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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  1. 19. Hashing I

19.6 Summary

In this chapter, we learned about hashing, a powerful technique for turning a more complex object like a String into a numerically representable value like an int.

The hash table is a data structure that combines the hash function with the fact that arrays can be indexed in constant time. Using the hash table and the map abstract data type, we can build a HashMap which allows for amortized constant time access to any key-value pair so long as we know which bucket the key falls into.

However, we quickly demonstrated that this naive implementation has several drawbacks: the ability to represent all different kinds of objects, memory efficiency, and collisions.

We investigated the importance of the hashCode() function to gain an understanding of how it affects the runtime of the hash table. To allow for smaller size() in the array, we used the modulo operator to shrink hash values down to a specified range of numbers. We then added external chaining to solve collisions by allowing multiple entries to live in a single bucket in the form of a LinkedList, and explored resizing functionality based on the load factor!

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Last updated 9 months ago