CS61B Textbook
  • Contributors
  • DISCLAIMER
  • 1. Introduction
    • 1.1 Your First Java Program
    • 1.2 Java Workflow
    • 1.3 Basic Java Features
    • 1.4 Exercises
  • 2. Defining and Using Classes
  • 3. References, Recursion, and Lists
  • 4. SLLists
  • 5. DLLists
  • 6. Arrays
  • 7. Testing
  • 8. ArrayList
  • 9. Inheritance I: Interface and Implementation Inheritance
  • 10. Inheritance II: Extends, Casting, Higher Order Functions
    • 10.1 Implementation Inheritance: Extends
    • 10.2 Encapsulation
    • 10.3 Casting
    • 10.4 Higher Order Functions in Java
    • 10.5 Exercises
  • 11. Inheritance III: Subtype Polymorphism, Comparators, Comparable
    • 11.1 A Review of Dynamic Method Selection
    • 11.2 Subtype Polymorphism vs Explicit Higher Order Functions
    • 11.3 Comparables
    • 11.4 Comparators
    • 11.5 Chapter Summary
    • 11.6 Exercises
  • 12. Inheritance IV: Iterators, Object Methods
    • 12.1 Lists and Sets in Java
    • 12.2 Exceptions
    • 12.3 Iteration
    • 12.4 Object Methods
    • 12.5 Chapter Summary
    • 12.6 Exercises
  • 13. Asymptotics I
    • 13.1 An Introduction to Asymptotic Analysis
    • 13.2 Runtime Characterization
    • 13.3 Checkpoint: An Exercise
    • 13.4 Asymptotic Behavior
    • 13.6 Simplified Analysis Process
    • 13.7 Big-Theta
    • 13.8 Big-O
    • 13.9 Summary
    • 13.10 Exercises
  • 14. Disjoint Sets
    • 14.1 Introduction
    • 14.2 Quick Find
    • 14.3 Quick Union
    • 14.4 Weighted Quick Union (WQU)
    • 14.5 Weighted Quick Union with Path Compression
    • 14.6 Exercises
  • 15. Asymptotics II
    • 15.1 For Loops
    • 15.2 Recursion
    • 15.3 Binary Search
    • 15.4 Mergesort
    • 15.5 Summary
    • 15.6 Exercises
  • 16. ADTs and BSTs
    • 16.1 Abstract Data Types
    • 16.2 Binary Search Trees
    • 16.3 BST Definitions
    • 16.4 BST Operations
    • 16.5 BSTs as Sets and Maps
    • 16.6 Summary
    • 16.7 Exercises
  • 17. B-Trees
    • 17.1 BST Performance
    • 17.2 Big O vs. Worst Case
    • 17.3 B-Tree Operations
    • 17.4 B-Tree Invariants
    • 17.5 B-Tree Performance
    • 17.6 Summary
    • 17.7 Exercises
  • 18. Red Black Trees
    • 18.1 Rotating Trees
    • 18.2 Creating LLRB Trees
    • 18.3 Inserting LLRB Trees
    • 18.4 Runtime Analysis
    • 18.5 Summary
    • 18.6 Exercises
  • 19. Hashing I
    • 19.1 Introduction to Hashing: Data Indexed Arrays
      • 19.1.1 A first attempt: DataIndexedIntegerSet
      • 19.1.2 A second attempt: DataIndexedWordSet
      • 19.1.3 A third attempt: DataIndexedStringSet
    • 19.2 Hash Code
    • 19.3 "Valid" & "Good" Hashcodes
    • 19.4 Handling Collisions: Linear Probing and External Chaining
    • 19.5 Resizing & Hash Table Performance
    • 19.6 Summary
    • 19.7 Exercises
  • 20. Hashing II
    • 20.1 Hash Table Recap, Default Hash Function
    • 20.2 Distribution By Other Hash Functions
    • 20.3 Contains & Duplicate Items
    • 20.4 Mutable vs. Immutable Types
  • 21. Heaps and Priority Queues
    • 21.1 Priority Queues
    • 21.2 Heaps
    • 21.3 PQ Implementation
    • 21.4 Summary
    • 21.5 Exercises
  • 22. Tree Traversals and Graphs
    • 22.1 Tree Recap
    • 22.2 Tree Traversals
    • 22.3 Graphs
    • 22.4 Graph Problems
  • 23. Graph Traversals and Implementations
    • 23.1 BFS & DFS
    • 23.2 Representing Graphs
    • 23.3 Summary
    • 23.4 Exercises
  • 24. Shortest Paths
    • 24.1 Introduction
    • 24.2 Dijkstra's Algorithm
    • 24.3 A* Algorithm
    • 24.4 Summary
    • 24.5 Exercises
  • 25. Minimum Spanning Trees
    • 25.1 MSTs and Cut Property
    • 25.2 Prim's Algorithm
    • 25.3 Kruskal's Algorithm
    • 25.4 Chapter Summary
    • 25.5 MST Exercises
  • 26. Prefix Operations and Tries
