Algorithms and Data Structures: Concepts and Applications

(アルゴリズムとデータ構造の概要と応用)

Data Structures and Algorithms

(データ構造とアルゴリズム)

1st lecture, September 17, 2014

http://www.sw.it.aoyama.ac.jp/2015/DA/lecture1.html

Martin J. Dürst

(テュールストマーティンヤコブ)

duerst@it.aoyama.ac.jp

Building O, Room 529

Today's Schedule

About this course
Data Structures: Concept and Example
Algorithms: Concept and Example
Course Schedule

自己紹介

スイスチューリッヒ生まれ
チューリッヒ大学で lic.oec.publ. (修士相当、情報科学専攻、経営学と日本学副専攻)
文部省奨学金で来日、東京大学で理学博士 (情報科学専攻)
チューリッヒ大学情報科学科主任助手
慶應義塾大学政策・メディア研究科特別研究助教授 (W3C プロジェクト)
米マサチューセッツ工科大学客員研究員
World Wide Web Consortium (W3C) 国際化活動責任者
2005年から青山学院大学理工学部情報テクノロジー学科

Teaching Assistant: Hiroaki Honda (本多洋朗、M1)

授業の位置づけ

情報テクノロジー学科: 2年後期、必修
経営システム工学科:
- 2012年入学生まで: 2年後期、選択必修、第一科目群 (▲)
- 2013年入学生から: 他学科科目 (自由選択科目)
機械創造工学科: 3年後期、選択必修、第一科目群 (△)

This is a JE course (理工学国際プログラム JE 科目): The explanations are in Japanese, the materials (mostly) in English

授業の進め方

資料の配布とウェブ公開
配布資料への書き込みが不可欠
ミニテストはアナウンスなし
出席は前提 (文科省); 遅延や未出席は大損
宿題、復習、予習は授業時間の二倍程度 (文科省)
質問はいつでも大歓迎
約束事 1: 私語禁止、脱帽、飲食禁止
約束事 2: 書き込み、宿題を必ずやること

Glossary

Each lecture handout comes with a glossary at the end
The glossary contains:
- technical terms for this lecture (e.g. data structure/データ構造) ⇐ part of examination
- technical terms for computer science (e.g. compiler/コンパイラ)
- technical terms from other fields (e.g. topology/位相幾何学)
- selected general terms/expressions (e.g. technical term/専門用語)
Please report missing terms

成績評価方法

おおよその割合:

授業中のミニテスト: ~20%
演習課題: ~30%
期末試験: ~50%

総合的な評価

ラボワーク

テーマ: 最高のウェブフレームワーク Ruby on Rails でウェブアプリ作り

時間: 水曜日の午後 (3限あたりから) 又は皆さんの津行のいい時間帯

Why Algorithms and Data Structures?

Example of what happens without data structures and algorithms:

Long program, difficult to maintain
Slow program, especially when number of data items increases

The Fascination of Algorithms and Data Structures

At the core of Computer Science/Information Technology
At the intersection of theory and practice
Clear evaluation criteria
Lots of interesting ideas
Highly practical (Examples: Google (PageRank algorithm), Netflix prize, algorithmic trading)
Advantageous for job search (Get that job at Google, Steve Yegge, 2008)
Advantageous for external Master Course entrance exams

Lecture Goal

Understand

Way of thinking for algorithms and data structures
Design of algorithms and data structures
Well-known algorithms and data structures

Example of Data Structure: Linked List

Data Structure: Concept

A data structure consists of:

A number of data items
Examples: Numbers, student data, ...
Relationships (connections) between the data items

The term data structure is used mostly for structures inside computer (main) memory.

There are two different views of data structures:

External view (functionality provided): Abstract data type (ADT)
Internal view (implementation): Construction out of arrays, structures, pointers, ...

Algorithm Examples

Problem: Searching a word (target) in a (real!) dictionary

Linear search:
- Starting with page 1, proceed page by page until the end
- For each page, search columns from left to right and entries from top to bottom
Binary search:
- Start with whole dictionary
- Repeatedly split dictionary in half
  - Check the word in the middle
  - If the word in the middle is smaller than the target, keep the second half of the pages/words
  - If the word in the middle is greater than the target, keep the first half of the pages/words
  - If the word in the middle is equal to the target, then return the target
  - If you only have one word left, return failure

Algorithm: Concept

An algorithm is a clear set of instruction for how to solve a well-defined problem in finite time.

