Introduction 1 About This Book 1 Foolish Assumptions 3 Icons Used in This Book 3 Beyond the Book 4 Where to Go from Here 5 Part 1: Getting Started with Algorithms 7 Chapter 1: Introducing Algorithms 9 Describing Algorithms 10 The right way to make toast: Defining algorithm uses 12 Finding algorithms everywhere 14 Using Computers to Solve Problems 15 Getting the most out of modern CPUs and GPUs 16 Working with special-purpose chips 17 Networks: Sharing is more than caring 18 Leveraging available data 18 Distinguishing between Issues and Solutions 19 Being correct and efficient 19 Discovering there is no free lunch 20 Adapting the strategy to the problem 20 Describing algorithms in a lingua franca 20 Facing problems that are like brick walls, only harder 21 Structuring Data to Obtain a Solution 21 Understanding a computer''s point of view 22 Arranging data makes the difference 22 Chapter 2: Considering Algorithm Design 23 Starting to Solve a Problem 24 Modeling real-world problems 25 Finding solutions and counterexamples 26 Standing on the shoulders of giants 27 Dividing and Conquering 28 Avoiding brute-force solutions 29 Keeping it simple, silly (KISS) 29 Breaking down a problem is usually better 30 Learning that Greed Can Be Good 30 Applying greedy reasoning 31 Reaching a good solution 31 Computing Costs and Following Heuristics 32 Representing the problem as a space 33 Going random and being blessed by luck 34 Using a heuristic and a cost function 34 Evaluating Algorithms 35 Simulating using abstract machines 36 Getting even more abstract 37 Working with functions 38 Chapter 3: Working with Google Colab 41 Defining Google Colab 42 Understanding what Google Colab does 42 Getting familiar with Google Colab features 44 Working with Notebooks 47 Creating a new notebook 47 Opening existing notebooks 47 Saving notebooks 50 Performing Common Tasks 51 Creating code cells 52 Creating text cells 54 Creating special cells 54 Editing cells 55 Moving cells 55 Using Hardware Acceleration 55 Executing the Code 56 Getting Help 57 Chapter 4: Performing Essential Data Manipulations Using Python 59 Performing Calculations Using Vectors and Matrixes 60 Understanding scalar and vector operations 61 Performing vector multiplication 63 Creating a matrix is the right way to start 63 Multiplying matrixes 64 Defining advanced matrix operations 65 Creating Combinations the Right Way 67 Distinguishing permutations 68 Shuffling combinations 69 Facing repetitions 70 Getting the Desired Results Using Recursion 71 Explaining recursion 71 Eliminating tail call recursion 74 Performing Tasks More Quickly 75 Considering divide and conquer 75 Distinguishing between different possible solutions 78 Chapter 5: Developing a Matrix Computation Class 79 Avoiding the Use of NumPy 80 Understanding Why Using a Class is Important 81 Building the Basic Class 82 Creating a matrix 83 Printing the resulting matrix 84 Accessing specific matrix elements 85 Performing scalar and matrix addition 86 Performing multiplication 87 Manipulating the Matrix 90 Transposing a matrix 91 Calculating the determinant 91 Flattening the matrix 95 Part 2: Understanding the Need to Sort and Search 97 Chapter 6: Structuring Data 99 Determining the Need for Structure 100 Making it easier to see the content 100 Matching data from various sources 101 Considering the need for remediation 102 Stacking and Piling Data in Order 105 Ordering in stacks 105 Using queues 107 Finding data using dictionaries 108 Working with Trees 109 Understanding the basics of trees 109 Building a tree 110 Representing Relations in a Graph 112 Going beyond trees 113 Building graphs 114 Chapter 7: Arranging and Searching Data 117 Sorting Data Using Merge Sort and Quick Sort 118 Understanding why sorting data is important 118 Employing better sort techniques 122 Using Search Trees and the Heap 127 Considering the need to search effectively 127 Building a binary search tree 129 Performing specialized searches using a binary heap 131 Relying on Hashing 132 Putting everything into