 42, 45, 47, 51, 55, 57, 59, 60, 63, 64, 65, 66, 71, 72, 73, 74, 78, 79, 85, 86, 88, 90, 94, 96, 97, 98, 100, 107, 117, 119, 123, 124, 129, 131, 133, 137, 138, 141, 147, 148, 150, 162, 163, 164, 166, 170, 174, 179, 182, 183, 184, 188, 190, 191, 193, 200, 201, 203, 208, 209, 211, 213, 214, 219, 220, 221, 222, 223, 224, 225, 226, 227, 235, 237, 239, 240, 244, 247, 253, 254, 255, 256, 258, 261, 262, 263, 265, 266, 269, 272, 273, 276, 279, 281, 283], "10000000": 2, "23": [2, 148, 149, 150, 152, 153, 154, 156, 159], "000019": 2, "significantli": [2, 201, 229, 256, 258], "faster": [2, 4, 12, 17, 183, 201, 228, 240, 241, 258, 259, 260, 262], "binarysearch": 3, "check": [3, 8, 13, 19, 20, 21, 22, 23, 24, 27, 28, 31, 32, 39, 42, 46, 49, 53, 54, 55, 56, 60, 63, 67, 72, 73, 74, 78, 80, 95, 96, 97, 101, 104, 105, 107, 112, 114, 118, 125, 129, 130, 131, 134, 137, 138, 140, 141, 142, 146, 148, 152, 164, 171, 172, 182, 190, 191, 197, 199, 213, 214, 215, 216, 218, 219, 220, 221, 222, 223, 224, 239, 241, 245, 250, 255, 256, 261, 278, 282, 283], "inform": [3, 19, 20, 21, 23, 24, 28, 42, 76, 86, 95, 100, 111, 115, 125, 133, 156, 164, 198, 201, 202, 203, 207, 208, 212, 218, 220, 221, 222, 225, 226, 234, 235, 236, 237, 244, 245, 247, 251, 252, 253, 255, 256, 258, 265, 268, 278, 281, 283, 285], "locat": [3, 6, 7, 8, 15, 30, 31, 36, 48, 52, 63, 65, 71, 73, 87, 90, 102, 125, 142, 147, 152, 156, 160, 163, 165, 168, 200, 201, 203, 235, 236, 237, 253, 256, 261, 263, 266, 267, 271, 280], "imagin": [3, 8, 13, 19, 21, 31, 42, 107, 111, 112, 123, 218, 250, 253, 258, 264, 275, 281], "pick": [3, 9, 19, 20, 31, 64, 65, 69, 71, 72, 74, 76, 88, 122, 147, 165, 181, 211, 213, 255], "phone": [3, 8, 85, 198, 236, 254], "book": [3, 8, 108, 122, 124, 138, 147, 166, 167, 196, 197, 235, 253], "davi": 3, "sue": [3, 115, 125], "flip": [3, 63, 66, 67, 72, 224, 249, 250], "middl": [3, 11, 13, 27, 86, 178, 203, 241, 271, 273], "somewher": [3, 12, 13, 155, 182], "jone": [3, 148, 157, 282], "oop": 3, "too": [3, 6, 13, 22, 24, 27, 30, 55, 72, 86, 88, 98, 105, 130, 131, 140, 156, 166, 203, 212, 214, 216, 220, 221, 222, 223, 224, 234, 235, 239, 241, 245, 250, 254, 256, 258, 259, 282, 283], "far": [3, 13, 14, 15, 37, 42, 63, 65, 66, 72, 101, 141, 162, 182, 201], "jump": [3, 6, 13, 90, 203, 235, 265, 266], "earlier": [3, 41, 52, 139, 175, 215, 249, 258, 266, 269, 275], "now": [3, 4, 10, 11, 19, 21, 22, 28, 31, 32, 42, 45, 47, 50, 51, 53, 63, 65, 66, 67, 71, 72, 81, 84, 85, 86, 87, 88, 89, 96, 97, 99, 101, 106, 107, 121, 122, 123, 131, 133, 145, 149, 150, 152, 153, 162, 163, 182, 183, 185, 188, 191, 199, 214, 215, 218, 222, 224, 229, 249, 250, 251, 256, 259, 261, 272, 275, 280, 284], "evan": 3, "still": [3, 51, 63, 121, 123, 124, 129, 133, 149, 175, 182, 185, 215, 219, 224, 228, 229, 251, 255, 256, 258, 260, 261, 263, 273, 280, 283], "back": [3, 10, 11, 21, 28, 30, 34, 66, 78, 88, 102, 122, 139, 162, 178, 192, 201, 202, 214, 215, 224, 246, 249, 255, 256, 258, 261, 266, 278], "again": [3, 5, 7, 10, 11, 13, 31, 42, 53, 57, 60, 67, 74, 95, 113, 121, 147, 149, 150, 152, 153, 154, 156, 165, 173, 178, 184, 222, 232, 244, 245, 256, 261, 266, 275, 284], "Then": [3, 5, 10, 30, 31, 35, 42, 46, 50, 53, 56, 57, 60, 63, 81, 86, 88, 98, 101, 122, 125, 138, 139, 141, 146, 148, 160, 162, 163, 165, 178, 180, 214, 253, 258, 261, 264, 271, 275, 280], "clark": [3, 149, 150, 152, 153, 154, 156, 159], "partwai": 3, "essenti": [3, 21, 22, 30, 59, 131, 138, 166, 206, 249, 263], "strategi": [3, 9, 15, 17, 88, 156, 162, 240, 260], "target": [3, 8, 152, 234, 266], "first": [3, 4, 5, 6, 8, 9, 10, 11, 14, 15, 16, 22, 27, 28, 29, 30, 31, 35, 36, 37, 40, 41, 42, 43, 45, 48, 50, 53, 55, 56, 57, 58, 60, 63, 72, 76, 79, 80, 85, 86, 88, 92, 100, 101, 106, 107, 108, 113, 115, 116, 122, 130, 131, 134, 135, 139, 140, 142, 147, 148, 152, 153, 156, 158, 162, 163, 170, 172, 174, 178, 180, 182, 183, 185, 191, 193, 195, 200, 206, 214, 220, 221, 223, 224, 226, 228, 230, 232, 233, 235, 236, 239, 241, 243, 244, 245, 248, 250, 251, 258, 261, 264, 268, 269, 272, 273, 275, 279, 283, 284], "half": [3, 10, 12, 13, 29, 31, 46, 98, 105, 160, 162, 184, 243, 259, 260], "larger": [3, 6, 8, 12, 24, 65, 162, 179, 200, 202, 218, 219, 243], "thu": [3, 11, 19, 78, 95, 124, 138, 156, 157, 172, 178, 179, 195, 200, 201, 207, 211, 218, 221, 222, 223, 224, 240, 243, 248, 258, 259, 260, 261, 269], "unsuccess": 3, "comparison": [3, 4, 13, 16, 41, 49, 57, 62, 81, 174, 176, 247, 280, 282], "reduc": [3, 31, 50, 63, 67, 222, 232, 240, 260, 283], "left": [3, 6, 7, 9, 10, 13, 14, 15, 40, 46, 58, 60, 63, 65, 71, 72, 73, 77, 81, 88, 104, 105, 106, 108, 112, 114, 116, 118, 122, 124, 125, 130, 132, 138, 139, 140, 141, 144, 146, 147, 162, 163, 164, 170, 178, 190, 192, 214, 215, 216, 218, 219, 227, 229, 247, 249, 254, 258], "continu": [3, 19, 57, 66, 80, 115, 122, 163, 169, 172, 173, 176, 178, 227, 240, 259], "less": [3, 4, 13, 30, 31, 32, 40, 51, 53, 57, 59, 60, 65, 67, 74, 76, 78, 86, 107, 113, 121, 139, 157, 170, 174, 201, 207, 213, 214, 219, 228, 229, 244, 258, 261, 264, 274], "throw": [3, 13, 113, 132], "everyth": [3, 14, 31, 55, 86, 106, 139, 143, 148, 156, 180, 181, 189, 200, 203, 224, 225, 243, 247, 265], "abov": [3, 8, 11, 15, 20, 22, 23, 27, 29, 30, 36, 41, 46, 50, 53, 56, 60, 63, 64, 65, 71, 75, 77, 78, 86, 97, 106, 107, 108, 111, 120, 122, 133, 134, 145, 162, 165, 166, 172, 178, 188, 191, 192, 195, 200, 201, 202, 213, 215, 218, 219, 220, 221, 243, 244, 251, 256, 261, 263, 279, 282], "bigger": [3, 63, 151], "repeat": [3, 4, 6, 7, 8, 9, 14, 15, 22, 31, 37, 54, 63, 66, 72, 76, 77, 78, 86, 94, 98, 108, 119, 121, 150, 172, 173, 179, 182, 183, 184, 186, 188, 193, 214, 265, 266, 288], "process": [3, 4, 9, 10, 13, 16, 23, 31, 37, 44, 50, 51, 54, 65, 66, 86, 92, 94, 125, 150, 153, 156, 157, 162, 168, 170, 176, 184, 185, 190, 198, 199, 202, 203, 206, 215, 224, 226, 227, 234, 235, 239, 240, 243, 252, 254, 256, 257, 258, 259, 261, 271, 280, 288], "thrown": [3, 235], "split": [3, 10, 14, 28, 31, 77, 148, 152, 156, 157, 258, 276], "noth": [3, 10, 30, 64, 95, 96, 101, 138, 148, 152, 155, 282], "watch": [3, 6, 8, 14, 30, 41, 72, 95, 100, 112, 170, 173, 215, 216, 231, 241, 250], "run": [3, 4, 5, 7, 10, 12, 28, 31, 36, 41, 42, 46, 47, 53, 55, 56, 57, 59, 60, 64, 65, 66, 67, 71, 72, 73, 74, 78, 81, 91, 94, 95, 96, 98, 100, 101, 106, 107, 108, 113, 114, 118, 119, 120, 121, 122, 124, 125, 127, 129, 131, 133, 137, 138, 139, 141, 148, 150, 156, 160, 162, 165, 166, 170, 171, 173, 174, 175, 178, 179, 187, 190, 191, 192, 197, 198, 199, 200, 201, 205, 215, 226, 227, 229, 230, 236, 239, 241, 244, 253, 254, 255, 256, 257, 259, 260, 261, 262, 264, 265, 266, 268, 280], "turn": [3, 4, 15, 20, 21, 28, 46, 49, 50, 60, 64, 66, 74, 77, 78, 79, 81, 82, 86, 101, 119, 126, 129, 138, 139, 140, 141, 144, 147, 148, 150, 152, 155, 156, 170, 172, 179, 180, 182, 183, 184, 188, 192, 197, 201, 202, 204, 215, 221, 224, 237, 247, 248, 249, 250, 251, 253, 255, 264, 265], "white": [3, 46, 47, 48, 49, 50, 160, 222, 246], "been": [3, 9, 19, 20, 30, 31, 36, 55, 65, 73, 87, 104, 105, 118, 122, 123, 126, 130, 140, 149, 150, 152, 153, 162, 173, 193, 222, 223, 232, 235, 237, 240, 255, 256, 269, 272, 281], "worri": [3, 5, 7, 9, 15, 21, 27, 28, 35, 42, 47, 78, 84, 86, 88, 90, 97, 101, 106, 113, 121, 138, 139, 148, 152, 153, 164, 165, 166, 179, 185, 195, 197, 199, 215, 218, 234, 236, 239, 250, 253, 263, 264, 278], "grai": [3, 50, 222, 256], "show": [3, 4, 7, 11, 16, 22, 36, 56, 57, 61, 72, 97, 106, 108, 112, 122, 136, 149, 150, 152, 153, 154, 156, 162, 165, 182, 185, 186, 190, 200, 213, 215, 218, 220, 234, 239, 248, 251, 256, 258, 259, 263, 264, 268, 284], "rang": [3, 28, 29, 30, 31, 32, 35, 63, 64, 65, 68, 74, 155, 163, 165, 171, 172, 178, 180, 186, 187, 190, 210, 211, 212, 213, 224, 254], "reset": [3, 7, 8, 9, 10, 15, 63, 67, 170, 249, 265], "anim": [3, 6, 7, 8, 9, 10, 14, 15, 16, 38, 215, 216, 217, 240, 255], "y": [3, 4, 7, 8, 9, 10, 15, 48, 50, 63, 65, 71, 74, 78, 80, 98, 105, 108, 113, 114, 146, 147, 160, 162, 163, 164, 167, 174, 182, 189, 190, 243, 246, 247, 248, 249, 259, 261], "daniel": [3, 7, 8, 9, 10, 15], "liang": [3, 7, 8, 9, 10, 15], "main": [3, 24, 27, 36, 66, 67, 71, 73, 90, 95, 97, 100, 119, 122, 125, 126, 131, 134, 150, 181, 183, 184, 198, 199, 201, 203, 204, 224, 237, 253, 256], "pseudocod": [3, 7, 9, 10], "keep": [3, 5, 6, 14, 15, 31, 42, 63, 66, 74, 94, 116, 141, 142, 149, 150, 170, 172, 173, 175, 179, 183, 192, 200, 203, 207, 216, 224, 254, 284], "track": [3, 14, 15, 41, 42, 63, 65, 116, 141, 142, 148, 160, 192, 200, 203, 207, 235, 253, 261, 264], "lowindex": 3, "lowest": [3, 41, 56, 88, 114], "highindex": 3, "loop": [3, 4, 8, 14, 28, 29, 30, 31, 32, 33, 36, 37, 38, 41, 50, 52, 61, 63, 66, 67, 72, 74, 82, 148, 150, 152, 156, 160, 162, 163, 165, 166, 167, 168, 169, 170, 174, 175, 176, 177, 180, 181, 184, 185, 186, 187, 188, 226, 249, 266], "those": [3, 5, 10, 11, 13, 23, 28, 32, 42, 45, 49, 50, 63, 64, 65, 75, 76, 77, 86, 92, 96, 99, 100, 101, 104, 111, 115, 124, 133, 139, 148, 150, 156, 162, 163, 164, 171, 174, 180, 183, 184, 185, 188, 190, 191, 192, 198, 199, 200, 201, 203, 206, 210, 214, 221, 222, 224, 226, 230, 234, 235, 238, 239, 240, 241, 243, 244, 247, 251, 253, 254, 262, 266, 268, 270, 273, 275, 282, 284], "middleindex": 3, "chang": [3, 4, 5, 10, 12, 19, 20, 21, 27, 28, 29, 30, 35, 36, 40, 41, 46, 47, 49, 50, 51, 53, 55, 57, 60, 64, 65, 66, 67, 71, 72, 74, 76, 79, 80, 88, 103, 104, 106, 107, 108, 114, 116, 123, 129, 132, 133, 135, 136, 138, 142, 147, 148, 152, 160, 161, 162, 164, 165, 166, 168, 171, 175, 178, 179, 180, 182, 188, 189, 190, 191, 193, 200, 215, 220, 221, 224, 227, 231, 235, 238, 239, 240, 244, 251, 266, 275, 281, 282, 283, 288], "either": [3, 15, 24, 27, 40, 46, 53, 57, 58, 61, 65, 73, 74, 76, 80, 82, 95, 115, 139, 140, 145, 157, 172, 174, 177, 200, 218, 228, 243, 244, 245, 247, 250, 251, 264, 280, 282], "boundari": 3, "remain": [3, 13, 14, 15, 182, 199, 224, 226, 254], "hand": [3, 6, 7, 10, 14, 15, 31, 106, 108, 114, 171, 217, 229, 232, 235, 239, 250, 256, 258, 265], "sure": [3, 24, 27, 28, 29, 30, 31, 35, 41, 42, 53, 56, 58, 60, 63, 64, 65, 66, 67, 72, 74, 77, 78, 80, 84, 86, 87, 88, 91, 92, 96, 97, 100, 104, 111, 115, 118, 119, 129, 133, 138, 139, 147, 148, 150, 152, 153, 156, 166, 169, 173, 175, 180, 181, 182, 188, 190, 191, 192, 234, 245, 246, 253, 256, 266, 273, 275, 280, 282, 283], "predict": [3, 7, 15, 68, 227, 237, 240, 241, 258, 259], "assum": [3, 4, 7, 8, 13, 15, 27, 56, 60, 88, 92, 123, 140, 142, 156, 218, 239, 256, 260, 261, 268, 280], "alreadi": [3, 5, 7, 8, 10, 13, 15, 25, 35, 38, 42, 50, 57, 80, 85, 88, 91, 94, 104, 121, 124, 152, 169, 171, 180, 197, 198, 240, 258, 261], "round": [3, 13, 67, 101, 108, 149, 150, 152, 153, 154, 156, 159], "middlevalu": 3, "7": [3, 6, 7, 8, 9, 10, 13, 14, 15, 19, 32, 37, 56, 66, 97, 106, 118, 139, 148, 149, 150, 152, 153, 154, 156, 159, 165, 170, 173, 188, 191, 198, 213, 220, 221, 223, 224, 240, 259, 266], "print": [3, 5, 8, 17, 27, 28, 30, 31, 35, 37, 38, 40, 42, 51, 53, 55, 56, 57, 58, 59, 60, 63, 66, 67, 72, 73, 74, 76, 78, 79, 81, 97, 101, 104, 105, 106, 107, 108, 111, 114, 118, 129, 130, 131, 133, 134, 139, 148, 150, 152, 156, 162, 169, 170, 171, 172, 173, 178, 180, 181, 183, 185, 193, 253, 269], "found": [3, 8, 41, 134, 148, 184, 208, 226, 231, 239, 256, 269, 282], "end": [3, 8, 9, 29, 31, 32, 33, 36, 38, 43, 45, 50, 55, 64, 67, 69, 75, 82, 88, 90, 101, 103, 107, 119, 129, 131, 133, 134, 135, 142, 143, 148, 160, 161, 174, 178, 185, 189, 213, 215, 222, 228, 242, 246, 261, 275, 280, 282, 283, 284], "didn": [3, 4, 51, 120, 133, 214], "11": [3, 7, 9, 10, 15, 31, 63, 97, 108, 148, 149, 150, 152, 153, 154, 156, 159, 163, 170, 173, 178, 182, 213, 214, 215, 216, 218, 219, 221, 222, 244, 251], "upper": [3, 28, 91, 116, 124, 130, 163, 283], "bound": 3, "13": [3, 7, 15, 31, 35, 63, 82, 97, 148, 149, 150, 152, 153, 154, 156, 159, 215, 221, 226, 263, 272, 279], "14": [3, 4, 7, 13, 15, 96, 97, 148, 149, 150, 152, 153, 154, 156, 159, 221], "els": [3, 5, 9, 10, 19, 21, 28, 31, 39, 51, 55, 56, 61, 62, 64, 73, 80, 82, 88, 115, 121, 139, 148, 182, 197, 203, 222, 224, 247, 256, 261, 281, 282], "15": [3, 13, 15, 32, 35, 58, 60, 73, 97, 105, 118, 148, 149, 150, 152, 153, 154, 156, 157, 159, 182, 218, 221, 241, 259, 261, 264], "lower": [3, 41, 78, 80, 116, 132, 134, 135, 136, 138, 142, 164, 189, 193, 213, 268, 283], "16": [3, 11, 15, 22, 24, 63, 98, 101, 109, 113, 148, 149, 150, 152, 153, 154, 156, 159, 200, 214, 216, 219, 221, 222, 223, 243, 261, 268], "17": [3, 11, 13, 15, 73, 134, 148, 149, 150, 152, 153, 154, 156, 159, 165], "18": [3, 15, 47, 53, 104, 109, 148, 149, 150, 152, 153, 154, 156, 159, 160, 183, 216, 259], "although": [3, 30, 37, 46, 55, 71, 84, 106, 155, 185, 200, 208, 210, 211, 212, 214, 219, 220, 227, 230, 231, 235, 240, 242, 251, 254, 256, 258, 259, 263, 269], "complex": [3, 30, 31, 40, 51, 62, 66, 78, 80, 84, 85, 86, 88, 92, 93, 97, 98, 113, 148, 155, 182, 183, 193, 198, 202, 210, 211, 212, 213, 218, 226, 231, 232, 237, 239, 240, 250, 252, 254, 259, 262, 283, 288], "being": [3, 7, 12, 14, 15, 18, 23, 42, 48, 49, 73, 78, 80, 90, 100, 101, 131, 150, 175, 200, 203, 212, 222, 223, 226, 235, 236, 243, 247, 251, 255, 256, 259, 261, 264, 274, 275, 281, 284], "rule": [30, 117, 120, 121, 128, 139, 185, 224, 232, 235, 244, 248, 250, 251, 252, 269, 281], "substanti": 3, "never": [3, 31, 58, 75, 88, 95, 120, 132, 142, 162, 173, 175, 178, 200, 256, 258, 261, 274, 275], "19": [3, 15, 129, 148, 149, 150, 151, 152, 153, 154, 156, 159, 165, 232], "closer": [3, 94, 97, 162, 175, 201, 264], "later": [3, 9, 40, 106, 113, 172, 195, 213, 222, 232, 251, 264, 266], "come": [4, 40, 49, 55, 75, 81, 86, 95, 97, 122, 142, 153, 155, 176, 191, 198, 201, 219, 225, 235, 236, 240, 243, 247, 249, 250, 253, 254, 258, 259, 260, 262, 264, 272, 273, 279, 284], "choos": [4, 64, 115, 199, 206, 256], "compet": 4, "measur": [4, 19, 20, 24, 31, 64, 154, 222, 280], "There": [4, 5, 9, 16, 21, 23, 29, 32, 36, 63, 72, 80, 88, 91, 94, 95, 98, 108, 115, 119, 120, 121, 124, 126, 129, 131, 133, 137, 138, 146, 149, 150, 153, 154, 162, 164, 165, 166, 170, 180, 183, 185, 193, 197, 198, 206, 211, 218, 219, 233, 235, 237, 242, 248, 249, 251, 253, 254, 258, 263, 268, 269, 273], "line": [4, 5, 7, 8, 15, 20, 22, 27, 28, 30, 56, 57, 60, 65, 66, 67, 71, 72, 74, 79, 84, 85, 86, 87, 88, 91, 97, 100, 101, 104, 106, 107, 111, 113, 119, 121, 122, 123, 125, 130, 132, 133, 137, 138, 139, 140, 141, 142, 143, 146, 147, 148, 149, 150, 152, 156, 160, 162, 163, 165, 166, 170, 171, 172, 173, 174, 178, 181, 182, 183, 184, 185, 188, 189, 190, 192, 213, 215, 219, 246, 247, 259, 264, 283], "code": [4, 5, 18, 27, 28, 29, 31, 35, 36, 37, 40, 41, 42, 45, 46, 48, 49, 50, 51, 53, 54, 55, 56, 57, 58, 59, 60, 63, 64, 66, 67, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 84, 85, 86, 87, 88, 89, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 104, 106, 107, 108, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 125, 127, 129, 131, 132, 133, 134, 135, 136, 137, 138, 139, 143, 144, 147, 148, 150, 152, 153, 156, 160, 163, 165, 166, 169, 170, 171, 172, 174, 176, 178, 180, 181, 182, 183, 185, 187, 188, 189, 191, 192, 193, 195, 197, 199, 207, 213, 215, 219, 220, 224, 227, 236, 239, 253, 255, 261, 263, 264, 265, 268, 273, 281, 283], "debug": [4, 35, 67, 72, 88, 101, 144, 148, 169, 177, 220, 263, 264], "memori": [4, 21, 24, 106, 116, 131, 156, 189, 191, 198, 199, 202, 203, 204, 220, 226, 227, 249, 253, 255, 257, 261, 263, 265, 266, 267, 268], "while": [4, 6, 8, 13, 15, 24, 35, 42, 57, 64, 72, 74, 76, 91, 95, 97, 113, 115, 119, 122, 125, 126, 132, 140, 142, 148, 160, 166, 169, 170, 173, 174, 175, 176, 177, 184, 185, 201, 203, 205, 206, 207, 209, 210, 211, 220, 234, 235, 241, 249, 255, 256, 261, 264, 268, 269, 273, 274, 282, 283, 284, 286], "taken": [4, 53, 73, 203, 226, 241, 271, 273], "might": [4, 13, 14, 21, 31, 38, 41, 45, 46, 47, 65, 71, 80, 81, 82, 86, 88, 111, 115, 118, 133, 139, 148, 151, 153, 156, 164, 165, 169, 172, 185, 190, 191, 200, 201, 202, 203, 211, 212, 226, 232, 234, 235, 241, 254, 258, 260, 261, 263, 264, 266, 268, 280, 281, 283], "metric": [4, 24], "usual": [4, 24, 45, 63, 64, 72, 85, 95, 106, 169, 174, 197, 200, 206, 222, 224, 254, 266, 268, 269], "user": [4, 28, 69, 73, 74, 75, 79, 80, 81, 82, 83, 96, 101, 129, 131, 170, 179, 197, 199, 207, 210, 211, 229, 230, 232, 234, 235, 236, 237, 253, 255, 259, 271, 278], "quick": [195, 203, 254, 257], "my": [4, 38, 84, 86, 88, 97, 214, 236, 264], "answer": [4, 13, 18, 22, 24, 27, 29, 38, 42, 47, 49, 50, 53, 55, 56, 63, 64, 66, 67, 73, 74, 75, 78, 81, 94, 97, 98, 100, 101, 104, 107, 108, 111, 113, 126, 138, 139, 151, 152, 153, 160, 163, 170, 171, 172, 174, 175, 176, 178, 179, 180, 191, 199, 208, 213, 214, 215, 218, 219, 220, 221, 222, 223, 224, 234, 239, 241, 243, 245, 250, 251, 274, 275, 282, 283, 284], "file": [4, 24, 148, 149, 150, 152, 153, 154, 155, 156, 157, 199, 213, 222, 246, 253, 254, 255, 264, 272], "result": [4, 5, 17, 28, 31, 32, 48, 57, 60, 63, 64, 65, 66, 67, 71, 74, 76, 80, 81, 97, 98, 101, 108, 109, 111, 113, 115, 116, 118, 124, 127, 132, 135, 138, 139, 156, 165, 166, 169, 170, 174, 191, 198, 203, 226, 228, 235, 241, 244, 245, 250, 258, 259, 261, 272, 273, 277, 279, 280, 282, 284], "great": [4, 65, 86, 156, 164, 227], "slow": [4, 28, 139, 147, 201, 203, 240, 255, 256, 258], "factor": [4, 12, 209, 239, 241, 258], "fast": [4, 18, 73, 107, 147, 201, 203, 239, 258, 260], "big": [4, 8, 9, 12, 13, 16, 18, 24, 28, 31, 47, 86, 97, 127, 146, 156, 162, 201, 216, 224, 239, 254, 261, 264], "fact": [4, 13, 22, 30, 64, 101, 239, 244, 251, 258], "tell": [4, 13, 19, 21, 74, 80, 104, 107, 120, 121, 122, 129, 131, 142, 147, 171, 173, 179, 185, 192, 193, 199, 214, 234, 250, 254, 258, 266, 271, 283], "u": [4, 7, 10, 11, 12, 13, 16, 17, 24, 30, 59, 66, 78, 82, 97, 113, 121, 127, 135, 138, 142, 149, 150, 154, 155, 162, 172, 175, 178, 179, 182, 184, 185, 189, 190, 192, 193, 216, 218, 224, 226, 227, 235, 238, 239, 240, 248, 250, 251, 258, 264, 267, 271, 275, 282, 284], "anyth": [4, 10, 21, 27, 86, 88, 96, 106, 113, 115, 120, 124, 131, 138, 139, 150, 174, 185, 189, 197, 200, 222, 261, 281, 282], "interest": [4, 71, 153, 156, 169, 179, 191, 195, 197, 209, 212, 239], "under": [4, 86, 190, 195, 259], "condit": [4, 28, 42, 46, 47, 52, 54, 55, 56, 57, 58, 61, 62, 74, 75, 78, 79, 82, 179, 195, 226, 228, 261, 265, 280, 284, 288], "exactli": [4, 5, 11, 19, 21, 29, 30, 46, 49, 58, 72, 146, 162, 166, 185, 215, 218, 219, 235, 241, 261, 268, 270], "let": [4, 11, 13, 22, 28, 31, 41, 42, 46, 51, 60, 65, 66, 71, 72, 85, 86, 87, 88, 96, 98, 111, 112, 118, 121, 122, 149, 150, 152, 162, 170, 188, 189, 190, 197, 258, 269, 283], "": [4, 8, 11, 14, 22, 24, 28, 31, 40, 41, 42, 46, 47, 50, 51, 54, 55, 56, 58, 60, 65, 66, 71, 72, 73, 75, 78, 79, 86, 88, 94, 95, 96, 98, 99, 103, 104, 106, 111, 112, 116, 118, 119, 120, 123, 129, 130, 132, 141, 142, 147, 150, 152, 154, 156, 158, 162, 165, 166, 171, 173, 175, 178, 179, 182, 183, 188, 190, 191, 192, 199, 200, 205, 206, 207, 208, 209, 210, 211, 213, 214, 219, 220, 225, 226, 227, 229, 230, 232, 234, 236, 239, 242, 243, 244, 245, 250, 254, 256, 257, 258, 260, 261, 262, 268, 269, 272, 273, 278, 283, 284, 288], "descript": [4, 11, 113, 147, 179, 198, 237, 272, 278, 279, 282], "pen": [4, 88, 146, 147, 181, 182, 183, 192], "move": [4, 7, 9, 14, 15, 21, 34, 50, 55, 56, 63, 65, 86, 87, 122, 123, 137, 139, 141, 142, 146, 147, 162, 178, 182, 183, 189, 192, 203, 219, 220, 232, 235, 254, 256, 260, 265, 266], "clockwis": [4, 142, 147, 254], "90": [4, 53, 55, 56, 65, 74, 107, 123, 124, 138, 139, 144, 147, 148, 180, 192, 213, 244, 258], "doesn": [4, 55, 86, 108, 113, 115, 118, 121, 124, 138, 139, 143, 144, 147, 201, 244, 256], "fix": [4, 27, 53, 60, 65, 88, 90, 94, 100, 119, 122, 129, 131, 137, 139, 152, 160, 162, 163, 171, 180, 183, 210, 216, 218, 219, 227, 254, 261], "happen": [4, 36, 42, 47, 57, 66, 72, 77, 79, 95, 96, 107, 113, 121, 124, 125, 127, 133, 147, 162, 165, 170, 172, 173, 174, 183, 185, 190, 198, 219, 224, 234, 244, 250, 261], "instantli": [4, 97, 241], "took": [4, 5, 81, 133, 227, 228, 259, 263, 278], "whatev": [4, 73, 85, 101, 113, 114, 131, 178, 265, 275], "360": [4, 65, 119, 126, 180, 183, 188], "draw": [4, 5, 63, 71, 84, 85, 86, 87, 88, 89, 90, 91, 119, 121, 122, 123, 126, 137, 138, 139, 140, 141, 142, 143, 145, 146, 147, 160, 162, 164, 165, 166, 180, 181, 182, 183, 184, 185, 188, 189, 190, 192, 222, 253, 259, 268], "stick": [4, 49, 125, 156, 166, 201], "our": [4, 13, 14, 16, 28, 31, 36, 38, 41, 42, 47, 51, 56, 59, 72, 74, 75, 78, 85, 86, 88, 89, 97, 98, 100, 101, 113, 120, 121, 122, 131, 152, 155, 156, 158, 162, 165, 166, 170, 171, 175, 178, 185, 192, 216, 223, 224, 235, 240, 244, 245, 250, 251, 258, 283], "origin": [4, 9, 33, 36, 66, 82, 105, 115, 119, 132, 134, 161, 162, 165, 171, 191, 192, 202, 213, 216, 224, 226, 234, 237, 258, 283], "account": [4, 179, 235], "method": [4, 8, 9, 31, 36, 94, 175, 179, 181, 219, 225, 226], "triangl": [4, 86, 91, 94, 96, 97, 98, 100, 122, 140, 147, 180, 182, 183, 184, 188, 247], "pentagon": [4, 126, 180, 183, 188], "decagon": 4, "22": [4, 5, 73, 148, 149, 150, 152, 153, 154, 156, 159], "littl": [4, 15, 24, 71, 100, 126, 149, 150, 152, 153, 154, 156, 159, 162, 164, 166, 175, 178, 190, 195, 203, 218, 221, 222, 229, 247, 255, 264, 270], "relat": [4, 13, 45, 127, 139, 205, 206, 207, 209, 211, 226, 227, 239, 253, 254, 288], "shape": [4, 57, 85, 90, 98, 119, 123, 126, 141, 