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 7. Graphs: Only Connect!

In this chapter, you will learn:

The stack abstract data type.
The indexed min priority queue data type, which is the final data type included in this book.
How to model a graph using nodes and edges. In a directed graph, the edges have an orientation. In a weighted graph, edges have an associated numeric value.
How Depth First Search uses a stack to organize searching in a graph.
How Breadth First Search uses a queue to search through a graph. If a path exists between a source node and a target node, Breadth First Search will return the shortest path that exists.
How to detect whether a directed graph contains a cycle: a sequence of edges starting from, and ending with, a specific node.
How to use Topological Sort in a directed graph to produce a linear ordering of nodes compatible with all dependencies in the directed graph.
How to determine the shortest accumulated path in a weighted graph from one node to all other nodes.
How to determine the shortest accumulated path in a weighted graph between any two nodes.

Graphs Efficiently Store Useful Information

I’ve covered algorithms for solving common problems in information systems regarding storing and processing data. These algorithms can solve countless real-world problems if only we could properly model these problems. Here are three such problems that I will solve by using graphs: