Brief Introduction of Algorithm. What is Algorithm A method with several definite steps to effectively complete a task. In general, it starts from the.

Brief Introduction of Algorithm

What is Algorithm

A method with several definite steps to effectively complete a task.

In general, it starts from the initial state with input data and ends at final states (not only one!!) with some output information.

Typically, it can be described with a flow chart.

An Example of Flow Chart

Flow chart is also a basic mechanism of language. There is a kind of “flow chart” which can be much more complicated and we are not going to talk about that in detail.

If You Want to Learn Algorithm…

This is a book for those without any fundamental knowledge of algorithm. However, some coding techniques and concept is prerequisite.

An Example of Algorithm

Sorting some disordered data Bubble sort Quick sort

Example – Bubble Sort

A step-by-step example

Example – Quick Sort

A step-by-step example

Example – Comparison

In general, quick sort can be much more faster than bubble sort.

However, there are some issues when making comparison A quantitative comparison? Is there a worst case?

Computational Complexity

Big O notation (infinite asymptotics) Ex: What does O(n2) means? Ex: What about O(2n)? Ex: If an algorithm takes several steps (listed below) to

finish, how do we denote its complexity using big O notation?

3210001510 nnn nnnn 2log12 32

Computational Complexity

Bubble sort: O(n2)Quick sort: O(n log n)

Worst case

For some algorithms, there are some cases will terribly downgrade their performance.

For example, complexity of quick sort will become O(n2) when encountering worst cases.

Other Considerations

Memory consumption Usually, we must strike a balance between

computation speed and memory consumption.

Programming difficulty Some legendary algorithm performs great.

However, writing the program can be a nightmare.

Other Considerations

More detailed complexity Doing multiplication is much slower than doing

addition. Some algorithms replace parts of multiplication

operations with additions. Ex: Conventional matrix multiplication: O(n3) Strassen’s matrix multiplication: O(n2.808) Is it truly much better than conventional method?

Algorithm and Computation Theory

There are huge number of algorithms designed for different kinds of problem. Common mathematical problem, numerical

evaluation, networking, etc.

However, all of them can be discussed in view of computation theory. It is doubtless that we should take care of their

computation behavior and concept. Hence, we can further improve them.

Some Methodology of Algorithm Design

Divide and conquerDynamic programmingGreedy methodLinear programmingGenetic algorithm

For Further Reading…

“The Art of Computer Programming” by Donald Knuth

Creator of TeX Turing award Be sure to have some program

ming knowledge before reading it!