146, 147, 180, 181, 182, 183, 185, 188, 192, 237], "cost": [4, 58, 59, 60, 73, 104, 105, 107, 111, 118, 131, 201, 238, 240, 259], "three": [4, 5, 13, 22, 27, 30, 36, 47, 49, 50, 55, 63, 71, 73, 75, 81, 84, 85, 98, 99, 100, 118, 121, 122, 150, 151, 152, 154, 156, 161, 164, 165, 180, 182, 199, 218, 220, 223, 224, 226, 232, 240, 243, 248, 261, 265], "3n": 4, "graph": [4, 12, 13, 65], "x": [4, 46, 48, 50, 53, 55, 56, 57, 58, 60, 61, 63, 65, 71, 74, 78, 82, 95, 98, 104, 105, 108, 113, 114, 116, 129, 146, 147, 160, 162, 163, 164, 167, 172, 174, 178, 181, 182, 189, 190, 213, 218, 220, 222, 239, 241, 243, 246, 247, 248, 249, 250, 261, 267], "axi": [4, 259], "repres": [4, 19, 20, 21, 22, 23, 24, 49, 56, 71, 72, 106, 115, 121, 124, 131, 147, 148, 164, 175, 176, 191, 199, 200, 201, 203, 205, 206, 207, 209, 210, 211, 214, 216, 218, 219, 220, 221, 223, 224, 225, 227, 232, 243, 244, 245, 250, 251, 252, 258, 259, 265], "blue": [4, 46, 47, 48, 49, 50, 71, 77, 88, 141, 146, 160, 161, 162, 163, 164, 165, 166, 167, 181, 189, 190, 215, 220, 241, 256], "gold": 4, "system": [4, 19, 21, 24, 64, 71, 125, 200, 202, 205, 207, 210, 211, 212, 213, 218, 219, 221, 225, 228, 229, 234, 236, 241, 252, 255, 256, 260, 264, 288], "By": [4, 34, 72, 121, 153, 172, 183, 220, 227, 228, 232, 240, 241, 244, 255, 273], "efficiencytest": 5, "real": [5, 10, 41, 69, 81, 86, 94, 115, 156, 161, 182, 197, 201, 218, 222, 229, 254, 265, 268], "procedur": [5, 50, 52, 59, 63, 71, 84, 86, 87, 88, 89, 90, 91, 92, 96, 97, 98, 100, 101, 103, 119, 122, 123, 125, 127, 139, 141, 143, 144, 156, 157, 166, 175, 180, 181, 182, 183, 184, 185, 188, 256, 288], "pattern": [5, 11, 12, 13, 18, 20, 21, 24, 25, 28, 38, 41, 67, 72, 106, 119, 151, 153, 168, 176, 177, 180, 183, 188, 200, 213, 221, 222, 225, 241, 245, 250, 266, 278, 282], "exhibit": 5, "o": [5, 9, 11, 12, 13, 16, 18, 142, 239, 255, 269, 272], "everi": [5, 8, 13, 29, 30, 46, 60, 81, 86, 101, 139, 141, 148, 149, 153, 163, 165, 172, 198, 200, 202, 207, 213, 226, 227, 231, 235, 238, 239, 240, 241, 247, 248, 249, 250, 251, 254, 255, 256, 257, 259, 260, 261, 262, 268, 269, 278, 279], "variabl": [5, 8, 15, 28, 30, 31, 35, 38, 40, 41, 42, 45, 53, 65, 80, 95, 96, 97, 100, 101, 106, 107, 108, 111, 113, 115, 116, 117, 118, 123, 125, 129, 131, 132, 133, 136, 138, 139, 148, 150, 166, 170, 173, 177, 185, 187, 189, 191], "regardless": [5, 13, 57], "produc": [5, 17, 19, 21, 29, 64, 66, 79, 97, 101, 106, 152, 163, 166, 174, 175, 176, 179, 185, 191, 202, 222, 224, 228, 232, 241, 243, 244, 245, 248, 249, 250, 251], "similar": [5, 16, 32, 37, 47, 48, 49, 50, 63, 138, 160, 164, 178, 188, 217, 254, 269], "39": [5, 105, 148, 224], "expect": [5, 49, 67, 77, 101, 153, 190, 210, 234, 251, 268], "absolut": [113, 124, 127], "perfect": [5, 19, 21, 46, 49, 86, 150, 175, 239], "32": [5, 10, 11, 22, 24, 35, 96, 148, 156, 200, 214, 216, 218, 219, 222, 223, 224, 232, 243, 248, 268, 272], "27": [5, 148, 149, 150, 152, 153, 154, 156, 159, 214, 239], "mayb": [5, 17, 29, 31, 65, 74, 80, 86, 108, 151, 155, 173, 251, 273, 280], "29": [5, 104, 148, 170], "precis": [5, 25, 237], "incres": [], "fairli": [5, 269], "steadi": [5, 240, 259], "rate": [5, 13, 191, 259, 272, 279], "61": [5, 11, 148, 241], "21": [5, 148, 149, 150, 152, 153, 154, 156, 159], "third": [5, 27, 30, 32, 54, 105, 233, 236, 243, 245], "78": [5, 148], "goe": [5, 48, 65, 72, 96, 108, 116, 201, 219, 227, 239, 256, 261, 264, 283], "bottom": [5, 9, 13, 14, 31, 40, 49, 88, 91, 92, 93, 112, 119, 160, 162, 164, 190, 201, 248, 251, 258], "lot": [5, 8, 20, 47, 65, 72, 76, 78, 121, 164, 166, 195, 201, 235, 236, 281], "defin": [5, 10, 60, 66, 90, 98, 103, 115, 119, 122, 123, 125, 126, 127, 128, 167, 175, 180, 182, 184, 186, 189, 220, 224, 227], "procedurea": 5, "procedureb": 5, "procedurec": 5, "procedure": 5, "At": [5, 12, 31, 38, 102, 163, 178, 183, 201, 205, 240, 261, 265, 266, 271], "top": [5, 9, 13, 17, 31, 40, 49, 59, 60, 66, 92, 93, 112, 146, 151, 160, 162, 163, 164, 183, 190, 210, 221, 237, 251, 254], "dotest": 5, "ran": [5, 227], "got": [5, 66, 162, 244], "97": [5, 16, 148, 213], "63": [5, 148], "here": [5, 6, 7, 8, 9, 13, 21, 22, 23, 30, 31, 41, 42, 47, 55, 57, 60, 67, 71, 76, 79, 84, 88, 97, 100, 109, 111, 113, 115, 120, 131, 133, 139, 156, 161, 165, 167, 170, 171, 174, 178, 179, 182, 185, 188, 193, 197, 199, 203, 215, 221, 222, 223, 224, 245, 246, 248, 267, 269, 272, 273, 278, 282], "77": [5, 148], "identifi": [5, 21, 28, 31, 35, 40, 48, 86, 115, 152, 188, 272, 278], "insertionsort": 6, "done": [6, 37, 50, 63, 65, 66, 67, 74, 86, 88, 97, 108, 114, 119, 121, 122, 131, 133, 138, 141, 142, 149, 155, 156, 157, 162, 166, 170, 183, 185, 199, 215, 229, 258, 261, 264, 268, 281], "anoth": [6, 17, 41, 55, 60, 65, 73, 75, 80, 101, 102, 116, 118, 122, 123, 131, 136, 141, 162, 166, 167, 169, 172, 183, 190, 192, 195, 197, 202, 203, 221, 226, 235, 243, 246, 256, 261, 275], "straightforward": [6, 214], "unsort": [6, 7, 13, 14, 15], "portion": [6, 7, 14, 15, 195, 258], "card": [6, 7, 14, 15, 23, 31, 54, 198, 226, 258, 260], "shift": [6, 15, 101, 122, 218, 255, 260], "neighbor": 6, "marker": [6, 7, 14, 15, 232], "section": [6, 14, 17, 121, 147, 149, 150, 152, 153, 156, 164, 173, 181, 196, 199], "after": [6, 28, 30, 31, 36, 47, 51, 55, 57, 58, 61, 63, 66, 82, 86, 95, 100, 101, 105, 106, 107, 116, 118, 120, 131, 132, 138, 139, 140, 145, 147, 153, 156, 157, 162, 166, 172, 173, 174, 175, 178, 182, 185, 188, 190, 191, 200, 202, 211, 226, 227, 235, 240, 249, 250, 255, 261, 266, 267, 271, 272, 280, 282, 284], "empti": [6, 9, 32, 38, 77, 170, 215], "swap": [6, 7, 14, 15, 16, 46, 47, 105, 255, 256], "arriv": 6, "posit": [6, 21, 43, 55, 101, 119, 134, 135, 141, 146, 147, 210, 218, 224, 234, 238, 244, 245, 251, 266, 278], "advanc": [6, 8, 14, 15, 36, 172, 178, 179, 197, 207, 208, 210, 230, 261, 262, 266], "right": [6, 7, 10, 14, 15, 19, 21, 35, 36, 40, 41, 42, 46, 49, 53, 55, 58, 60, 63, 64, 65, 66, 71, 72, 73, 74, 77, 78, 81, 85, 88, 90, 95, 96, 97, 99, 101, 104, 105, 106, 108, 112, 114, 116, 118, 120, 122, 123, 129, 130, 132, 138, 139, 140, 141, 142, 144, 146, 147, 149, 152, 153, 162, 163, 164, 169, 170, 178, 183, 184, 185, 188, 190, 191, 192, 195, 200, 201, 203, 214, 215, 216, 218, 219, 235, 247, 249, 251, 258, 261, 266, 273, 275], "stop": [6, 14, 17, 29, 32, 66, 86, 121, 122, 139, 147, 166, 169, 170, 173, 178, 179, 182, 183, 185, 223, 237, 241, 244], "video": [6, 9, 10, 14, 16, 112, 122, 199, 211, 216, 221, 223, 239, 241, 254, 265, 266, 267], "pai": [6, 53, 100, 105, 120, 138, 266], "attent": [6, 67, 100, 101, 120, 138, 139, 266], "built": [6, 19, 113, 124, 134, 166, 174, 185, 201, 202, 204, 227, 229, 231, 232, 239, 263], "rest": [6, 11, 50, 55, 57, 66, 95, 138, 172, 203, 224, 241, 268, 272, 279, 280, 283], "spot": [6, 23, 63, 67], "directli": [6, 81, 101, 124, 173, 197, 202, 203, 210, 212, 253, 256, 257, 263, 264], "smallest": [6, 9, 14, 15, 17, 44, 113, 151, 180, 218, 284], "virginia": [6, 14, 16, 149, 150, 151, 152, 153, 154, 156, 159, 215, 216, 217, 255], "tech": [6, 14, 16, 215, 216, 217, 255], "insertionsort2": 7, "appropri": [7, 14, 24, 38, 41, 42, 53, 63, 73, 115, 180, 203, 206, 207, 243, 251, 268], "detail": [7, 15, 97, 113, 121, 127, 164, 192, 199, 204, 212, 217, 218, 223, 227, 237, 239, 253, 255, 263, 264, 270], "equival": [7, 15, 78], "black": [7, 14, 15, 46, 48, 49, 50, 89, 147, 160, 162, 220, 222, 248], "mark": [7, 15, 24, 71, 125, 147, 149, 156, 195, 261], "start": [7, 10, 11, 12, 13, 15, 16, 18, 22, 28, 29, 31, 32, 35, 36, 37, 38, 41, 42, 43, 46, 50, 56, 61, 64, 66, 69, 71, 76, 81, 82, 85, 86, 88, 98, 100, 101, 106, 112, 115, 122, 125, 129, 130, 131, 133, 134, 135, 139, 140, 141, 143, 147, 148, 153, 156, 162, 163, 169, 170, 171, 178, 180, 185, 189, 190, 191, 192, 195, 197, 200, 201, 212, 213, 214, 215, 219, 224, 227, 240, 241, 246, 253, 254, 255, 256, 258, 261, 262, 263, 264, 266, 271, 273, 274, 275, 278, 280, 282, 283, 284], "j": [7, 15, 213, 227, 272], "point": [7, 9, 10, 12, 14, 19, 29, 31, 32, 38, 64, 66, 71, 81, 85, 98, 118, 122, 142, 149, 150, 152, 153, 154, 156, 159, 163, 173, 178, 183, 185, 192, 199, 202, 212, 213, 219, 220, 225, 235, 241, 258, 261, 263, 268, 271, 274], "indic": [7, 20, 40, 56, 142, 148, 191, 218, 221, 223, 224, 243, 248], "index": [7, 8, 10, 18, 25, 27, 28, 29, 32, 33, 34, 36, 41, 43, 44, 130, 134, 135, 147, 197, 204, 212, 225, 233, 238, 242, 252, 257, 258, 262, 270, 278, 288], "exist": [7, 15, 30, 31, 36, 50, 85, 95, 98, 163, 169, 192, 201, 207, 208, 211, 234, 240, 241, 256, 261], "current": [7, 8, 14, 21, 29, 30, 38, 41, 60, 63, 65, 74, 84, 104, 134, 135, 142, 146, 147, 152, 156, 163, 166, 169, 175, 180, 185, 191, 201, 203, 215, 219, 220, 226, 228, 240, 243, 244, 248, 251, 255, 256, 259, 262, 263], "home": [7, 133, 151, 231, 236, 254], "temp": [7, 35, 56, 95], "currentmin": [7, 15], "befor": [7, 15, 27, 31, 32, 36, 37, 38, 54, 56, 61, 64, 65, 71, 79, 82, 88, 92, 98, 101, 106, 108, 111, 114, 121, 122, 125, 134, 135, 139, 140, 141, 142, 145, 146, 147, 152, 156, 161, 169, 170, 172, 173, 178, 181, 183, 190, 195, 201, 203, 226, 227, 232, 236, 239, 255, 259, 261, 268, 272, 273, 282, 284], "memor": [7, 15, 22, 113, 250, 278], "consist": [5, 7, 24, 85, 199, 200, 202, 213, 218, 220, 221, 222, 229, 230, 239, 253, 272], "partial": [7, 15, 272], "why": [7, 25, 56, 71, 77, 78, 101, 103, 106, 115, 120, 128, 131, 152, 163, 170, 173, 184, 206, 221, 236, 239, 241, 247, 254, 259], "approach": [7, 18, 30, 55, 160, 162, 195, 207, 214, 239], "own": [7, 28, 31, 35, 75, 77, 84, 85, 96, 97, 101, 126, 141, 150, 166, 178, 183, 195, 197, 230, 232, 269, 280, 283], "advantag": [7, 25, 55, 59, 215, 224, 235], "disadvantag": [7, 228], "click": [7, 15, 22, 105, 108, 112, 114, 118, 121, 130, 138, 140, 141, 142, 146, 149, 150, 152, 153, 154, 156, 192, 205, 206, 207, 209, 210, 211, 215, 246, 247, 248, 255, 265, 266, 267, 269], "button": [7, 9, 15, 105, 108, 112, 114, 118, 120, 130, 138, 140, 141, 149, 150, 152, 153, 154, 156, 166, 190, 191, 192, 197, 215, 247, 253, 265], "almost": [7, 10, 46, 202, 213, 214, 215, 227, 238], "effect": [7, 8, 49, 95, 165, 208, 234, 235, 238, 240, 253, 258], "linearsearch": 8, "spend": [8, 199, 261], "data": [8, 17, 21, 24, 30, 37, 38, 42, 43, 45, 57, 142, 148, 149, 150, 151, 152, 153, 157, 162, 164, 165, 166, 168, 170, 171, 190, 193, 195, 197, 199, 201, 202, 203, 207, 212, 213, 218, 226, 234, 235, 236, 237, 251, 255, 256, 261, 265, 270, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 286, 288], "One": [8, 9, 24, 50, 55, 60, 65, 78, 86, 95, 105, 116, 125, 133, 134, 135, 139, 153, 170, 172, 175, 176, 183, 189, 191, 202, 216, 236, 239, 261, 262, 264, 281], "fundament": [8, 200, 211, 226, 227, 230, 231, 238, 239, 242, 253, 269], "record": [8, 148, 152, 153, 154, 218, 235, 236, 245, 271, 272, 273, 275, 277, 279, 280, 282, 284, 286], "displai": [8, 76, 107, 166, 173, 175, 190, 191, 198, 200, 220, 221, 224, 229, 263, 272, 273], "simplest": [8, 254], "element": [8, 31, 164, 167, 189, 190, 269], "reach": [8, 11, 13, 21, 78, 122, 148, 169, 178, 179, 235, 251, 261], "progress": [8, 11, 14, 195, 240], "straight": [8, 137, 259], "Of": [8, 31, 96, 183], "cours": [8, 22, 31, 48, 96, 156, 183, 206, 209, 211, 222], "specifi": [8, 24, 29, 31, 32, 36, 43, 55, 85, 86, 97, 101, 102, 119, 120, 123, 124, 125, 128, 135, 142, 147, 148, 157, 164, 165, 166, 172, 220, 222, 256, 268, 275, 282, 283, 284, 286], "fill": [8, 28, 64, 88, 91, 137, 139, 146, 160, 180, 218, 253], "integ": [8, 24, 27, 29, 64, 65, 69, 72, 79, 104, 109, 113, 116, 117, 124, 153, 163, 170, 172, 174, 200, 213, 218, 220, 224], "uniqu": [8, 22, 200, 219, 236, 272, 277, 278, 279], "often": [8, 9, 13, 19, 37, 39, 40, 45, 54, 55, 88, 139, 155, 164, 165, 175, 185, 191, 200, 202, 203, 207, 208, 210, 213, 217, 219, 222, 223, 226, 227, 237, 238, 245, 250, 253, 256, 263, 264, 271, 281], "standard": [8, 108, 140, 155, 211, 217, 218, 229, 231, 235, 239], "wish": [8, 75, 213, 261], "text": [8, 16, 21, 24, 28, 79, 81, 136, 153, 154, 156, 157, 191, 193, 195, 197, 202, 213, 220, 235, 246, 282], "box": [8, 40, 106, 215, 218, 243, 282], "pretti": [8, 13, 49, 72, 75, 86, 139, 160, 175, 239], "easi": [8, 21, 30, 35, 78, 86, 121, 139, 152, 153, 157, 195, 219, 221, 224, 239, 241], "weak": 8, "potenti": [8, 49, 100, 207, 226, 235, 236, 241, 261], "someon": [8, 18, 24, 53, 73, 81, 96, 115, 120, 121, 211, 212, 234, 235, 258, 261, 264, 278], "fine": [8, 71, 78, 88, 226, 283], "scale": [8, 31, 240, 241, 259, 260], "mergesort": [9, 10], "util": 9, "conquer": 9, "paradigm": 9, "repeatedli": [9, 11, 202], "sub": [9, 84, 86, 203, 241], "solut": [9, 73, 86, 105, 112, 118, 130, 140, 146, 148, 184, 239, 240, 242, 261, 275], "individu": [9, 40, 45, 107, 195, 207, 208, 213, 223, 229, 230, 235, 238, 257, 273, 278], "obviou": [9, 173], "combin": [9, 22, 36, 38, 52, 74, 78, 79, 80, 88, 142, 148, 170, 190, 193, 202, 208, 209, 229, 230, 244, 245, 248, 250, 251, 259, 260, 271, 284], "learn": [9, 13, 17, 18, 21, 34, 44, 57, 62, 66, 70, 83, 93, 95, 103, 108, 114, 117, 124, 125, 128, 136, 142, 144, 158, 165, 168, 177, 184, 185, 187, 195, 208, 211, 219, 220, 222, 234, 238, 239, 269, 273, 277, 281, 284, 286], "insert": [9, 12, 16, 18, 36, 43, 104, 219, 239], "worst": [9, 16, 153], "better": [9, 22, 31, 41, 55, 78, 80, 88, 121, 123, 193, 201, 235, 258], "featur": [9, 54, 84, 171, 192, 198, 201, 208, 213, 229, 231, 237, 240, 247, 255, 258, 259, 260, 269, 270, 272, 279], "relianc": 9, "examin": [9, 50, 121, 139, 203, 217, 280, 282], "won": [9, 31, 41, 55, 63, 72, 86, 122, 139, 178, 250, 258, 272], "lista": [9, 10], "listb": [9, 10], "sortedlist": 9, "AND": [9, 78, 163, 195, 243, 245, 246, 247, 248, 250, 252, 280], "b": [9, 21, 35, 36, 46, 47, 55, 56, 57, 74, 76, 81, 96, 98, 99, 100, 115, 138, 153, 174, 204, 213, 220, 221, 236, 237, 243, 244, 256, 260, 261, 272], "demonstr": [9, 10, 13, 22, 55, 112, 144, 199, 215, 217, 244, 251, 256, 266], "new": [9, 11, 15, 18, 28, 31, 36, 38, 41, 42, 50, 54, 72, 74, 82, 85, 94, 95, 96, 98, 100, 103, 106, 111, 112, 115, 120, 121, 123, 125, 127, 128, 131, 132, 134, 135, 136, 138, 148, 149, 150, 151, 152, 153, 154, 156, 159, 162, 163, 165, 169, 175, 182, 189, 192, 193, 195, 207, 208, 211, 214, 215, 219, 223, 224, 226, 227, 228, 229, 237, 238, 240, 241, 242, 250, 255, 259, 260, 262, 265, 266, 267, 269], "mention": [9, 77, 215, 261], "mergesort2": 10, "help": [10, 55, 58, 85, 92, 98, 99, 115, 150, 169, 183, 184, 192, 211, 215, 218, 235, 239, 253, 258, 259, 264, 271, 273], "cheat": 10, "cut": [10, 28, 34, 240, 258, 260], "halv": [10, 31], "togeth": [10, 11, 21, 28, 38, 45, 78, 101, 115, 131, 135, 136, 149, 156, 164, 183, 243, 247], "definit": [10, 87, 96, 120, 122, 127, 258, 261], "recurs": 10, "itself": [10, 30, 88, 164, 182, 185, 192, 193, 201, 202, 203, 205, 209, 234, 237], "initi": [10, 14, 38, 41, 73, 130, 137, 153, 170, 175, 178, 218], "final": [10, 15, 30, 40, 47, 55, 73, 74, 77, 85, 91, 93, 96, 99, 100, 101, 115, 139, 148, 169, 198, 218, 241, 245, 248, 256, 266, 271, 275, 280, 283], "feel": [10, 35, 78, 148, 241], "free": [10, 35, 58, 73, 105, 115, 148, 197, 235, 241, 254, 259, 261, 283], "ignor": [10, 12, 20, 42, 73, 75, 108, 112, 139, 143, 169, 189, 191, 224, 254, 266, 283], "implement": [10, 23, 50, 59, 84, 86, 92, 93, 215, 218, 227, 232, 247, 248, 251, 266], "backtrack": 10, "notic": [10, 22, 30, 32, 50, 57, 59, 74, 79, 81, 85, 90, 91, 107, 113, 124, 131, 132, 134, 162, 163, 179, 185, 188, 191, 195, 215, 219, 223, 235, 243, 244, 249, 258, 259, 263, 265, 275, 280, 282, 283], "allow": [10, 11, 15, 19, 22, 59, 86, 97, 101, 113, 121, 125, 127, 142, 172, 179, 183, 190, 201, 202, 222, 227, 229, 235, 236, 237, 240, 247, 248, 253, 256, 257, 261, 264, 267, 273, 282], "randomli": [10, 64, 275], "mergesorteffici": 11, "starter": [11, 28, 148, 181], "word": [11, 28, 35, 36, 38, 45, 53, 81, 115, 116, 130, 185, 196, 213, 227, 248, 250, 255, 256, 261, 269, 282], "etc": [11, 24, 28, 80, 81, 87, 97, 138, 142, 147, 162, 163, 164, 178, 182, 192, 197, 201, 207, 216, 219, 220, 222, 243, 253, 266, 272, 279], "rough": [11, 12, 86, 94], "analysi": [11, 207, 234], "hard": [11, 13, 21, 24, 45, 94, 101, 139, 152, 171, 198, 201, 215, 218, 221, 239, 240, 253, 255, 256, 258, 261, 263, 264], "singl": [11, 13, 19, 21, 23, 24, 32, 45, 107, 131, 133, 135, 144, 189, 193, 200, 229, 234, 241, 250, 255, 260, 264, 280], "512": [11, 243], "level": [11, 53, 55, 59, 86, 88, 92, 121, 149, 153, 164, 180, 183, 185, 201, 204, 210, 234, 235, 243, 257, 263, 265, 266, 267, 268, 269, 270], "256": [11, 24, 156, 164, 221, 222, 248, 249], "tabl": [11, 12, 13, 22, 109, 112, 114, 147, 158, 213, 215, 219, 221, 223, 225, 227, 232, 243, 248, 271, 272, 275, 276, 277, 279, 282, 283, 286], "128": [11, 214, 223, 243, 248, 249], "full": [11, 28, 31, 75, 105, 107, 115, 131, 139, 163, 166, 171, 183, 191, 222, 243, 254, 256, 275], "skip": [11, 55, 56, 57, 172, 173, 266], "few": [11, 17, 30, 51, 64, 71, 72, 79, 84, 88, 95, 115, 124, 149, 171, 188, 190, 195, 201, 203, 218, 221, 234, 235, 240, 255, 268], "add": [11, 16, 28, 35, 36, 42, 43, 44, 46, 51, 56, 61, 63, 66, 67, 71, 72, 75, 82, 90, 91, 95, 96, 98, 101, 104, 106, 114, 123, 131, 133, 135, 136, 139, 145, 148, 149, 150, 160, 169, 170, 178, 180, 181, 185, 188, 199, 202, 204, 207, 214, 215, 216, 219, 223, 224, 243, 246, 252, 258, 260, 261, 263, 264, 267, 268, 271, 273, 274, 275], "64": [11, 24, 148, 200, 214, 218, 223, 241, 243, 247, 248, 268], "group": [11, 24, 38, 45, 86, 127, 183, 189, 200, 209, 221, 264, 272, 274, 288], "formula": [11, 94, 98, 99, 113, 115, 175, 179, 191, 258, 264], "overal": [11, 16, 74, 87, 161, 259, 275], "total": [11, 16, 35, 38, 42, 44, 53, 60, 63, 73, 104, 111, 118, 183, 256, 258, 260, 261, 264, 271, 272, 273, 274, 277], "per": [11, 22, 53, 58, 59, 104, 105, 107, 112, 118, 150, 151, 154, 169, 222, 239, 260], "mergesortefficiency2": 12, "establish": [12, 13], "obvious": [12, 31, 47], "500": [12, 13, 24, 104, 105, 224, 246], "around": [12, 22, 50, 67, 114, 129, 147, 192, 224, 232, 235, 239, 254, 265, 280], "250": [12, 13, 47, 49, 156, 243, 247, 248, 249], "483": 12, "33": [12, 148, 149, 150, 152, 153, 154, 156, 159, 239], "664": 12, "966": 12, "132": 12, "877": 12, "660": 12, "964": 12, "estim": [12, 18, 94, 107, 226, 237], "overhead": 12, "copi": [12, 21, 22, 30, 31, 32, 33, 36, 42, 43, 50, 75, 95, 97, 107, 111, 119, 121, 147, 150, 160, 162, 163, 173, 182, 185, 192, 193, 197, 201, 221, 246, 249, 250, 255], "due": [12, 119, 192, 258], "hold": [12, 21, 30, 41, 43, 44, 65, 105, 111, 115, 116, 118, 125, 132, 166, 170, 189, 190, 191, 199, 202, 203, 214, 224, 255, 261], "certainli": [12, 250], "timer": [12, 203], "simul": [12, 31, 63, 64, 65, 69, 72, 206, 241, 265, 288], "slider": [12, 66, 213, 220], "win": [12, 166, 227, 236], "searchbigo": 13, "discuss": [13, 37, 54, 88, 138, 240], "quantifi": 13, "pile": [13, 258], "belong": [13, 89, 125, 152], "best": [13, 37, 41, 86, 88, 97, 122, 139, 174, 175, 201, 218, 239, 258, 260, 266], "sometim": [13, 36, 40, 41, 76, 81, 86, 115, 173, 183, 189, 198, 201, 203, 210, 212, 218, 238, 254, 265, 269, 273], "lucki": [13, 63, 67], "earli": [13, 17, 66, 202, 224, 226, 227, 228, 229, 230, 259], "scenario": 13, "summar": [13, 109, 251], "model": [13, 69, 101, 202, 241, 242, 250, 253, 255], "true": [13, 21, 23, 28, 46, 47, 48, 53, 54, 55, 56, 57, 60, 61, 66, 67, 73, 74, 76, 77, 78, 82, 88, 92, 104, 115, 139, 153, 172, 173, 174, 175, 176, 177, 178, 195, 203, 219, 244, 246, 250, 251, 252], "rare": [13, 264], "except": [13, 20, 115, 182, 214], "mislead": 13, "sens": [13, 18, 77, 81, 101, 106, 138, 150, 154, 156, 175, 269, 273, 280, 283], "normal": [13, 19, 21, 53, 107, 108, 149, 150, 152, 153, 154, 156, 159, 183, 191, 201, 203, 216, 219, 224, 250, 258, 264, 266], "though": [13, 20, 23, 37, 64, 132, 178, 222, 229, 237, 249, 260], "reli": [13, 64, 215, 232, 237, 282], "uncheck": 13, "event": [13, 64, 195, 232, 254, 255], "125": [13, 51, 131, 134, 214], "62": [13, 148], "31": [13, 148, 149, 150, 152, 153, 154, 156, 159, 213], "ask": [13, 27, 28, 30, 32, 48, 54, 64, 66, 73, 74, 75, 80, 96, 124, 142, 144, 156, 172, 174, 179, 189, 193, 195, 219, 234, 235, 256, 268, 271, 273, 274, 282, 283], "96": [13, 148, 243, 246, 248, 249], "30": [13, 24, 46, 59, 91, 104, 140, 163, 169, 174, 178, 239, 258], "stori": [13, 34, 129, 136, 254], "appear": [13, 27, 28, 66, 73, 135, 149, 150, 152, 153, 154, 156, 215, 232, 237, 241, 272, 273, 279, 280], "selectionsort": 14, "elect": [14, 227], "part": [14, 15, 18, 23, 27, 30, 31, 32, 33, 34, 35, 41, 42, 47, 48, 50, 61, 66, 67, 71, 73, 76, 77, 78, 81, 82, 83, 84, 86, 88, 90, 95, 97, 100, 101, 108, 114, 115, 119, 120, 122, 124, 125, 126, 129, 130, 135, 136, 139, 148, 150, 152, 156, 162, 163, 164, 165, 167, 171, 178, 181, 183, 184, 185, 186, 188, 189, 193, 198, 200, 201, 202, 206, 213, 227, 234, 248, 250, 258, 264, 265, 275, 277, 280, 282], "begin": [14, 29, 119, 172, 182, 282, 284], "therebi": 14, "plai": [14, 22, 75, 106, 112, 191, 192, 220, 231, 241, 243], "front": [14, 31, 48, 200], "highlight": [14, 50], "panel": 14, "vertic": [14, 164, 167, 189, 190], "bar": [14, 163, 173, 215, 253], "On": [14, 21, 31, 76, 132, 162, 178, 203, 210, 219, 239, 250, 255, 256, 272, 284], "pair": [14, 16, 63, 98, 105, 107, 131, 133, 135, 160, 163, 189, 193, 241, 245, 284], "seen": [14, 15, 30, 37, 41, 66, 72, 79, 107, 124, 138, 141, 142, 148, 149, 153, 156, 170, 182, 185, 202, 213, 218, 222, 231, 232, 239, 249, 256], "selectionsort2": 15, "scan": 15, "currentminindex": 15, "sweep": [15, 235], "recal": [15, 