    • 26.1 Introduction to Tries
    • 26.2 Trie Implementation
    • 26.3 Trie String Operations
    • 26.4 Summary
    • 26.5 Exercises
  • 27. Software Engineering I
    • 27.1 Introduction to Software Engineering
    • 27.2 Complexity
    • 27.3 Strategic vs Tactical Programming
    • 27.4 Real World Examples
    • 27.5 Summary, Exercises
  • 28. Reductions and Decomposition
    • 28.1 Topological Sorts and DAGs
    • 28.2 Shortest Paths on DAGs
    • 28.3 Longest Path
    • 28.4 Reductions and Decomposition
    • 28.5 Exercises
  • 29. Basic Sorts
    • 29.1 The Sorting Problem
    • 29.2 Selection Sort & Heapsort
    • 29.3 Mergesort
    • 29.4 Insertion Sort
    • 29.5 Summary
    • 29.6 Exercises
  • 30. Quicksort
    • 30.1 Partitioning
    • 30.2 Quicksort Algorithm
    • 30.3 Quicksort Performance Caveats
    • 30.4 Summary
    • 30.5 Exercises
  • 31. Software Engineering II
    • 31.1 Complexity II
    • 31.2 Sources of Complexity
    • 31.3 Modular Design
    • 31.4 Teamwork
    • 31.5 Exerises
  • 32. More Quick Sort, Sorting Summary
    • 32.1 Quicksort Flavors vs. MergeSort
    • 32.2 Quick Select
    • 32.3 Stability, Adaptiveness, and Optimization
    • 32.4 Summary
    • 32.5 Exercises
  • 33. Software Engineering III
    • 33.1 Candy Crush, SnapChat, and Friends
    • 33.2 The Ledger of Harms
    • 33.3 Your Life
    • 33.4 Summary
    • 33.5 Exercises
  • 34. Sorting and Algorithmic Bounds
    • 34.1 Sorting Summary
    • 34.2 Math Problems Out of Nowhere
    • 34.3 Theoretical Bounds on Sorting
    • 34.4 Summary
    • 34.5 Exercises
  • 35. Radix Sorts
    • 35.1 Counting Sort
    • 35.2 LSD Radix Sort
    • 35.3 MSD Radix Sort
    • 35.4 Summary
    • 35.5 Exercises
  • 36. Sorting and Data Structures Conclusion
    • 36.1 Radix vs. Comparison Sorting
    • 36.2 The Just-In-Time Compiler
    • 36.3 Radix Sorting Integers
    • 36.4 Summary
    • 36.5 Exercises
  • 37. Software Engineering IV
    • 37.1 The end is near
  • 38. Compression and Complexity
    • 38.1 Introduction to Compression
    • 38.2 Prefix-free Codes
    • 38.3 Shannon-Fano Codes
    • 38.4 Huffman Coding Conceptuals
    • 38.5 Compression Theory
    • 38.6 LZW Compression
    • 38.7 Summary
    • 38.8 Exercises
  • 39. Compression, Complexity, P = NP
    • 39.1 Models of Compression
    • 39.2 Optimal Compression, Kolmogorov Complexity
    • 39.3 Space/Time-Bounded Compression
    • 39.4 P = NP
    • 39.5 Exercises
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  • Metacognitive
  1. 34. Sorting and Algorithmic Bounds

34.5 Exercises

Factual

  1. Which of the following function(s) have the slowest order of growth in terms of Big Theta?

  2. To solve puppy, cat, dog for 12 items, what is the theoretical minimum number of comparisons we have to make, based on the argument used in lecture? Please round your answer up to the nearest whole number.

  3. Which of the following statements are true?

Problem 1

In lecture, we proved that log⁡N!∈Θ(Nlog⁡N)\log N! \in \Theta(N \log N)logN!∈Θ(NlogN). Thus, both Nlog⁡NN \log NNlogN and log⁡N!\log N!logN! have the same order of growth, and are slower than N2N^2N2 or N!log⁡N!N! \log N!N!logN!.

Problem 2

ceil(log⁡212!)=29ceil(\log_2 12!) = 29ceil(log2​12!)=29, based on the equation we saw in lecture.

Problem 3

Metacognitive

  1. Suppose we add a new method to Arrays.sort that takes in an array of strings. What algorithm should Arrays.sort(String[] x) use?

Problem 1

Quicksort. We don't need stability, since strings are only equal by .equals if they are exactly the same. Quicksort, then, is the best algorithm since it is empirically the fastest.

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Last updated 2 years ago