Hi,

I spent 6 years to write the book ‘Elementary Algorithms’. I finally completed it yesterday.

This book is open and free, the PDF version can be downloaded from:

https://github.com/liuxinyu95/AlgoXY/blob/algoxy/preview/elementary-algorithms.pdf?raw=true
Why

There are plenty of books about algorithms, such as ‘Introduction to algorithms’, ‘The art of computer programming’, ‘structure and interpretation of computer programs’… why another book? Is it reinvention of wheel?

This book can’t compare with the above classic bibles at all. It has some features like:

1. All algorithms are described in math formulas and pseudo codes. I hope it bring some taste of elegant by using algebraic symbols.

2. All algorithms are realized in both purely functional and imperative approaches.

3. The examples are provided in multiple programming languages, including C, Haskell, Python, C++, Scheme/Lisp. Haskell is the main language for all functional implementations.

Content

The following content are covered in this book (in the order of appearance)

• Binary search tree, insertion sort, red-black tree, AVL tree, Trie, Patricia, suffix tree, B-tree;

• Binary heap, Leftist heap, skew heap, splay heap, selection sort, binomial heap, Fibonacci heap, pairing heap;

• Queue, Finger tree based sequence, quick sort, merge sort, binary search, saddle-back search, KMP, Boyer-Moore, DFS, BFS, Greedy algorithm, Dynamic programming.

There are two books influenced me most, one is ‘Purely functional data structure’ by Chris Okasaki, the other is ‘Introduction to algorithms’.

Problems

I always don’t have enough time in writing this book during the past 6 years. I am not a native speaker, the biggest problem is about English. It is lack of proof reading by native speakers. I used some result directly, if I had time, I should add more proof for those results.

Future work

Ideally, I think a serious algorithm book should be written in a stable environment. I planned to write this book in 10 years. But everything changes so fast in modern society. I experienced lay-offs once in 2012 due to Symbian business cut off, and now again in MS. I am not sure if I can continue this work. I think the best way is to open this book to the community. Some future work in my mind:

• Proof reading and review

• Provide answers to the exercises

• Provide proof for the directly referenced result

The whole manuscript is available at github:

https://github.com/liuxinyu95/AlgoXY
Best regards

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Larry, LIU Xinyu