29, 37, 99, 101, 123, 153, 163, 172, 273, 283], "refer": [15, 19, 24, 65, 85, 106, 115, 156, 164, 185, 198, 200, 203, 250, 254, 255, 256, 259, 261, 281], "curentminindex": 15, "outcom": [15, 64, 72], "sortbigo": 16, "analyz": [16, 18, 158, 235, 236, 237, 238, 281], "did": [16, 66, 78, 97, 108, 114, 120, 139, 224, 228, 254, 257, 275], "99": [16, 105, 118, 148, 258], "98": [16, 148], "trick": [16, 21, 22, 40, 79, 80, 98, 122, 146, 147, 169, 185, 215, 218, 219, 256], "were": [16, 19, 35, 38, 40, 42, 45, 53, 55, 73, 97, 105, 107, 129, 133, 139, 156, 165, 191, 213, 218, 222, 226, 227, 228, 229, 230, 232, 236, 238, 241, 250, 257, 259, 260, 263, 264, 268, 271, 274, 275, 278, 279, 284], "web": [17, 155, 166, 219, 221, 224, 235, 237, 239, 254, 265, 281, 284], "rank": 17, "state": [17, 19, 20, 21, 23, 73, 141, 142, 149, 153, 156, 158, 159, 201, 241, 243, 244, 245, 246, 247, 248, 249, 250, 255, 282], "popul": [17, 158], "rearrang": 17, "behav": [17, 211, 240, 266], "situat": [17, 58, 60, 69, 76, 79, 86, 155, 179, 182, 251, 253, 254, 261, 263], "complet": [17, 22, 37, 42, 53, 67, 80, 96, 104, 119, 126, 169, 179, 180, 200, 203, 213, 226, 229, 240, 255, 256, 261, 283], "perhap": [17, 18, 30, 213, 282], "accur": [18, 21, 42, 125, 175, 179, 193, 218, 219, 221, 237, 265], "heart": [18, 154], "question": [18, 47, 49, 64, 75, 100, 107, 111, 148, 151, 153, 174, 199, 208, 209, 219, 221, 234, 235, 243, 274, 278, 283, 284], "recogn": [18, 28, 165, 183, 188, 213, 223, 227, 237, 243, 254, 263], "ones": [18, 28, 42, 49, 81, 115, 124, 125, 148, 156, 181, 205, 213, 214, 217, 218, 219, 223, 239, 248, 258, 260, 271, 280], "chapter": [18, 25, 28, 34, 44, 52, 62, 70, 83, 93, 103, 113, 117, 128, 131, 136, 138, 142, 144, 155, 158, 166, 168, 177, 187, 195, 196, 204, 225, 238, 239, 242, 252, 257, 262, 270, 273, 277, 281, 286], "focu": [18, 42, 67, 88, 97, 124, 127, 139, 166, 199, 206, 207, 209, 211, 226, 234, 239, 250, 253, 281], "addit": [18, 59, 109, 114, 116, 123, 146, 185, 195, 205, 207, 208, 210, 214, 224, 225, 232, 240, 265, 267], "studi": [18, 206, 208], "simpl": [18, 20, 21, 28, 31, 76, 84, 88, 92, 145, 148, 173, 184, 195, 197, 198, 199, 201, 202, 203, 213, 215, 216, 217, 218, 222, 224, 239, 254, 263, 265, 268, 269, 280, 284], "scientist": [18, 197, 202, 206, 208, 211, 241, 242, 250, 262], "programm": [18, 30, 88, 106, 115, 138, 139, 155, 191, 220, 226, 227, 257, 259, 260, 261, 262, 263, 264, 265, 268, 281], "concern": [18, 150, 206, 207, 209, 211, 235, 237], "theoret": [18, 206, 211, 239, 241], "practic": [18, 31, 117, 128, 136, 144, 187, 195, 209, 239, 240, 242, 256], "finish": [18, 44, 63, 73, 104, 118, 149, 178, 183, 227, 254, 255, 256, 261], "reason": [18, 19, 21, 49, 64, 88, 97, 121, 172, 184, 239, 240, 263], "topic": [18, 25, 164, 195, 197, 204, 207, 211, 222, 225, 231, 234, 238, 242, 252, 257, 262, 270], "introduct": [18, 19, 20, 21, 22, 23, 24, 200, 229, 264, 288], "With": [18, 22, 187, 214, 216, 218, 222, 223, 224, 227, 249, 264], "merg": [18, 31, 152, 226, 243, 258, 275, 276, 277], "familiar": [19, 108, 198, 216, 254], "devic": [19, 21, 198, 200, 204, 207, 212, 226, 227, 230, 231, 232, 236, 238, 239, 243, 246, 247, 248, 249, 253, 254, 260, 263], "signal": [19, 20, 21, 23, 199, 202, 203, 204, 216, 236, 251], "phenomenon": 19, "voltag": [19, 20, 23, 106, 260], "flow": [19, 57, 58, 226, 240], "circuit": [19, 20, 198, 201, 202, 204, 205, 216, 230, 243, 244, 249, 250, 251, 259, 288], "wave": [19, 241], "wire": [19, 23, 227, 244, 247], "smoothli": [19, 21], "00000": [19, 220], "volt": 19, "00001": [19, 202, 220], "Not": [44, 82, 83, 97, 198, 201, 212, 220, 221, 222, 223, 235, 245, 249, 250, 253, 256, 264], "veri": [19, 20, 40, 48, 49, 63, 65, 66, 118, 131, 157, 166, 170, 200, 201, 202, 203, 205, 206, 207, 209, 210, 211, 215, 222, 239, 256, 260, 261, 263, 264, 265, 268, 269, 275], "difficult": [19, 155, 157, 183], "build": [19, 21, 36, 38, 42, 54, 63, 65, 70, 75, 85, 87, 88, 92, 93, 129, 164, 170, 195, 204, 206, 211, 212, 219, 226, 227, 228, 229, 230, 232, 236, 240, 249, 251, 269, 271, 275, 284], "reliabl": [19, 21, 67, 211, 228, 240], "slightest": 19, "bit": [19, 21, 24, 27, 58, 72, 97, 156, 164, 183, 188, 190, 199, 200, 203, 213, 214, 216, 218, 219, 220, 221, 222, 223, 224, 238, 243, 245, 249, 250, 252, 256, 268, 288], "nois": [19, 20, 21, 64], "limit": [19, 30, 75, 162, 163, 171, 187, 195, 197, 201, 216, 219, 227, 238, 239, 240, 253, 258, 269, 286, 288], "off": [19, 20, 21, 22, 23, 36, 71, 97, 105, 191, 200, 201, 228, 241, 243, 244, 247, 248, 249, 251, 252, 271, 280], "plot": 19, "halfwai": [19, 29], "english": [19, 77, 139, 195, 215, 226, 250, 267, 269], "26": [19, 104, 105, 148, 149, 150, 151, 152, 153, 154, 156, 159, 214], "z": [19, 132, 174, 213], "self": [19, 20, 21, 22, 23, 24, 125, 213, 214, 215, 216, 218, 219, 220, 221, 222, 223, 224, 245, 250, 256], "random": [19, 31, 63, 66, 69, 198, 261, 288], "lost": [19, 20, 235, 236], "java": [19, 20, 21, 22, 23, 24, 200, 264], "bradlei": [19, 20, 21, 22, 23, 24, 200, 264], "kjell": [19, 20, 21, 22, 23, 24, 200, 264], "cc": [19, 20, 21, 22, 23, 24, 195, 198, 200, 201, 226, 227, 229, 230, 231, 232, 239, 253, 258, 259, 264], "BY": [19, 20, 21, 22, 23, 24, 195, 198, 200, 201, 226, 227, 229, 230, 231, 232, 239, 253, 258, 259, 264, 272, 273, 274, 275, 284], "nc": [19, 20, 21, 22, 23, 24, 149, 150, 152, 153, 154, 156, 159, 200, 264], "analogtodigit": 20, "interpret": [20, 24, 115, 199, 218, 219, 220, 221, 222, 264, 268, 280], "against": [20, 63, 152], "threshold": 20, "imag": [20, 21, 24, 40, 45, 46, 48, 50, 51, 124, 156, 160, 161, 162, 163, 167, 183, 196, 198, 200, 201, 213, 220, 225, 239, 240, 241, 243, 254, 256, 258, 259, 260, 263, 268, 288], "t1": 20, "t2": 20, "abl": [20, 21, 22, 74, 150, 152, 165, 195, 213, 226, 234, 235, 237, 239, 240, 251, 261], "distinguish": [20, 57, 174, 183], "intend": [20, 139, 189, 195, 206], "red": [20, 21, 46, 47, 48, 49, 50, 71, 129, 134, 140, 145, 147, 149, 150, 152, 153, 154, 156, 159, 160, 161, 162, 163, 164, 165, 166, 167, 189, 190, 220, 222, 241, 248, 259, 269], "grei": [20, 21], "bounc": 20, "confid": [20, 31, 41, 235, 241], "inari": 21, "fals": [21, 23, 28, 46, 47, 48, 53, 55, 57, 58, 61, 66, 73, 74, 76, 77, 82, 104, 115, 172, 173, 174, 176, 177, 178, 243, 244, 246, 247, 248, 249, 251, 252], "good": [21, 24, 31, 49, 75, 80, 88, 122, 133, 174, 189, 195, 197, 212, 218, 234, 238, 239], "toggl": [21, 243, 246, 247, 248, 249], "switch": [21, 22, 23, 106, 221, 227, 228, 241, 244, 246, 247, 248, 249, 250, 251, 255, 256, 268], "light": [21, 23, 47, 88, 190, 222, 244, 248, 251], "dimmer": 21, "fulli": [21, 192], "carefulli": [21, 139, 183, 191], "adjust": [21, 65, 150], "four": [21, 22, 78, 85, 86, 112, 123, 164, 180, 207, 218, 219, 221, 223, 224, 234, 240, 244, 248, 251, 260], "somewhat": 21, "overlap": [21, 211], "claud": 21, "shannon": 21, "mathematician": [21, 227, 232], "bell": 21, "laboratori": 21, "hi": [21, 43, 124, 131, 134, 135, 141, 149, 150, 152, 153, 154, 156, 159, 189, 193, 226, 232, 235, 259], "1948": [21, 227], "theori": [21, 68, 195, 206, 211], "commun": [21, 55, 164, 195, 202, 208, 209, 258], "foundat": [21, 115, 208, 211], "piec": [21, 23, 45, 76, 79, 81, 86, 100, 115, 133, 139, 170, 191, 201, 220, 226, 251, 253, 254, 256, 261, 265, 278], "metal": 21, "apart": [21, 236], "gradual": [21, 42], "compon": [21, 190, 199, 202, 203, 204, 227, 228, 240, 246, 254], "assembl": [21, 237, 253, 267], "harder": [21, 86, 88, 97, 101, 139, 219, 239, 240], "tini": [21, 23, 153, 258], "insid": [21, 42, 50, 73, 78, 85, 88, 95, 100, 101, 102, 107, 114, 118, 120, 122, 125, 131, 135, 147, 165, 167, 183, 188, 203, 247, 254, 282], "silicon": [21, 240], "chip": [21, 205, 230, 231, 240, 259, 260], "fabric": [21, 240], "cheap": [21, 201], "million": [21, 230, 235, 262, 264], "fit": [21, 195, 221, 253, 256, 260], "area": [21, 65, 94, 98, 99, 113, 137, 139, 151, 152, 192, 202, 203, 205, 206, 207, 209, 210, 211, 213, 215, 237, 246, 260], "immun": 21, "digit": [21, 22, 23, 24, 25, 74, 75, 79, 84, 108, 115, 169, 175, 191, 200, 213, 214, 215, 216, 218, 219, 220, 221, 222, 223, 224, 227, 235, 243, 245, 250], "suppos": [21, 27, 46, 53, 63, 73, 81, 85, 86, 95, 137, 139, 156, 165, 169, 173, 226, 248, 260, 268, 275], "clearli": [21, 115, 238], "flawless": 21, "made": [21, 46, 66, 88, 106, 125, 164, 229, 235, 236, 247, 258, 264, 271, 272, 273, 278], "pictur": [21, 47, 52, 85, 97, 127, 138, 142, 146, 161, 163, 164, 167, 168, 183, 189, 190, 198, 200, 202, 241], "attempt": [21, 30, 60, 88, 170, 171, 240], "read": [21, 33, 40, 47, 55, 71, 78, 79, 97, 98, 115, 121, 122, 139, 148, 149, 150, 152, 153, 154, 157, 158, 159, 163, 171, 183, 185, 189, 195, 200, 203, 213, 220, 221, 224, 237, 253, 255, 263, 267, 283], "easili": [21, 45, 66, 121, 147, 148, 150, 152, 154, 164, 170, 179, 215, 226, 261, 262], "restor": [21, 256], "introduc": [21, 44, 62, 113, 136, 141, 144, 177, 195, 252, 260, 261, 265, 267, 281], "immedi": [21, 81, 95, 139, 254, 274], "filter": [21, 42, 155, 190, 271, 272, 273, 277, 286], "error": [21, 53, 60, 88, 94, 106, 115, 119, 121, 122, 125, 129, 131, 137, 144, 160, 163, 173, 180, 183, 191, 216, 234, 261, 269, 274, 280], "compound": 21, "forth": [21, 284], "processor": [21, 24, 198, 199, 200, 201, 204, 227, 231, 240, 253, 255, 256, 258, 259, 260, 262, 263, 265, 268], "seem": [21, 30, 31, 75, 86, 88, 120, 139, 152, 165, 274], "divers": [21, 253], "music": [21, 24, 226, 243], "convert": [21, 80, 81, 95, 96, 115, 124, 131, 136, 148, 153, 179, 214, 215, 219, 221, 224, 264, 268], "bitpattern": 22, "prefix": 22, "yet": [22, 42, 53, 84, 86, 90, 121, 122], "yourself": [22, 63, 71, 108, 114, 121, 123, 129, 185, 221], "muddl": 22, "wast": [22, 156, 228, 254, 259], "futur": [22, 139, 235, 239, 262, 288], "enough": [22, 24, 31, 84, 86, 171, 195, 201, 214, 216, 220, 221, 222, 223, 224, 234, 242, 245, 250, 258, 269], "hint": [22, 24, 27, 35, 42, 46, 49, 56, 80, 88, 98, 122, 126, 133, 160, 169, 180, 182, 214, 218, 220, 221, 222, 223, 240, 245, 250, 271, 272, 273, 275, 283, 284], "hole": 23, "punch": [23, 105, 226], "short": [23, 55, 98, 105, 130, 140, 195, 249], "mechan": [23, 226, 227, 239, 241], "bulb": [23, 244, 251], "transistor": [23, 228, 229, 230, 231, 240, 247, 251, 259], "magnet": 23, "charg": [23, 54, 59, 235, 253], "surfac": 23, "disk": [23, 198, 199, 253], "presenc": 23, "absenc": 23, "reflect": 23, "cd": [23, 201, 253], "radio": [23, 64], "manipul": [23, 132, 134, 155, 163, 190, 225, 251, 252, 270], "sequenc": [23, 29, 107, 118, 120, 121, 124, 131, 133, 134, 135, 180, 182, 189, 193, 195, 199, 200, 203, 204, 220, 222], "organ": [24, 154, 195, 207, 209, 210, 258], "eight": [24, 45, 63, 156, 219, 223, 248], "charact": [24, 63, 74, 107, 115, 120, 130, 131, 133, 134, 