buckets 132 Avoiding collisions 134 Creating your own hash function 135 Part 3: Exploring the World of Graphs 139 Chapter 8: Understanding Graph Basics 141 Explaining the Importance of Networks 142 Considering the essence of a graph 142 Finding graphs everywhere 145 Showing the social side of graphs 146 Understanding subgraphs 147 Defining How to Draw a Graph 148 Distinguishing the key attributes 149 Drawing the graph 150 Measuring Graph Functionality 151 Counting edges and vertexes 152 Computing centrality 154 Putting a Graph in Numeric Format 157 Adding a graph to a matrix 157 Using sparse representations 158 Using a list to hold a graph 159 Chapter 9: Reconnecting the Dots 161 Traversing a Graph Efficiently 162 Creating the graph 163 Applying breadth-first search 164 Applying depth-first search 165 Determining which application to use 167 Sorting the Graph Elements 168 Working on Directed Acyclic Graphs (DAGs) 169 Relying on topological sorting 169 Reducing to a Minimum Spanning Tree 170 Getting the minimum spanning tree historical context 170 Working with unweighted versus weighted graphs 171 Creating a minimum spanning tree example 171 Discovering the correct algorithms to use 173 Introducing priority queues 174 Leveraging Prim''s algorithm 175 Testing Kruskal''s algorithm 177 Determining which algorithm works best 179 Finding the Shortest Route 180 Defining what it means to find the shortest path 180 Adding a negative edge 182 Explaining Dijkstra''s algorithm 184 Explaining the Bellman-Ford algorithm 187 Explaining the Floyd-Warshall algorithm 190 Chapter 10: Discovering Graph Secrets 195 Envisioning Social Networks as Graphs 196 Clustering networks in groups 196 Discovering communities 199 Navigating a Graph 202 Counting the degrees of separation 202 Walking a graph randomly 204 Chapter 11: Getting the Right Web page 207 Finding the World in a Search Engine 208 Searching the Internet for data 208 Considering how to find the right data 209 Explaining the PageRank Algorithm 210 Understanding the reasoning behind the PageRank algorithm 210 Explaining the nuts and bolts of PageRank 212 Implementing PageRank 212 Implementing a Python script 213 Struggling with a naive implementation 216 Introducing boredom and teleporting 219 Looking inside the life of a search engine 220 Considering other uses of PageRank 221 Going Beyond the PageRank Paradigm 221 Introducing semantic queries 222 Using AI for ranking search results 222 Part 4: Wrangling Big Data 223 Chapter 12: Managing Big Data 225 Transforming Power into Data 226 Understanding Moore''s implications 226 Finding data everywhere 228 Getting algorithms into business 231 Streaming Flows of Data 233 Analyzing streams with the right recipe 234 Reserving the right data 235 Sketching an Answer from Stream Data 240 Filtering stream elements by heart 240 Demonstrating the Bloom filter 243 Finding the number of distinct elements 246 Learning to count objects in a stream 247 Chapter 13: Parallelizing Operations 249 Managing Immense Amounts of Data 250 Understanding the parallel paradigm 251 Distributing files and operations 253 Employing the MapReduce solution 255 Working Out Algorithms for MapReduce 259 Setting up a MapReduce simulation 260 Inquiring by mapping 262 Chapter 14: Compressing and Concealing Data 267 Making Data Smaller 268 Understanding encoding 268 Considering the effects of compression 270 Choosing a particular kind of compression 271 Choosing your encoding wisely 273 Encoding using Huffman compression 276 Remembering sequences with LZW 278 Hiding Your Secrets with Cryptography 282 Substituting characters 283 Working with AES encryption 285 Part 5: Challenging Difficult Problems 289 Chapter 15: Working with Greedy Algorithms 291 Deciding When It Is Better to Be Greedy 292 Understanding why greedy is good 293 Keeping greedy algorithms under control 294 Considering NP complete problems 297 Finding Out How Greedy Can Be Useful 299 Arranging cached computer data 299 Competing for resources 301 Revisiting Huffman coding 303 Chapt.