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Computational Algorithms

A comprehensive guide on solving real-world problems using computational algorithms in a structured and efficient manner. Learn problem-solving strategies, design principles, coding examples, and key implementation techniques.

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Computational Algorithms

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  1. Computational Algorithms ...a lightning introduction to real-world algorithms David Davenport Computer Eng. Dept., Bilkent UniversityAnkara - Turkey. email: david@bilkent.edu.tr

  2. IMPORTANT… • Students… This presentation is designed to be used in class as part of a guided discovery sequence. It is not self-explanatory! Please use it only for revision purposes after having taken the class. Simply flicking through the slides will teach you nothing. You must be actively thinking, doing and questioning to learn! • Instructors… You are free to use this presentation in your classes and to make any modifications to it that you wish. All I ask is an email saying where and when it is/was used. I would also appreciate any suggestions you may have for improving it. thank you,David.

  3. Do this For each x if something then do this else do the other Print “all done” From problem to program • In “real world”… • Problem in Natural language • Top-Down Design in pseudo-code • Program in computer code(code in almost any computer language.) The Problem Requirements: A program that does this and that and theother. It must take data fromthis source and The Design The Program // Program example // David, Oct 2002 import java.io.*; Import cs1.JRobo; public class Example { public static void mai System.out.println( JRobo robby = new J robby.f(100); robby.rect( 150, 50); } } DESIGN Reduce cognitive load • separating design and coding • using top-down design IMPLEMENT

  4. Example… The Circle computer

  5. Area-Circumference Problem Requirements: Compute and report the area and circumference of a circle whose radius the user gives. Example interaction Welcome to circle computer… Please enter the radius: 5 The area of a circle of radius 5 is 78.55 and its circumference is 31.42

  6. Area-Circumference Problem To find area & circumference of circle… First say “Welcome to circle computer…” and then ask the user for the radius of their circle and get the radius value the user gives in response. Next, compute the corresponding area as pi times the radius squared, and then compute the circumference as two times pi times the radius. Finally, tell the user that the area of a circle of the radius they gave is the area value you computed, and the circumference is the circumference value you computed. Put yourself in the place of the computer and explain what you would do in plain English

  7. Area-Circumference Problem To find area & circumference of circle… Firstsay “Welcome to circle computer…” and then ask the user for the radius of their circle and get the radius value the user gives in response. Next, compute the corresponding area as pi times the radius squared, and thencompute the circumference as two times pi times the radius. Finally, tell the user that the area of a circle of the radius they gave is the area value you computed, and the circumference is the circumference value you computed.

  8. Area-Circumference Problem To find area & circumference of circle… Firstsay “Welcome to circle computer…” and then ask the user for the radius of their circle and get the radius value the user gives in response Next, compute the corresponding area as pi times the radius squared, and thencompute the circumference as two times pi times the radius. Finally, tell the user that the area of a circle of the radius they gave is the area value you computed, and the circumference is the circumference value you computed.

  9. Area-Circumference Problem To find area & circumference of circle… • Say “Welcome to circle computer…” • Ask the user for the radius of their circle and get the radius value the user gives in response • Compute the corresponding area as pi times the radius squared, • Compute the circumference as two times pi times the radius. • Tell the user that the area of a circle of the radius they gave is the area value you computed, and the circumference is the circumference value you computed.

  10. Area-Circumference Problem To find area & circumference of circle… • Print welcome message • Ask for & get radius from user • Compute area as pi.radius.radius • Compute circumference as 2.pi.radius • Report area, circumference & radius Identify preconditions ( for each step )& ensure they are satisfied. Once we are sure that this is correct, move on to solve any non-trivial sub-problems.

  11. Area-Circumference Problem Solve… • Ask for & get radius from user • Ask (prompt) the user to enter radius • Get radius value from user Welcome to circle computer… _ Welcome to circle computer… Please enter the radius: _

  12. Area-Circumference Problem To find area & circumference of circle… • Print welcome message • Ask for & get radius from user • Compute area as pi.radius.radius • Compute circumference as 2.pi.radius • Report area, circumference & radius The area of a circle of radius 5 is 78.55 and its circumference is 31.42 The area of a circle of radius 10 is 312.4 and its circumference is 62.84

  13. Area-Circumference Problem Solve… • Report area, circumference & radius • Print msg “The area of a circle with radius ” • Print radius value • Print msg “ is ” • Print area value and move to next line • Print msg “ and its circumference is ” • Print circumference value • Print blank line Take care with spaces, number formats & line breaks!

  14. Example… Exam average problem

  15. Exam average problem Requirements: Given a set of already graded exam papers,compute and report the average grade. Algorithm • Print welcome message • Given the set of exam papersfind the number of papers and the sum of all the grades on the papers • Compute average grade as sum of all the grades / number of papers • Report the average grade • Print “all done” message

  16. Exam average problem Revised algorithm Algorithm 1. Print welcome message 2. Given the set of exam papers find the number of papers and the sum of all the grades on the papers 3. ifnumber of papers is zero then3T Print msg “no grades entered” else 3F.1 Compute average grade as sum of all the grades / number of papers 3F.2 Report the average grade 4. Print “all done” message

  17. Exam average problem Solve… • Given the set of exam papersfind the number of papers and the sum of all the grades on the papers • Ask user for & get the number of papers • For each paper read the grade from the paper and add it to the sum of grades so far. • Sum of all the grades is now sum of grades so far

  18. Exam average problem Solve… (Alternative) • Given the set of exam papersfind the number of papers and the sum of all the grades on the papers • Set count of papers so far to zero, then for each paper add one to the count of papers so far. • Set sum of grades so far to zero, and then for each paper read the grade from the paper and add it to the sum of grades so far. • Number of papers is now count of papers so far • Sum of all grades is now sum of grades so far

  19. Exam average problem Solve… (Yet another alternative) • Given the set of exam papersfind the number of papers and the sum of all the grades on the papers • Set count of papers so far to zero • Set sum of grades so far to zero • For each paper, read the grade from the paper, add it to the sum of grades so far and add one to the count of papers so far • Number of papers is now count of papers so far • Sum of all grades is now sum of grades so far

  20. Exam average problem Solve… (& yet another alternative) • Given the set of exam papersfind the number of papers and the sum of all the grades on the papers 1. Set count of papers so far to zero 2. Set sum of grades so far to zero 3. For each paper 3.1 read the grade from the paper, 3.2 add grade to the sum of grades so far 3.3 add one to the count of papers so far 4. Number of papers is now count of papers so far 5. Sum of all grades is now sum of grades so far

  21. Of note…

  22. Sentence forms - control • Sequence • “Do this and then do that and then do the other and …” • Decision/alternation • “if this condition is true then do this else do that” • “if this condition is true then do this” • Repetition • “for each/every/all do this” • “repeat this until condition is true” • “while this condition is true do this” • “do this while condition holds”

  23. Sentence forms - data • Input • “get value from user” • Computation • “compute this as some function of that” • Output • “print this message” • “print/report this value” ERRORS • Syntax • Logical • Run-time

  24. Sequence Decision • step • step • step • step n. if condition then nT step else nF step indent Repetition n. while condition do step n. do step while condition indent indent Types & Layout(of algorithm steps) Any step can be replaced with one of the other types or input, output, assignment. n. for so many times do step

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