135, 138, 142, 154, 156, 157, 189, 193, 200, 213, 220], "letter": [24, 36, 55, 74, 78, 81, 115, 116, 130, 134, 135, 137, 138, 139, 147, 189, 193, 221, 222, 225], "punctuat": [24, 213], "sever": [24, 55, 116, 234], "typic": [24, 122, 172, 205, 206, 207, 208, 209, 210, 211, 220, 263, 268], "decim": [24, 27, 100, 108, 116, 124, 148, 160, 163, 170, 175, 179, 191, 202, 218, 219, 220, 221, 223, 224, 258, 265], "color": [24, 46, 47, 48, 49, 50, 51, 71, 77, 84, 86, 88, 89, 119, 129, 130, 137, 141, 144, 146, 147, 160, 161, 162, 163, 164, 165, 166, 167, 182, 183, 188, 189, 190, 191, 200, 222, 225, 247], "repent": 24, "24": [24, 104, 148, 149, 150, 152, 153, 154, 156, 159, 220, 222, 243, 258], "talk": [24, 45, 75, 77, 100, 164, 172, 198, 201, 202, 223, 253, 273, 275], "chunk": [24, 37, 86, 104, 147, 156, 171, 185, 218, 253, 258], "entir": [24, 121, 152, 156, 166, 195, 256, 280], "kibibyt": 24, "mebibyt": 24, "gibibyt": 24, "quantiti": 24, "kibiby": 24, "kib": 24, "mib": [24, 222], "048": 24, "576": 24, "gib": 24, "073": 24, "741": 24, "824": 24, "tebibyt": 24, "tib": 24, "099": 24, "511": 24, "627": 24, "776": 24, "40": [24, 46, 53, 111, 182, 183, 224, 243, 246, 258, 259], "kilo": 24, "mega": 24, "giga": 24, "kilobyt": 24, "kb": [24, 213], "megabyt": 24, "mb": [24, 213], "gigabyt": 24, "gb": [24, 256], "terabyt": 24, "tb": 24, "unfortun": [24, 139, 162, 201, 259, 260, 262, 274], "distinct": [24, 138, 235, 239, 271, 273], "recent": [24, 238, 249, 256, 279, 284], "sourc": [24, 195, 234, 236, 237, 254], "notat": [24, 101, 124, 134, 136, 189, 192, 193, 218, 224, 226], "bui": [24, 105, 111, 133], "advert": [], "ram": [24, 198, 201, 253, 256], "drive": [24, 68, 117, 131, 198, 201, 235, 237, 253, 255, 256], "fortun": [24, 81, 152, 258], "close": [24, 46, 49, 72, 76, 97, 108, 139, 148, 152, 156, 157, 162, 173, 175, 188, 191, 206, 221, 239, 240, 253, 254, 275, 278], "aren": [24, 42, 47, 64, 73], "desir": [24, 148, 152, 248, 280], "tradition": [24, 247, 269], "network": [24, 198, 207, 210, 235], "space": [24, 28, 71, 84, 106, 115, 120, 122, 123, 125, 129, 131, 134, 135, 138, 142, 143, 146, 180, 185, 189, 201, 222, 228, 229, 256, 259, 282], "confus": [24, 78, 85, 100, 115, 125, 223, 268], "send": [24, 199, 202, 203, 236, 255], "connect": [24, 98, 227, 238, 241, 246, 268], "4kib": 24, "probabl": [25, 30, 31, 37, 108, 114, 121, 123, 160, 164, 208, 211, 219, 223, 235, 239, 250, 254, 258, 263, 268, 283], "analog": 25, "Its": [25, 224, 264], "byte": [25, 200, 222, 256], "csp_global": 26, "mount_hood": [26, 47, 48, 49, 50, 51, 54, 57, 58, 59, 60, 63, 64, 65, 66, 67, 68, 71, 72, 74, 76, 77, 78, 84, 85, 86, 87, 88, 89, 90, 91, 95, 96, 97, 98, 99, 100, 101, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 118, 119, 120, 121, 122, 123, 124, 125, 126, 129, 130, 131, 132, 133, 134, 138, 139, 141, 142, 145, 146, 147, 160, 161, 162, 163, 165, 166, 167, 170, 171, 172, 173, 174, 175, 180, 181, 182, 183, 184, 185, 188], "jpg": [26, 47, 48, 49, 50, 51, 54, 57, 58, 59, 60, 63, 64, 65, 66, 67, 68, 71, 72, 74, 76, 77, 78, 84, 85, 86, 87, 88, 89, 90, 91, 95, 96, 97, 98, 99, 100, 101, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 118, 119, 120, 121, 122, 123, 124, 125, 126, 129, 130, 131, 132, 133, 134, 138, 139, 141, 142, 145, 146, 147, 160, 161, 162, 163, 165, 166, 167, 170, 171, 172, 173, 174, 175, 180, 181, 182, 183, 184, 185, 188], "graduat": [26, 47, 48, 49, 50, 51, 54, 57, 58, 59, 60, 63, 64, 65, 66, 67, 68, 71, 72, 73, 74, 76, 77, 78, 84, 85, 86, 87, 88, 89, 90, 91, 95, 96, 97, 98, 99, 100, 101, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 118, 119, 120, 121, 122, 123, 124, 125, 126, 129, 130, 131, 132, 133, 134, 138, 139, 141, 142, 145, 146, 147, 160, 161, 162, 163, 165, 166, 167, 170, 171, 172, 173, 174, 175, 180, 181, 182, 183, 184, 185, 188, 206, 208, 211], "goalkeep": [26, 47, 48, 49, 50, 51, 54, 57, 58, 59, 60, 63, 64, 65, 66, 67, 68, 71, 72, 74, 76, 77, 78, 84, 85, 86, 87, 88, 89, 90, 91, 95, 96, 97, 98, 99, 100, 101, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 118, 119, 120, 121, 122, 123, 124, 125, 126, 129, 130, 131, 132, 133, 134, 138, 139, 141, 142, 145, 146, 147, 160, 161, 162, 163, 165, 166, 167, 170, 171, 172, 173, 174, 175, 180, 181, 182, 183, 184, 185, 188], "student1": [26, 47, 48, 49, 50, 51, 54, 57, 58, 59, 60, 63, 64, 65, 66, 67, 68, 71, 72, 74, 76, 77, 78, 84, 85, 86, 87, 88, 89, 90, 91, 95, 96, 97, 98, 99, 100, 101, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 118, 119, 120, 121, 122, 123, 124, 125, 126, 129, 130, 131, 132, 133, 134, 138, 139, 141, 142, 145, 146, 147, 160, 161, 162, 163, 165, 166, 167, 170, 171, 172, 173, 174, 175, 180, 181, 182, 183, 184, 185, 188], "student2": [26, 47, 48, 49, 50, 51, 54, 57, 58, 59, 60, 63, 64, 65, 66, 67, 68, 71, 72, 74, 76, 77, 78, 84, 85, 86, 87, 88, 89, 90, 91, 95, 96, 97, 98, 99, 100, 101, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 118, 119, 120, 121, 122, 123, 124, 125, 126, 129, 130, 131, 132, 133, 134, 138, 139, 141, 142, 145, 146, 147, 160, 161, 162, 163, 165, 166, 167, 170, 171, 172, 173, 174, 175, 180, 181, 182, 183, 184, 185, 188], "green_screen": [26, 47, 48, 49, 50, 51, 54, 57, 58, 59, 60, 63, 64, 65, 66, 67, 68, 71, 72, 74, 76, 77, 78, 84, 85, 86, 87, 88, 89, 90, 91, 95, 96, 97, 98, 99, 100, 101, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 118, 119, 120, 121, 122, 123, 124, 125, 126, 129, 130, 131, 132, 133, 134, 138, 139, 141, 142, 145, 146, 147, 160, 161, 162, 163, 165, 166, 167, 170, 171, 172, 173, 174, 175, 180, 181, 182, 183, 184, 185, 188], "scooter": [26, 47, 48, 49, 50, 51, 54, 57, 58, 59, 60, 63, 64, 65, 66, 67, 68, 71, 72, 74, 76, 77, 78, 84, 85, 86, 87, 88, 89, 90, 91, 95, 96, 97, 98, 99, 100, 101, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 118, 119, 120, 121, 122, 123, 124, 125, 126, 129, 130, 131, 132, 133, 134, 138, 139, 141, 142, 145, 146, 147, 160, 161, 162, 163, 165, 166, 167, 170, 171, 172, 173, 174, 175, 180, 181, 182, 183, 184, 185, 188], "logo": [26, 47, 48, 49, 50, 51, 54, 57, 58, 59, 60, 63, 64, 65, 66, 67, 68, 71, 72, 74, 76, 77, 78, 84, 85, 86, 87, 88, 89, 90, 91, 95, 96, 97, 98, 99, 100, 101, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 118, 119, 120, 121, 122, 123, 124, 125, 126, 129, 130, 131, 132, 133, 134, 138, 139, 141, 142, 145, 146, 147, 160, 161, 162, 163, 165, 166, 167, 170, 171, 172, 173, 174, 175, 180, 181, 182, 183, 184, 185, 188, 192, 254], "cat": [26, 47, 48, 49, 50, 51, 54, 57, 58, 59, 60, 63, 64, 65, 66, 67, 68, 71, 72, 74, 76, 77, 78, 84, 85, 86, 87, 88, 89, 90, 91, 95, 96, 97, 98, 99, 100, 101, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 118, 119, 120, 121, 122, 123, 124, 125, 126, 129, 130, 131, 132, 133, 134, 138, 139, 141, 142, 145, 146, 147, 160, 161, 162, 163, 165, 166, 167, 170, 171, 172, 173, 174, 175, 180, 181, 182, 183, 184, 185, 188], "printfirst": 27, "numberitem": 27, "output": [27, 28, 67, 98, 101, 106, 129, 148, 152, 156, 171, 178, 191, 198, 202, 204, 234, 243, 244, 245, 246, 247, 248, 249, 250, 251, 265, 266, 272, 273, 284], "remov": [27, 31, 35, 43, 44, 65, 79, 81, 88, 139, 148, 162, 166, 190, 215], "improv": [27, 88, 175, 258], "wrote": [27, 171, 269], "previou": [27, 55, 56, 58, 122, 138, 139, 182, 200, 201, 202, 214, 215, 235, 243, 249, 283], "greater": [27, 47, 48, 56, 57, 76, 153, 169, 172, 174, 222, 244, 266], "ok": [27, 85, 86, 149, 150, 152, 153, 154, 156, 159, 185, 202], "invalid": 27, "numitem": [27, 79], "255": [27, 46, 47, 49, 51, 71, 162, 163, 164, 165, 167, 189, 190, 200, 220, 223], "fixnumb": 27, "paramet": [27, 46, 50, 56, 66, 73, 80, 85, 86, 88, 94, 96, 98, 100, 103, 119, 120, 127, 128, 148, 180, 182, 188], "middlethird": 27, "accept": [27, 46, 47, 50, 73, 78, 80, 96, 115, 152, 234], "slice": [27, 31, 33, 34, 129, 134, 135, 142], "return": [27, 28, 35, 40, 42, 43, 46, 47, 48, 50, 51, 53, 56, 59, 61, 63, 66, 73, 74, 80, 81, 82, 94, 96, 98, 99, 100, 101, 102, 103, 108, 113, 115, 116, 124, 127, 131, 134, 135, 138, 143, 144, 147, 148, 150, 156, 157, 189, 235, 258, 271, 278, 280, 283, 284], "evenli": [27, 108], "issu": [27, 56, 64, 67, 103, 155, 180, 203, 207, 209, 210, 215, 219, 256, 260, 261], "player": [28, 31, 260], "provid": [28, 36, 55, 58, 68, 69, 94, 120, 122, 123, 124, 125, 133, 149, 150, 152, 153, 154, 156, 159, 172, 180, 181, 189, 195, 198, 201, 221, 226, 229, 234, 238, 242, 253, 254, 256, 257, 262, 270, 271], "incorpor": [28, 226, 237], "hope": [28, 195], "amusingli": 28, "silli": [28, 129, 150, 188, 193], "placehold": 28, "all_cap": 28, "easier": [28, 32, 37, 42, 55, 58, 59, 66, 67, 72, 81, 82, 86, 88, 92, 97, 98, 121, 123, 147, 148, 156, 165, 171, 175, 183, 184, 185, 191, 195, 203, 214, 215, 221, 253, 254, 260, 262, 263, 264, 265, 267, 269, 281, 283], "string": [28, 36, 38, 40, 43, 56, 73, 74, 77, 78, 82, 101, 107, 124, 129, 133, 138, 139, 142, 147, 148, 152, 153, 156, 157, 170, 172, 174, 189, 193, 213, 221, 222, 263, 275, 280, 282, 288], "chop": [28, 31, 152, 288], "everywher": [28, 231], "break": [28, 41, 66, 84, 86, 92, 98, 115, 121, 147, 156, 157, 221, 227, 268, 283], "isupp": 28, "modifi": [28, 29, 33, 41, 47, 50, 52, 60, 63, 66, 73, 94, 106, 111, 121, 129, 145, 148, 152, 153, 156, 161, 162, 163, 164, 165, 166, 168, 171, 175, 180, 203, 214, 243, 280], "storylist": 28, "readi": [28, 73, 86, 91, 147, 182, 255], "special": [28, 74, 101, 115, 157, 195, 199, 201, 202, 205, 207, 208, 210, 211, 213, 217, 218, 239, 240, 250, 254], "cap": [28, 135], "replac": [28, 30, 41, 48, 87, 101, 131, 153, 174, 180, 228, 236, 260, 267], "stuck": [28, 88, 261], "mix": [28, 37, 46, 55, 56, 58, 60, 72, 73, 78, 80, 112, 115, 116, 117, 118, 122, 123, 136, 137, 138, 141, 142, 144, 146, 156, 170, 178, 181, 182, 184, 190, 220], "automat": [28, 30, 37, 63, 73, 129, 131, 178, 180, 197, 232, 255, 264, 283], "enter": [28, 73, 79, 81, 82, 101, 170, 172, 179, 241, 266], "join": [28, 76, 82, 115, 272, 276, 288], "opposit": [28, 39, 74, 241, 250], "glue": 28, "pleas": [28, 80, 112, 190, 202], "match": [28, 63, 80, 100, 148, 150, 153, 248, 263, 272, 275, 282, 283], "rangechang": 29, "hit": [29, 66, 95, 162, 163, 166, 173, 182, 192, 259], "includ": [29, 31, 32, 33, 42, 43, 61, 64, 69, 73, 74, 80, 82, 84, 92, 102, 105, 107, 110, 116, 118, 122, 127, 130, 134, 135, 143, 157, 167, 169, 176, 178, 180, 182, 186, 189, 191, 194, 195, 208, 222, 227, 232, 234, 237, 240, 253, 255, 269, 273, 274, 276, 279, 282, 285], "visit": [29, 160, 162, 163, 235, 239], "odd": [29, 53, 58, 63, 64, 67, 120, 170, 174], "len": [29, 30, 40, 42, 43, 80, 116, 134, 135, 136, 215], "list_nam": 29, "whole": [29, 31, 64, 67, 72, 76, 78, 87, 101, 108, 113, 118, 163, 169, 175, 195, 234, 264], "rangeloop": 30, "syntax": [30, 32, 33, 96, 117, 119, 120, 122, 129, 137, 139, 160, 