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Book of Elementary Algorithms and Data structures

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Elementary Algorithms

Edition: 1.6180339887498949


This book introduces about elementary algorithms and data structure. It includes side-by-side comparison about purely functional realization and their imperative counterpart.


From 2020/12, I started re-writing this book. The PDF can be downloaded for preview (EN, 中文). The 1st edition in Chinese (中文) was published in 2017. I recently switched my focus to the Mathematics of programming, the new book is also available in (github)

  • Preface
  • Chapter 0, List;
  • Chapter 1, Binary Search Tree;
  • Chapter 2, Insertion sort;
  • Chapter 3, Red-black tree;
  • Chapter 4, AVL tree;
  • Chapter 5, Radix tree, Trie and Prefix Tree;
  • Chapter 6, B-Trees;
  • Chapter 7, Binary Heaps;
  • Chapter 8, Selection sort;
  • Chapter 9, Binomial heap, Fibonacci heap, and pairing heap;
  • Chapter 10, Queue;
  • Chapter 11, Sequences;
  • Chapter 12, Divide and conquer sort;
  • Chapter 13, Search;
  • Appendix


To build the book in PDF format from the sources, you need the following software pre-installed.

  • TeXLive, The book is built with XeLaTeX, a Unicode friendly version of TeX;

Install TeXLive

In Debian/Ubuntu like Linux environment, do NOT install the TeXLive through apt-get. Go to TeXLive official site to download the setup script.

$ wget
$ unzip
$ cd install-tl
$ sudo ./install-tl -gui text -repository

In Windows, TeXLive provide a gui based installer, in Mac OS X, there's a MacTeX.

Install ImageMagick and Graphviz

$ sudo apt-get install imagemagick
$ sudo apt-get install graphviz

For Windows and Mac OS X installer, ImageMagick can be download through; Graphviz can be download from:


You need the GNU make tool, in Debian/Ubuntu like Linux, it can be installed through the apt-get command:

$ sudo apt-get install build-essential

In Windows, you can install the MSYS for it. In Mac OS X, please install the developer tool from this command line:

$ xcode-select --install

Build the book PDF

enter the folder contains the book TeX manuscript, run

$ make

This will generate algoxy-en.pdf and algoxy-zh-cn.pdf. If you only need the Chinese version for example, you can run

make cn

Other branches

The other two branches,

are deprecated. Please do NOT checkout/track them.


LIU Xinyu

[email protected]

``Cogito ergo sum''

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