algorithms 1up

8/3/2019 Algorithms 1up

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ENGN2219 Computing for Engineering Simulation

Algorithms

Ramesh Sankaranarayana

Research School of Computer ScienceAustralian National University

Canberra, ACT

ENGN2219 Computing for Engineering Simulation Algorithms 1 / 14
http://goforward/http://find/http://goback/


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1 Introduction

Problem - Spacecraft LaunchAlgorithmsProgramming Languages

http://find/http://goback/


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Problem Statement

Spacecraft Launch

A reusable spacecraft, Space Ship One, is to be launched from amother ship at an altitude of 25, 000 feet. Assuming that thespacecraft uses all its fuel to achieve a vertical velocity u atlaunch, what is the value of u for the spacecraft to reach outerspace (an altitude of 100 km)?



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Algorithms

Definition

Informally, an algorithm is a step-by-step procedure to solve aproblem. A recipe, as it were. There is no commonly accepted

formal definition of an algorithm. We will use the following one byStone (1972):

We define an algorithm to be a set of rules that precisely

defines a sequence of operations such that each rule is

effective and definite and such that the sequenceterminates in a finite time.


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Algorithms

Definition

He explains that:

For people to follow the rules of an algorithm, the rules

must be formulated so that they can be followed in arobot-like manner, that is, without the need for thought...

however, if the instructions are to be obeyed by someone

who knows how to perform arithmetic operations but

does not know how to extract a square root, then we

must also provide a set of rules for extracting a square

root in order to satisfy the definition of algorithm.


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Algorithms

Definition

and

Not all instructions are acceptable, because they may

require the robot to have abilities beyond those that weconsider reasonable.

as well

An intuitive definition of an acceptable sequence of

instructions is one in which each instruction is precisely

defined so that the robot is guaranteed to be able to

obey it.


Problem Spacecraft Launch


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Algorithms

Examples

Print the first 100 positive integers.

The long division algorithm.

Maintaining an aircrafts altitude in flight.


Problem Spacecraft Launch


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Algorithms

Representation

FlowchartsPseudocode

Natural language

Programming language


Problem - Spacecraft Launch


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Problem Spacecraft LaunchAlgorithmsProgramming Languages

Problem Statement

Spacecraft Launch

A reusable spacecraft, Space Ship One, is to be launched from amother ship at an altitude of 25, 000 feet. Assuming that thespacecraft uses all its fuel to achieve a vertical velocity u atlaunch, what is the value of u for the spacecraft to reach outerspace (an altitude of 100 km)?


O liProblem - Spacecraft Launch


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Problem Spacecraft LaunchAlgorithmsProgramming Languages

Algorithms

PseudocodecmsPerInch = 2.54 % from conversion tables

inchesPerFt = 12 % from conversion tables

metersPerCm = 1/100 % from conversion tables

metersPerFt = metersPerCm * cmsPerInch *

inchesPerFt

g = 9.81 % m/sec^2

finalAltitude = 100 % km. Given

initialAltitude = 25000 % ft. Given.

s = (finalAltitude * 1000) -

(initialAltitude * metersPerFt)

u = sqrt(2*g*s) % required initial velocity


O tliProblem - Spacecraft Launch


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pAlgorithmsProgramming Languages

Architecture

The Von Neumann Architecture

memory

ALU

input/output

control unit

AC


OutlineProblem - Spacecraft Launch


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pAlgorithmsProgramming Languages

Architecture

Main components

Central Processing Unit (CPU)

Memory - main (RAM) and secondary (hard drives, flash

cards, etc.)Bus - Data, Address and Control

Program Counter (PC)

Arithmetic and Logic Unit (ALU)

Registers - instruction, status, index, accumulator

Input/Output (I/O) Devices


Outline Problem - Spacecraft Launch


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AlgorithmsProgramming Languages

Programming Languages

GenerationsFirst generation - machine language. Processor dependent.Hard to program. Not portable.

Second generation - assembly language. More like a symbolicversion of machine language. Easier to program, but still

tedious. Examples - 8086 and PDP-11 assembly languages.

Third generation - more similar to spoken language. Mucheasier to program. Much more portable. Examples - C,Fortran.

Fourth generation - completely portable between supportedprocessor types. Each line of code produces significant amountof machine instructions. Examples - Java, Ada, C#, Matlab,SQL. Includes Domain Specific Languages like OCL, QVT,Eclipse Modeling Framework, grep, sed.


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AlgorithmsProgramming Languages

Programming Languages

Programming ParadigmsImperative - Also called procedural. Traditional approach. Asequence of commands that leads to the desired output.Examples - C, FORTRAN, COBOL and Ada.

Declarative - Develop a precise statement of the problem,

rather than an algorithm for solving the problem. Built on anunderlying general problem-solving algorithm. Formal logicprovides such an algorithm. Example - Prolog.

Functional - Programs written as a bunch of functions.

Recursion and nesting is natural in this approach. Example -Haskell.

Object Oriented - The system is specified as a collection ofobjects and interactions between these objects. Examples -Simula, Smalltalk, Java, C++, C#.


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