book

Learning Algorithms

by George Heineman

August 2021

Intermediate to advanced

280 pages

7h 10m

English

O'Reilly Media, Inc.

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Includes

Includes Quizzes

Who This Book Is ForAbout the CodeConventions Used in This BookO’Reilly Online LearningHow to Contact UsAcknowledgments
What Is an Algorithm?Finding the Largest Value in an Arbitrary ListCounting Key OperationsModels Can Predict Algorithm PerformanceFind Two Largest Values in an Arbitrary ListTournament AlgorithmTime Complexity and Space ComplexitySummaryChallenge Exercises
Using Empirical Models to Predict PerformanceMultiplication Can Be FasterPerformance ClassesAsymptotic AnalysisCounting All OperationsCounting All BytesWhen One Door Closes, Another One OpensBinary Array SearchAlmost as Easy as πTwo Birds with One StonePulling It All TogetherCurve Fitting Versus Lower and Upper BoundsSummaryChallenge Exercises
Associating Values with KeysHash Functions and Hash CodesA Hashtable Structure for (Key, Value) PairsDetecting and Resolving Collisions with Linear ProbingSeparate Chaining with Linked ListsRemoving an Entry from a Linked ListEvaluationGrowing HashtablesAnalyzing the Performance of Dynamic HashtablesPerfect HashingIterate Over (key, value) PairsSummaryChallenge Exercises
Max Binary HeapsInserting a (value, priority)Removing the Value with Highest PriorityRepresenting a Binary Heap in an ArrayImplementation of Swim and SinkSummaryChallenge Exercises
Sorting by SwappingSelection SortAnatomy of a Quadratic Sorting AlgorithmAnalyze Performance of Insertion Sort and Selection SortRecursion and Divide and ConquerMerge SortQuicksortHeap SortPerformance Comparison of O(N log N) AlgorithmsTim SortSummaryChallenge Exercises
Getting StartedBinary Search TreesSearching for Values in a Binary Search TreeRemoving Values from a Binary Search TreeTraversing a Binary TreeAnalyzing Performance of Binary Search TreesSelf-Balancing Binary TreesAnalyzing Performance of Self-Balancing TreesUsing Binary Tree as (key, value) Symbol TableUsing the Binary Tree as a Priority QueueSummaryChallenge Exercises
Graphs Efficiently Store Useful InformationUsing Depth First Search to Solve a MazeBreadth First Search Offers Different Searching StrategyDirected GraphsGraphs with Edge WeightsDijkstra’s AlgorithmAll-Pairs Shortest PathFloyd–Warshall AlgorithmSummaryChallenge Exercises
Python Built-in Data TypesImplementing Stack in PythonImplementing Queues in PythonHeap and Priority Queue ImplementationsFuture Exploration

Content preview from Learning Algorithms

Chapter 6. Binary Trees: Infinity in the Palm of Your Hand

In this chapter, you will learn:

How to create and manipulate binary trees by inserting, removing, and searching for values.
How to manage a binary search tree that enforces the global property that:
- Values in the left subtree of a node are all smaller than or equal to that node’s value.
- Values in the right subtree of a node are all larger than or equal to that node’s value.
That search, insert, and remove operations can be O(log N) in balanced binary trees but can degrade to become an unacceptable O(N) if you aren’t careful.
How to rebalance a binary search tree after insert and remove operations to guarantee O(log N) performance for search, insert, and remove.
How to traverse a binary search tree to process each value in ascending order in O(N) performance.
How to use a binary tree structure to implement a symbol table data type with the added benefit that its keys can be retrieved in sorted order.
How to use a binary tree structure to implement a priority queue with the added benefit that you can generate the (key, value) entries in priority order without disrupting the priority queue.

Getting Started

Linked lists and arrays store information in a linear arrangement. In this chapter, I introduce the binary tree recursive data structure, one of the most important concepts in the field of computer science. In Chapter 5, you learned about the concept of recursion, where a function calls itself. ...