Introduction-to-Algorithms
Introduce Origin of this library
Some implementations of the topics in Introduction to Algorithms and some reflections on the content of the book, if there is anything wrong, please correct me.
Preliminary preparation
Before implementing and understanding this book, we need to have some mathematical foundation, and some tools to run our code.
We choose python to implement various algorithms, and we will also use some TS languages. If there is a need later, we will use more languages(most likely TS) to implement.
Environmental preparation
For a better user experience, we will install some version management and running environment/running tools.
We will also add some testing tools in the future for a better learning experience
Just google it and install.
If you need to add new languages later, please add them to the list below according to the format: version manager; running environment; running tools (if the running environment is already installed, such as js and ts)
If there is none, it will be empty and separated by ";"
python: pyenv; python;
js: nvm; node;
ts: ;node; ts-node
Preparation of basic knowledge of mathematics
some basic knowledge of mathematics need to learn
Summations
Summation formulas and properties
Bounding summations
Sets and discrete mathematics
Sets
Relations
Functions
Graphs
Trees
Counting and Probability
Counting
Probability
Discrete random variables
The geometric and binomial distributions
The tails of the binomial distribution
Matrices
Matrices and matrix operations
Basic matrix properties
If you're ready, let's get started
We will go through the writing of all the algorithms in the book chapter by chapter, including thought problems and practice problems.
First of all
we need to know what is algorithm
Informally, an algorithm is any well-defined computational procedure that takes some value, or set of values, as input and produces some value, or set of values, as output.
An algorithm is thus a sequence of computational steps that transform the input into the output.
as the same
an algorithm is a tool for solving a well-specified computational problem.
properties
correctly solve the given computational problem
common interesting algorithmic problems:
1.They have many candidate solutions, the overwhelming majority of which do not solve the problem at hand. Finding one that does, or one that is “best,” can present quite a challenge.
2. They have practical applications. Of the problems in the above list, finding the shortest path provides the easiest examples. A transportation firm, such as a trucking or railroad company, has a financial interest in finding shortest paths through a road or rail network because taking shorter paths results in lower labor and fuel costs. Or a routing node on the Internet may need to find the shortest path through the network in order to route a message quickly. Or a person wishing to drive from New York to Boston may want to find driving directions from an appropriate Web site, or she may use her GPS while driving.
loop invariant:
Initialization: It is true prior to the first iteration of the loop.
Maintenance: If it is true before an iteration of the loop, it remains true before the
next iteration.
Termination: When the loop terminates, the invariant gives us a useful property that helps show that the algorithm is correct.
some algorithms contain
iterative method
recursive method
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