183, 270, 275, 281], "revers": [30, 31, 74, 179, 215], "surpris": [30, 133], "codelen": [30, 35, 36, 42, 56, 57, 60, 72, 95, 100, 107, 124, 139, 148, 169, 171, 173, 175, 179, 215], "separ": [30, 37, 45, 63, 64, 107, 120, 123, 131, 134, 148, 152, 154, 166, 188, 205, 221, 241, 245, 261, 272, 278, 279, 283], "habit": 30, "among": [30, 256], "stand": [30, 50, 128, 237, 251, 281], "violat": [30, 139, 269], "meaning": [30, 115, 120], "capit": [30, 107, 115, 132, 134, 135, 136, 138, 139, 141, 142, 146, 193, 213, 278], "access": [30, 32, 33, 40, 64, 113, 125, 160, 162, 163, 192, 193, 198, 201, 203, 235, 237, 254, 256, 261, 267, 272, 276], "arrang": [30, 35, 46, 66, 86, 105, 149, 152, 156, 161, 181, 182, 183, 184, 188, 278], "indent": [30, 35, 36, 38, 46, 53, 55, 57, 58, 60, 63, 65, 72, 85, 86, 95, 99, 100, 119, 120, 128, 149, 152, 156, 160, 161, 169, 170, 172, 178, 180, 181, 182, 184, 185, 186, 188, 190, 273, 283], "block": [30, 35, 36, 38, 46, 57, 58, 60, 61, 63, 66, 72, 73, 82, 84, 85, 86, 87, 88, 95, 99, 105, 112, 118, 122, 130, 133, 137, 138, 139, 140, 141, 142, 146, 149, 152, 156, 161, 169, 170, 178, 181, 182, 183, 184, 188, 227, 228, 229, 240, 251, 253, 256, 273], "correctli": [30, 35, 36, 41, 42, 51, 55, 58, 60, 62, 66, 72, 88, 95, 96, 106, 119, 122, 129, 137, 139, 149, 152, 160, 171, 180, 181, 182, 184, 227, 284], "game": [31, 63, 75, 81, 106, 116, 133, 189, 191, 197, 211, 216, 227, 237], "abil": [31, 54, 228, 229, 240, 258], "deck": 31, "ac": 31, "deal": [31, 72, 200, 227, 253, 254, 268], "leftov": 31, "explor": [31, 118, 153, 154, 220, 225, 234, 238, 240, 265], "whenev": [31, 124, 171], "tackl": [31, 89], "seri": [31, 38, 45, 65, 72, 156, 180, 181, 182, 185, 199, 201, 203, 222, 227, 234, 266], "exercis": [31, 34, 44, 52, 62, 70, 83, 93, 103, 117, 128, 136, 139, 144, 158, 168, 177, 187, 195, 277, 286], "guid": [31, 234], "reassembl": 31, "cutpoint": 31, "valid": [31, 32, 54, 86, 115, 148, 280, 283], "contain": [31, 33, 36, 42, 57, 80, 103, 105, 115, 116, 122, 125, 129, 131, 152, 156, 164, 200, 201, 203, 213, 232, 264, 268, 278], "plu": [31, 58, 59, 108, 213, 258], "review": [31, 57, 153, 221], "verifi": [31, 48, 63, 66, 72, 74, 80, 139, 162, 171, 180, 248], "hopefulli": [31, 76], "bunch": [31, 66, 78, 80, 139, 175], "jumbl": [31, 99, 258], "selectindex": 31, "pop": [31, 36, 43], "link": [31, 82, 95, 154, 207, 234, 258, 265, 266], "append": [31, 32, 36, 43, 82, 135, 136, 193, 280], "repetit": [31, 58, 67, 123, 168, 175, 179, 182, 183, 185, 187, 188], "prove": [31, 239], "optimum": 31, "optim": [31, 239, 241, 254, 260, 281], "tri": [31, 95, 120, 126, 203, 224, 232, 254, 265, 280], "ey": 31, "superior": 31, "iter": [32, 33, 34, 35, 72, 150, 156, 160, 162, 163, 170, 171, 172, 175, 178, 182, 183, 185], "month": [32, 42, 80, 105, 148, 169, 191, 235, 259], "summer": 32, "june": [32, 227], "august": [32, 35], "summermonth": 32, "rather": [32, 51, 179, 195, 224, 253, 265, 275], "ourselv": [32, 78, 184, 185, 188], "python": [32, 37, 44, 53, 56, 57, 62, 64, 65, 70, 77, 79, 80, 83, 95, 96, 103, 108, 113, 115, 116, 120, 121, 122, 124, 127, 131, 133, 134, 135, 139, 143, 156, 166, 174, 177, 183, 185, 186, 189, 190, 191, 192, 195, 215, 264, 280, 281, 283, 288], "handi": [32, 40], "shortcut": 32, "sep": [32, 148], "oct": [32, 148], "nov": [32, 148], "dec": [32, 80, 148], "past": [32, 48, 50, 97, 111, 119, 121, 150, 162, 185, 216, 224, 246, 259], "startindex": 33, "endindex": 33, "leav": [33, 42, 50, 54, 104, 139, 182, 185, 191, 198, 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"synchron": 261, "assembli": [263, 267], "languag": [263, 264, 268, 270], "high": 264, "level": 264, "fortran": 264, "littl": [265, 266, 267], "branch": 266, "varieti": 269, "hello": 269, "aggreg": [271, 274], "uniqu": 271, "group": [273, 277], "filter": [274, 280, 282], "result": 274, "join": [275, 277], "sql": [277, 286], "record": 278, "like": 282, "welcom": 288, "c": 288, "explor": 288}, "envversion": {"sphinx.domains.c": 2, "sphinx.domains.changeset": 1, "sphinx.domains.citation": 1, "sphinx.domains.cpp": 8, "sphinx.domains.index": 1, "sphinx.domains.javascript": 2, "sphinx.domains.math": 2, "sphinx.domains.python": 3, "sphinx.domains.rst": 2, "sphinx.domains.std": 2, "sphinx": 57}, "alltitles": {"Algorithms Introduction": [[0, "algorithms-introduction"]], "Big-O": [[1, "big-o"]], "Estimating With Big-O": [[2, "estimating-with-big-o"]], "Binary Search": [[3, "binary-search"]], "Algorithm Efficiency": [[4, "algorithm-efficiency"]], "Efficiency Testing": [[5, "efficiency-testing"]], "Insertion Sort": [[6, "insertion-sort"]], "Insertion Sort Code": [[7, "insertion-sort-code"]], "Linear Search": [[8, "linear-search"]], "Merging": [[9, "merging"]], "Merge Sort": [[10, "merge-sort"]], "Merge Sort Efficiency": [[11, "merge-sort-efficiency"]], "Wolfram Alpha": [[11, null], [13, null]], "Merge Sort Compared": [[12, "merge-sort-compared"]], "Search Efficiencies": [[13, "search-efficiencies"]], "Worst Case Work": [[13, "id1"]], "Selection Sort": [[14, "selection-sort"]], "Selection Sort Code": [[15, "selection-sort-code"]], "Sorting Efficiency": [[16, "sorting-efficiency"]], "Sorting": [[17, "sorting"], [284, "sorting"]], "Algorithms": [[18, "algorithms"]], "Analog and Digital": [[19, "analog-and-digital"]], "Analog To Digital": [[20, "analog-to-digital"]], "Binary and Its Advantages": [[21, "binary-and-its-advantages"]], "Bit Patterns": [[22, "bit-patterns"]], "Bits": [[23, "bits"], [23, null]], "Bytes": [[24, "bytes"]], "Powers of 2 vs 10": [[24, "powers-of-2-vs-10"]], "Binary and Bits": [[25, "binary-and-bits"]], "Chapter Exercises": [[27, "chapter-exercises"], [35, "chapter-exercises"], [46, "chapter-exercises"], [53, "chapter-exercises"], [63, "chapter-exercises"], [73, "chapter-exercises"], [84, "chapter-exercises"], [94, "chapter-exercises"], [104, "chapter-exercises"], [119, "chapter-exercises"], [137, "chapter-exercises"], [148, "chapter-exercises"], [160, "chapter-exercises"], [169, "chapter-exercises"], [180, "chapter-exercises"], [272, "chapter-exercises"], [279, "chapter-exercises"]], "Making a MadLib Story": [[28, "making-a-madlib-story"]], "Iterating Parts of a List": [[29, "iterating-parts-of-a-list"]], "Iterating with Indexes": [[30, "iterating-with-indexes"]], "Shuffle A List": [[31, "shuffle-a-list"]], "Shuffle By Cuts": [[31, "shuffle-by-cuts"]], "Shuffle By Move To Back": [[31, "shuffle-by-move-to-back"]], "Slicing a List": [[32, "slicing-a-list"]], "Chapter Concept Summary": [[33, "chapter-concept-summary"], [43, "chapter-concept-summary"], [157, "chapter-concept-summary"]], "Changing and Chopping up Lists": [[34, "changing-and-chopping-up-lists"]], "Adding and Removing Items": [[36, "adding-and-removing-items"]], "What is a List?": [[37, "what-is-a-list"]], "List Accumulation": [[38, "list-accumulation"]], "In and Not In": [[39, "in-and-not-in"]], "Working with Indexes": [[40, "working-with-indexes"]], "Finding the Largest or Smallest Value": [[41, "finding-the-largest-or-smallest-value"]], "Rainfall Problem": [[42, "rainfall-problem"]], "Rainfall Step 1": [[42, "rainfall-step-1"]], "Rainfall Step 2": [[42, "rainfall-step-2"]], "Rainfall Step 3": [[42, "rainfall-step-3"]], "Rainfall Finished": [[42, "rainfall-finished"]], "Summary of Python Keywords and Functions": [[43, "summary-of-python-keywords-and-functions"], [61, "summary-of-python-keywords-and-functions"], [69, "summary-of-python-keywords-and-functions"], [82, "summary-of-python-keywords-and-functions"], [157, "summary-of-python-keywords-and-functions"], [176, "summary-of-python-keywords-and-functions"]], "Working with Lists": [[44, "working-with-lists"]], "The Need for Lists": [[45, "the-need-for-lists"]], "A Pixel Selection Function": [[47, "a-pixel-selection-function"]], "Combining Pictures": [[48, "combining-pictures"]], "Using Decisions with Images": [[49, "using-decisions-with-images"], [52, "using-decisions-with-images"]], "Location based Conditions": [[50, "location-based-conditions"]], "Posterizing": [[51, "posterizing"]], "Making Decisions": [[54, "making-decisions"], [62, "making-decisions"]], "Using elif for more options": [[55, "using-elif-for-more-options"]], "Using elif correctly": [[56, "using-elif-correctly"]], "The if Statement": [[57, "the-if-statement"]], "Using if and else": [[58, "using-if-and-else"]], "Functions that make Decisions": [[59, "functions-that-make-decisions"]], "Using Multiple if statements": [[60, "using-multiple-if-statements"]], "Chapter Summary": [[61, "chapter-summary"], [69, "chapter-summary"], [82, "chapter-summary"], [92, "chapter-summary"], [102, "chapter-summary"], [116, "chapter-summary"], [127, "chapter-summary"], [135, "chapter-summary"], [143, "chapter-summary"], [167, "chapter-summary"], [176, "chapter-summary"], [186, "chapter-summary"], [189, "chapter-summary"], [276, "chapter-summary"], [285, "chapter-summary"]], "Random Numbers": [[64, "random-numbers"]], "Random Walks": [[65, "random-walks"]], "Building a Simulation": [[66, "building-a-simulation"]], "Building a Simulation - 2": [[67, "building-a-simulation-2"]], "Simulations": [[68, "simulations"]], "Decisions, Randomness, and Simulations": [[70, "decisions-randomness-and-simulations"]], "Turtles And Randomness": [[71, "turtles-and-randomness"]], "Using Random Numbers": [[72, "using-random-numbers"]], "And, Or, and Not": [[74, "and-or-and-not"]], "And": [[74, "and"]], "Or": [[74, "or"]], "Not": [[74, "not"]], "Making a Chatbot": [[75, "making-a-chatbot"]], "Complex Conditionals": [[76, "complex-conditionals"]], "Complex Conditional Dangers": [[77, "complex-conditional-dangers"]], "When to use And and Or": [[78, "when-to-use-and-and-or"]], "Using Decisions with Strings": [[79, "using-decisions-with-strings"]], "Testing parts of strings and length": [[80, "testing-parts-of-strings-and-length"]], "Comparing Strings": [[81, "comparing-strings"]], "Decisions with Strings and Complex Conditions": [[83, "decisions-with-strings-and-complex-conditions"]], "Procedures that Call Procedures": [[85, "procedures-that-call-procedures"]], "Program Design": [[86, "program-design"]], "Top-Down Design Example": [[86, "top-down-design-example"]], "Program Implementation - Final": [[87, "program-implementation-final"]], "Program Implementation - 1": [[88, "program-implementation-1"]], "Program Implementation - 2": [[89, "program-implementation-2"]], "Program Implementation - 3": [[90, "program-implementation-3"]], "Program Implementation - 4": [[91, "program-implementation-4"]], "Designing with Procedures": [[93, "designing-with-procedures"]], "Common Function Issues": [[95, "common-function-issues"]], "Returning Ends a Function": [[95, "returning-ends-a-function"]], "Trying to Change a Parameter": [[95, "trying-to-change-a-parameter"]], "Defining Functions - How": [[96, "defining-functions-how"]], "Defining Functions - Why": [[97, "defining-functions-why"]], "Functions Calling Functions - 1": [[98, "functions-calling-functions-1"]], "Functions Calling Functions - 2": [[99, "functions-calling-functions-2"]], "Functions Calling Functions - 3": [[100, "functions-calling-functions-3"]], "Functions and Composition": [[101, "functions-and-composition"]], "Function Composition": [[101, "function-composition"]], "Names for Functions": [[103, "names-for-functions"]], "Mixed Up Code Practice": [[105, "mixed-up-code-practice"], [130, "mixed-up-code-practice"], [140, "mixed-up-code-practice"]], "Assigning a Name": [[106, "assigning-a-name"]], "Driving from Chicago to Dallas": [[107, "driving-from-chicago-to-dallas"]], "Expressions": [[108, "expressions"]], "Operations": [[108, "operations"]], "Division and Integer Division": [[108, "division-and-integer-division"]], "Modulo": [[108, "modulo"]], "Summary of Expression Types": [[109, "summary-of-expression-types"]], "Figuring out an Invoice": [[111, "figuring-out-an-invoice"]], "Following the Ketchup Ooze": [[112, "following-the-ketchup-ooze"]], "Math Library Functions": [[113, "math-library-functions"]], "Math functions": [[113, "id1"]], "How Expressions are Evaluated": [[114, "how-expressions-are-evaluated"]], "Rules for Names": [[115, "rules-for-names"]], "Naming Syntax": [[115, "naming-syntax"]], "Naming Convention": [[115, "naming-convention"]], "Names for Numbers": [[117, "names-for-numbers"]], "Walking through Assignment more Generally": [[118, "walking-through-assignment-more-generally"]], "Defining Procedures - How": [[120, "defining-procedures-how"]], "Defining Procedures - Why": [[121, "defining-procedures-why"]], "Order and Indentation": [[122, "order-and-indentation"]], "Indentation": [[122, "indentation"]], "Indentation Rules": [[122, "indentation-rules"]], "Multiple Parameters": [[123, "multiple-parameters"]], "Stand Alone Procedures and Functions": [[124, "stand-alone-procedures-and-functions"]], "Parameters": [[125, "parameters"]], "Practice - Write a Procedure": [[126, "practice-write-a-procedure"]], "Names for Procedures": [[128, "names-for-procedures"]], "Chapter 3 Exercises": [[129, "chapter-3-exercises"]], "Assign a Name to a String": [[131, "assign-a-name-to-a-string"]], "Concatenating (Appending) Strings": [[131, "concatenating-appending-strings"]], "Inputting Strings": [[131, "inputting-strings"]], "Concatenating Strings and Numbers": [[131, "concatenating-strings-and-numbers"]], "Strings are Immutable": [[132, "strings-are-immutable"]], "Making a MadLib story": [[133, "making-a-madlib-story"]], "Strings are Objects": [[134, "strings-are-objects"]], "Getting Part of a String": [[134, "getting-part-of-a-string"]], "Some Other String Functions": [[134, "some-other-string-functions"]], "Summary of String Functions": [[135, "summary-of-string-functions"]], "Names for Strings": [[136, "names-for-strings"]], "Procedures and Functions": [[138, "procedures-and-functions"]], "Errors in Programs": [[139, "errors-in-programs"]], "Debugging Programs": [[139, "debugging-programs"]], "Single and Multiple Turtles": [[141, "single-and-multiple-turtles"]], "Turtles as Objects": [[142, "turtles-as-objects"]], "What does a left turn of 90 mean?": [[142, "what-does-a-left-turn-of-90-mean"]], "Names for Turtles": [[144, "names-for-turtles"]], "Turtle Art": [[145, "turtle-art"]], "Turtle Coordinates": [[146, "turtle-coordinates"]], "Turtle Procedures": [[147, "turtle-procedures"]], "Turtle procedures": [[147, "id1"]], "What\u2019s the average pollution?": [[149, "what-s-the-average-pollution"]], "Comparing States": [[150, "comparing-states"]], "Most Populated and Least Populated States": [[151, "most-populated-and-least-populated-states"]], "Finding the Pollution for a State": [[152, "finding-the-pollution-for-a-state"]], "What\u2019s the largest pollution values?": [[153, "what-s-the-largest-pollution-values"]], "Our first data set: Air pollution in the United States": [[154, "our-first-data-set-air-pollution-in-the-united-states"]], "Data and Python": [[155, "data-and-python"]], "Reading the data": [[156, "reading-the-data"]], "Working with Data in Python": [[158, "working-with-data-in-python"]], "Increasing and decreasing brightness": [[161, "increasing-and-decreasing-brightness"]], "Thinking About Pixel Locations": [[162, "thinking-about-pixel-locations"]], "Changing which data we use": [[163, "changing-which-data-we-use"]], "Understanding Image Representation": [[164, "understanding-image-representation"]], "A Pattern for Image Processing": [[165, "a-pattern-for-image-processing"]], "Using Repetition with Images": [[166, "using-repetition-with-images"]], "A Library of Images": [[166, "a-library-of-images"]], "Repeating Steps with Images": [[168, "repeating-steps-with-images"]], "The Accumulator Pattern": [[170, "the-accumulator-pattern"]], "Debugging Loops": [[171, "debugging-loops"]], "Introducing the While Loop": [[172, "introducing-the-while-loop"]], "Infinite Loops": [[173, "infinite-loops"]], "Booleans and Logical Expressions": [[174, "booleans-and-logical-expressions"]], "Repeating Calculations": [[175, "repeating-calculations"]], "Repeating Steps with Numbers": [[177, "repeating-steps-with-numbers"]], "Counting with a While Loop": [[178, "counting-with-a-while-loop"]], "Loop Control Variable": [[178, "loop-control-variable"]], "While Loops - While vs Until": [[179, "while-loops-while-vs-until"]], "More Turtle Repetition Practice": [[181, "more-turtle-repetition-practice"]], "Using the Loop Variable": [[182, "using-the-loop-variable"]], "Range Recipes": [[182, "range-recipes"]], "Range Recipes With Turtles": [[182, "range-recipes-with-turtles"]], "Nesting Loops": [[183, "nesting-loops"]], "Execution Limit & Run Amok Programs": [[183, "execution-limit-run-amok-programs"]], "Indirect Nesting": [[183, "indirect-nesting"]], "Using Repetition with Turtles": [[184, "using-repetition-with-turtles"]], "Repeating Steps & Range": [[185, "repeating-steps-range"]], "Range": [[185, "range"]], "Repeating Steps with Turtles": [[187, "repeating-steps-with-turtles"]], "A Regular Polygon Recipe": [[188, "a-regular-polygon-recipe"]], "Compute with Images": [[190, "compute-with-images"]], "Compute with Numbers": [[191, "compute-with-numbers"]], "Compute with Turtles": [[192, "compute-with-turtles"]], "Compute with Words": [[193, "compute-with-words"]], "About This Section of the Book": [[195, "about-this-section-of-the-book"]], "License": [[195, "license"]], "An introduction to programming": [[196, "an-introduction-to-programming"]], "What\u2019s Next?": [[197, "what-s-next"]], "Full Python On The Web": [[197, "full-python-on-the-web"]], "Python On Your Computer": [[197, "python-on-your-computer"]], "More Python": [[197, "more-python"]], "Applications": [[197, "applications"]], "Computer Components": [[198, "computer-components"]], "The Machine Cycle": [[199, "the-machine-cycle"]], "Main Memory": [[200, "main-memory"]], "Memory Hierarchy": [[201, "memory-hierarchy"]], "The Processor": [[202, "the-processor"]], "The Processor, cont.": [[203, "the-processor-cont"]], "Computer Architecture & The Machine Cycle": [[204, "computer-architecture-the-machine-cycle"]], "Computer Engineering": [[205, "computer-engineering"]], "Computer Science": [[206, "computer-science"]], "Cybersecurity": [[207, "cybersecurity"]], "Data Science": [[208, "data-science"]], "Information Systems": [[209, "information-systems"]], "Information Technology": [[210, "information-technology"]], "Software Engineering": [[211, "software-engineering"]], "Computing Related Fields": [[212, "computing-related-fields"]], "Representing Letters with ASCII": [[213, "representing-letters-with-ascii"]], "ASCII Art": [[213, null]], "Binary Conversions - Table Method": [[214, "binary-conversions-table-method"]], "Binary to Decimal": [[214, "binary-to-decimal"], [215, "binary-to-decimal"]], "Decimal to Binary": [[214, "decimal-to-binary"], [215, "decimal-to-binary"]], "Binary Conversions - Multiplication/Division Method": [[215, "binary-conversions-multiplication-division-method"]], "Binary Addition": [[216, "binary-addition"]], "Real-world overflow": [[216, null]], "Other Operations": [[217, "other-operations"]], "Floating Point Numbers": [[218, "floating-point-numbers"]], "IEEE 754": [[218, null]], "Fractional Values": [[219, "fractional-values"]], "Hex Data & Colors": [[220, "hex-data-colors"]], "Hexadecimal": [[221, "hexadecimal"]], "Representing Images": [[222, "representing-images"]], "Number Systems & Binary": [[223, "number-systems-binary"]], "Negative Values - Two\u2019s Complement": [[224, "negative-values-two-s-complement"]], "Two\u2019s Complement Interpretation": [[224, null]], "Two\u2019s Complement Conversion": [[224, null]], "Data Representation": [[225, "data-representation"]], "Dawn of Computers": [[226, "dawn-of-computers"]], "Ada Lovelace": [[226, null]], "The First Generation": [[227, "the-first-generation"]], "Vacuum tube": [[227, null]], "The Second Generation": [[228, "the-second-generation"]], "The Third Generation": [[229, "the-third-generation"]], "Integrated Circuit": [[229, null]], "The Fourth Generation": [[230, "the-fourth-generation"]], "Microprocessors": [[230, null]], "Modern Computers": [[231, "modern-computers"]], "Prehistory": [[232, "prehistory"]], "The Antikythera Mechanism": [[232, null]], "History of computers": [[233, "history-of-computers"]], "Analyzing Impacts": [[234, "analyzing-impacts"]], "Choosing a Technology": [[234, "choosing-a-technology"]], "Describing the Technology": [[234, "describing-the-technology"]], "Describing the Impacts": [[234, "describing-the-impacts"]], "Blown To Bits": [[235, "blown-to-bits"]], "Good and Ill, Promise and Peril": [[235, "good-and-ill-promise-and-peril"]], "Technology Is Neither Good nor Bad": [[235, "technology-is-neither-good-nor-bad"]], "New Technologies Bring Both Risks and Opportunities": [[235, "new-technologies-bring-both-risks-and-opportunities"]], "Example: Smart Locks": [[236, "example-smart-locks"]], "Example: Street Maps": [[237, "example-street-maps"]], "Impacts of Computing": [[238, "impacts-of-computing"]], "Computability": [[239, "computability"]], "P = NP?": [[239, null]], "End of Moore\u2019s Law?": [[240, "end-of-moore-s-law"]], "How Big?": [[240, null]], "Quantum Computing": [[241, "quantum-computing"]], "Limits and Future of Computing": [[242, "limits-and-future-of-computing"]], "Adding Numbers with Logic": [[243, "adding-numbers-with-logic"]], 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