Requirements:

Clear definition of problem and result
Detailled and precise step-by-step instructions (similar to a program)
Termination in a finite number of steps

Counterexamples

"Let's create world peace!"
Problem: Result unclear.
"Just look it up in the dictionary!"
Problem: Precise instructions are missing.
Random dictionary search: Open the dictionary at random locations, stop if you find the word you searched for.
Problem: May take infinite number of steps.

Difference between Algorithms and Programs

Algorithms cannot be executed directly,
they have to be implemented as programs in order to be executed.
The same algorithm can be implemented in many different programming languages, and in many different ways in the same program language
Programs concentrate on details, algorithms are concepts (ideas)

History of Algorithms

Land area calculations in ancient Egypt
Abstraction in ancient Greece (Example: Euclid's algorithm for the greatest common denominator)
Origin of the name algorithm: Persian Mathematician Muhammad ibn Mūsā al-Khwārizmī (الخوارزمي, ca. 800 A.D.)
In the 1930ies: Establishing the Mathematical base of algorithms (Gödel, Turing ...)
From the 1950ies: Used in practice with computers, dramatic increase in numbers
From the 1990ies: Increased economic importance

Relationship between Data Structures and Algorithms

Data structures represent state (static aspect of a computation)
algorithms represent processing (dynamic aspect of a computation)
Some algorithms use more than one data structure
More than one algorithm may use the same data structure

Summary of this Lecture

Data Structures and Algorithms are core concepts of Computer Science.
A data structure describes a number of data items with their relationships.
An algorithm is a clear set of instruction for how to solve a well-defined problem in finite time.
Algorithms are not programs: Algorithms are abstract ideas, programs can be executed.
Algorithms are more than 2000 years old, but have been gaining enormous economic importance recently.

Lecture Schedule

Data Structures and Algorithms: Schedule

参考書 (どれか一冊を買って、授業の内容に合わせて読むことは強く推奨)

宿題 1: 膨大なデータ

提出: 来週の水曜日 (9月23日) 18時30分締切; O 棟 529号室の前の箱に提出; A4 一枚 (両面可) 厳守

(それぞれの問題で、想定の根拠となる理由、参考にした文献など必ず明記のこと。Wikipedia などへの参照の場合、URI のではなく IRI を使用のこと (例: http://ja.wikipedia.org/wiki/%E6%83%85%E5%A0%B1 のではなく http://ja.wikipedia.org/wiki/情報))

東京証券取引所の第一部の取引で、一つの株式会社の株が営業時間内に平均で 30秒で一回売買されていると想定して、合計で年間に (一売買行為を一つの項目と考えるとき) 何項目のデータが集まるかを、計算しなさい。
問題 1 の結果よりもデータ項目数がもっと多くて、実際に計算機で扱えそうな問題を考え、説明しなさい (他人と同じものの場合には減点対象)。

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)

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?

(no need to submit)

Homework 4: Install Ruby

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

Main installation methods:

Download and install Ruby 2.2.3 (or any other version) from RubyInstaller
Add Ruby to your Cygwin installation (use cygwin setup.exe; detailled instructions)
(maybe already installed for Computer Programming I, please check)

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, come to my lab to fix it before the next lecture.

Preparation for the Next Lecture

Submit Homework 1 (deadline: September 23, 18:30)
Complete Homework 2 (no need to submit)
Complete Homework 3 (no need to submit)
Review today's lecture's content
Complete Homework 4
Bring your notebook computer (with Ruby installed) with you next time

Glossary

job search: 就職活動
data structure: データ構造
linked list: 連続リスト
data item: データ項目
abstract data type (ADT): 抽象データ型
algorithm: アルゴリズム
linear search: 線形探索
binary search: 二分探索
implement(ation): 実装 (する)
land area calculations: 土地面積の計算
ancient Egypt: 古代エジプト
Euclid: ユークリッド
greatest common denominator (GCD): 最大公約数
Mathematician: 数学者
ancient Greece: 古代ギリシャ
state: 状態
static aspect: 静的側面
dynamic aspect: 動的側面
economic: 経済的