Learning Algorithms

2.54 MB·English

by  George Heineman

Foreword Page: 4
Preface Page: 5
Who This Book Is For Page: 5
About the Code Page: 5
Conventions Used in This Book Page: 6
O’Reilly Online Learning Page: 6
How to Contact Us Page: 6
Acknowledgments Page: 6
1. Problem Solving Page: 7
What Is an Algorithm? Page: 7
Finding the Largest Value in an Arbitrary List Page: 8
Counting Key Operations Page: 8
Models Can Predict Algorithm Performance Page: 8
Find Two Largest Values in an Arbitrary List Page: 10
Tournament Algorithm Page: 11
Time Complexity and Space Complexity Page: 13
Summary Page: 14
Challenge Exercises Page: 14
2. Analyzing Algorithms Page: 15
Using Empirical Models to Predict Performance Page: 15
Multiplication Can Be Faster Page: 16
Performance Classes Page: 16
Asymptotic Analysis Page: 17
Counting All Operations Page: 18
Counting All Bytes Page: 18
When One Door Closes, Another One Opens Page: 19
Binary Array Search Page: 19
Almost as Easy as π Page: 19
Two Birds with One Stone Page: 20
Pulling It All Together Page: 21
Curve Fitting Versus Lower and Upper Bounds Page: 22
Summary Page: 22
Challenge Exercises Page: 23
3. Better Living Through Better Hashing Page: 24
Associating Values with Keys Page: 24
Hash Functions and Hash Codes Page: 25
A Hashtable Structure for (Key, Value) Pairs Page: 26
Detecting and Resolving Collisions with Linear Probing Page: 26
Separate Chaining with Linked Lists Page: 28
Removing an Entry from a Linked List Page: 29
Evaluation Page: 30
Growing Hashtables Page: 31
Analyzing the Performance of Dynamic Hashtables Page: 32
Perfect Hashing Page: 33
Iterate Over (key, value) Pairs Page: 34
Summary Page: 34
Challenge Exercises Page: 35
4. Heaping It On Page: 37
Max Binary Heaps Page: 38
Inserting a (value, priority) Page: 39
Removing the Value with Highest Priority Page: 40
Representing a Binary Heap in an Array Page: 41
Implementation of Swim and Sink Page: 41
Summary Page: 42
Challenge Exercises Page: 42
5. Sorting Without a Hat Page: 44
Sorting by Swapping Page: 44
Selection Sort Page: 44
Anatomy of a Quadratic Sorting Algorithm Page: 45
Analyze Performance of Insertion Sort and Selection Sort Page: 45
Recursion and Divide and Conquer Page: 46
Merge Sort Page: 47
Quicksort Page: 48
Heap Sort Page: 49
Performance Comparison of O(N log N) Algorithms Page: 49
Tim Sort Page: 50
Summary Page: 51
Challenge Exercises Page: 51
6. Binary Trees: Infinity in the Palm of Your Hand Page: 52
Getting Started Page: 52
Binary Search Trees Page: 53
Searching for Values in a Binary Search Tree Page: 55
Removing Values from a Binary Search Tree Page: 55
Traversing a Binary Tree Page: 57
Analyzing Performance of Binary Search Trees Page: 57
Self-Balancing Binary Trees Page: 58
Analyzing Performance of Self-Balancing Trees Page: 60
Using Binary Tree as (key, value) Symbol Table Page: 60
Using the Binary Tree as a Priority Queue Page: 61
Summary Page: 62
Challenge Exercises Page: 62
7. Graphs: Only Connect! Page: 64
Graphs Efficiently Store Useful Information Page: 64
Using Depth First Search to Solve a Maze Page: 65
Breadth First Search Offers Different Searching Strategy Page: 67
Directed Graphs Page: 69
Graphs with Edge Weights Page: 72
Dijkstra’s Algorithm Page: 72
All-Pairs Shortest Path Page: 76
Floyd–Warshall Algorithm Page: 77
Summary Page: 78
Challenge Exercises Page: 79
8. Wrapping It Up Page: 80
Python Built-in Data Types Page: 80
Implementing Stack in Python Page: 81
Implementing Queues in Python Page: 81
Heap and Priority Queue Implementations Page: 82
Future Exploration Page: 82
Index Page: 84