Book of Elementary Algorithms and Data structures
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Elementary Algorithms

Edition: $\displaystyle e = \sum \limits _{n=0}^{\infty }{\frac {1}{n!}} = 1 + {\frac {1}{1}}+{\frac {1}{1\cdot 2}}+{\frac {1}{1\cdot 2\cdot 3}}+\cdots = 2.718283$


This book introduces about elementary algorithms and data structure. It includes side-by-side comparison about purely functional realization and their imperative counterpart, with 119 exercises and answers.


I am adding exercises and answers to the second edition from 2023/03 (added 119 answers as of 2023/05). I wrote the first edition from 2009 to 2017, then rewrote from 2020 to 2023. The PDF can be downloaded for preview (EN, ). The 1st edition in Chinese () 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, Sequence;
  • Chapter 12, Divide and conquer sort;
  • Chapter 13, Search;
  • Appendix and answers


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

  • TeXLive, The book is built with LuaLaTeX, to support both EN and CN.

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.


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

Font setting

The default build supports Linux, Mac OS X, and Windows. You can install additional font (like Noto CJK) typesetting (see prelude.sty). Some system fonts, e.g. STKaiti, were moved to /System/Library/AssetsV2/com_apple_MobileAsset_Font7 in Mac OS X, you need add the path to the local TeXLive configuration:

sudo tlmgr conf texmf OSFONTDIR /System/Library/AssetsV2/com_apple_MobileAsset_Font7

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 instead. Run make force-cn or make force-en to force build the book.


LIU Xinyu

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