COEN 352Data structures and Algorithms

R. Dssouli

Abu Abdullah Muhammad ibn Musa al-Khwarizmi

(c. 780 -- 850 AD)Persian astronomer and mathematician lived in Baghdad, father of algebra

“On calculating with hindu numerals”

a treatise in Arabic, 825

“Agoritmi de numero Indorum” translation into Latin, 12th century author’s name, mistaken for a plural noun, came to

mean “calculation methods”

Algorithm: Etymology

Al-Khwārizmī (in Arabic: خوارزمی), Persian astronomer and mathematician, wrote a treatise in the Arabic language in 825 AD, On Calculation with Hindu–Arabic numeral system. (See algorism). It was translated from Arabic into Latin in the 12th century as Algoritmi de numero Indorum (al-Daffa 1977), whose title is supposedly likely intended to mean "Algoritmi on the numbers of the Indians", where "Algoritmi" was the translator's rendition of the author's name; but people misunderstanding the title treated Algoritmi as a Latin plural and this led to the word "algorithm" (Latin algorismus) coming to mean "calculation method". The intrusive "th" is most likely due to a false cognate with the Greek ἀριθμός (arithmos) meaning "numbers".

Source Wikipedia

Why Study Data Structures?

• Data structures organize Data– Good choice better program (more efficient

program)– Bad choice poor program performance

• Changes over time– More powerful computers– More complex applications– More complex tasks

Why Study Data Structures?

• Characteristics of problem’s solution– Efficiency: a solution is efficient if it solves

problem within resource constraints• Time• Space

– Cost: the amount of resources a solution will consume

Why study Algorithms

• Algorithms solve problems– Good choice more efficient program– Bad choice poor program performance

• Impact– Different algorithms perform better on different

inputs– Input size can affect the performance

Why study algorithms? (2)

• a language for talking about program behavior• standard set of algorithms and design techniques• feasibility (what can and cannot be done)• halting problem, NP-completeness

• analyzing correctness and resource usage• successful companies (Google, Mapquest, Akamai)• computation is fundamental to understanding the world• cells, brains, social networks, physical systems all can be• viewed as computational devices

• IT IS FUN!!!

Goal

• Designing “clever" algorithms to solve problems efficiently.

• Analyzing algorithms. This means:– proving that they are correct. It is not part

of this course.– estimating their running time and/or other

resources needed (e.g., memory space).• A

Abstract Data TypesADT

• Basic definitions– Type: a set of objects– Data item or element: a piece of information or record– Member: a data item is said to be a member of a data type– Simple data item: a data item containing no subparts– Aggregate data item: a data item that may contain several

pieces of information– Abstract data type: a type and a collection of operations to

manipulate that type

ADT are mathematical abstractions, an ADT only mentions what is to be done, not how.

Data Structure

• A data Structure is a physical implementation of an ADT– Each ADT operation is implemented by one or

more subroutines– Data structures are organizations for data in the

main memory

Relations between notions

Abstract data structure

Concrete data structure

Software library

Problem

Algorithms

Program

Resolves /ImplementsSpecify

Selecting a Data Structure

• Analyze problem• Determine basic operations• Select a data structure• Questions

– At what times(s) in the program run do inserts occur

– Are deletes allowed?– Is there any Order to data processing?

Algorithm/ Data Structure

• Each data structure requires:– Space to store each item, including overhead– Time to perform basic operations– Programming effort

• Algorithms are closely related:– Poor data structure choice higher complexity

algorithms– Good data structure choice algorithm trivial

Performance isn’t everything

Typical goal: Find most space- and time-efficient algorithm for given problem.

• What else is important?

– modularity – user-friendliness

– correctness – programmer time

– maintainability – simplicity

– functionality – extensibility

– robustness – reliability

Problems, Algorithms and Programs

What is the difference among these?• Key questions that relate:

– Can the problem be solved efficiently?– What do we mean by efficient?– Which algorithms are more efficient?– How one can answer the above questions?– How to estimate the time required for a program?– Hoe to reduce the running time of a program?– The consequences of careless use of recusion

Problems

• Problem: task to be performed– Can be seen as: a set of inputs and matching outputs– Problem definition includes resource constraints

• Problems are analogous to mathematical functions– Function: mapping inputs (domain) to outputs (range)– The input to a function can vary:

• Single number• Multiple numbers• Set of information

– Parameters: the value making up an input– A given input must always map to the same output

Algorithms

Definition: Finite set of unambiguous instructions for solving a problem.

• An algorithm is correct if on all legitimate inputs, it

outputs the right answer in a finite amount of time

• Can be expressed as– Pseudocode– flow charts– text in a natural language (e.g. English)– computer code

Algorithms and Programs

• Algorithms: a method or process to solve a problem– Algorithm transforms the input of a problem to its

outputs– Algorithm proprieties

1) Must be correct2) It must be composed of a series of correct steps3) There can be no ambiguity about which step is next4) It must be finite in length5) It must terminate

• Program: an instance of an algorithm, written in some programming language.