Representation and Evaluation of Algorithms

(アルゴリズムの表現と評価)

Data Structures and Algorithms

2nd lecture, September 29, 2022

https://www.sw.it.aoyama.ac.jp/2022/DA/lecture2.html

Martin J. Dürst

Today's Schedule

Summary of last lecture・last week's homework
Representation of algorithms
The programming language Ruby
Evaluation of algorithms

Introduce TA

Teaching Assistant (TA): YU JINSONG (于津松、M1)

Covid Precautions

Every morning, measure your body temperature
If you have increased temperature (above 37.5°), contact the health center
Observe social distance
Always wear a mask (correctly!)
Regularly wash/disinfect your hands thoroughly
Eat/drink quietly, alone
If you are not vaccinated yet, get vaccinated as soon as possible

About Moodle

There are some differences between official registration and Moodle enrollment
Both are necessary if you want to take this course
In Moodle, there are some Japanese people with names in Latin letters,...
These also need to be fixed
I call out students who are affected at the end of this lecture

Summary of Last Lecture

Course overview
The fascination of algorithms and data structures
Data structures: A number of data items and their relationships.
Example: linked list
Algorithm: A clear set of instructions for how to solve a well-defined problem in finite time.
Examples: linear search, binary search

Solution to Homework 1, Question 1

[都合により削除]

Tokyo Stock Exchange: Actual system capacity

(source: The Japan News, 2015/9/22, p. 6)

	old system	new system
used	until 2015/9/18	from 2015/9/24
Orders per day (max)	137 million	270 million
Orders per second (max)	30'000~40'000	>50'000
Time to process orders	0.001s	0.0005s

Last Week's Homework 3: Help Ms. Noda

Design an efficient (=fast) algorithm for Ms. Noda's problem.

Hint: Can you use an algorithm that you already know?

[都合により削除]

Last Week's Homework 2: Representation of Algorithms

Examine the algorithm representations on the additional handout, and think about each representation's advantages and disadvantages.

(no need to submit)

Methods for Representing Algorithms

Algorithms are abstract ideas
But we need some way to represent them
There are 4 main representation methods:
1. Text
2. Diagrams
3. Pseudocode
4. Programming languages
Each method has advantages and disadvantages

Text

Principle: Describe the algorithm in a natural language

Advantages: Possible to write and understand for non-experts

Disadvantages:

Ambiguity of natural language
Difficulty to be precise
Structure is unclear
Dependent on natural language choice (e.g. Japanese vs. English)

Diagrams

Examples: Flowchart, ...

Advantages: Visual expression

Disadvantages:

Creation is time-consuming
Problem of data exchange (many different formats)
Gap to structured programming

(structured programming: replacing goto (jump to an arbitrary location in a program) with structured branches (if/switch/...) and loops (for/while/...) only)

What is Pseudocode

Notation that is similar to actual program code
Commonalities (not required):
- Simple notation (e.g.: no semicolon at end of line)
- Ignoring type details
- No variable declarations
- Use of special symbols (e.g. ←, ∨, ∧, ≤, ∈,...)
- Partial use of natural language (including comments)
Important: You can create your own pseudocode!

(Dis)Advantages of Pseudocode

Advantages:

Middle ground between (natural language) text and program
Adjustable to author's preferences
Adjustable to the characteristics of the algorithm
Strong connection to structured programming
Possible to concentrate on the essence of the algorithm

Disadvantages:

Many different variations
Obfuscation is possible
Not executable

Programing Language

Advantages:

Precision
Executability

Disadvantages:

Many different programming languages
Dependent on execution environment
More precise than necessary
Different from essence of algorithm

The Programming Language Ruby

Created in Japan by Yukihiro Matsumoto (松本行弘; nickname: Matz) starting in 1993
Gaining popularity outside Japan since 2000
Increased attention after publication of Ruby on Rails in 2004

Completely object-oriented
Easy-to-use scripting language
Easy for beginners, satisfying for experts
Contributions to Ruby implementation by Master/Bachelor students of my Lab (internationalization,...)

Ruby for Algorithm Representation

Simple syntax
No need to declare variables
Data structures (e.g. array) are orthogonal to data types (e.g. int)
(i.e. no need for "array of int", "array of float", ...)
Ruby is often called "executable pseudocode"
Very flexible (can change almost everything)
Excellent environment

Last Week's Homework 4: Install Ruby

Install Ruby on your notebook computer (and/or on your computer at home)

Main installation methods (choose at least one):

Add Ruby to your Cygwin installation (use cygwin setup.exe; detailled instructions)
Download and install Ruby 3.1.2-1 (x64) (or some other version) from RubyInstaller

How to check: Open a Cygwin Terminal or start Command Prompt with Ruby and execute ruby -v

Important: If you have problems with installing Ruby, contact me before the next lecture.

Reading and Writing Ruby

For this course, you have to learn how to read Ruby programs
(as pseudocode to understand algorithms)
For this course, you do not have to learn how to write Ruby programs
But you have to be able to write algorithms in (your own) pseudocode
We will write Ruby programs in the spring term of 2023
(Projects in Information Technology II/情報総合プログラミング実習 II)
Writing Ruby programs now will help you both for this course and next year

First Ruby Example

Linear search and binary search: 2search.rb

How to execute:

Open a Cygwin Terminal or Start Command Prompt with Ruby
Use the cd command to move to a directory of your choice
Download the file into the choosen directory
Execute ruby 2search.rb

Basics of Ruby Syntax

# starts a comment (up to end of line)
(we use # for comments about the algorithms,
## for comments about Ruby itself)
No need for ; (semicolon) at end of line
No need for () for conditions (if/while, ...) and most method calls
Methods (functions) are defined using def
class/def/if/while/do all end with end (no {}!)
Classes can be reopened to add or redefine methods

Overview of Algorithm Evaluation

Main evaluation criteria:

Execution time (computational (time) complexity)
(this is the main focus of this lecture, and of research on algorithms)
Amout of memory used (space complexity)
(in general, the difference between different algorithms or data structures for the same problem is small)
Ease of implementation
(this is highly subjective, but in general, faster algorithms may be more difficult to implement)

Contextual information used for evaluation:

How often will the algorithm be used?
With how much data will the algorithm be used?

Comparing the Execution Time of Algorithms