Problem Solving & Algorithm Design 01-1 Problem solving The - - PowerPoint PPT Presentation

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Problem Solving & Algorithm Design 01-1 Problem solving The - - PowerPoint PPT Presentation

Aug 11, 2023 579 likes •908 views

Problem Solving & Algorithm Design 01-1 Problem solving The act of finding a solution to a perplexing, distressing, vexing, or unsettled question 01-2 How to Solve it Written by George Polya in 1945 01-3 How to Solve it

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SLIDE 1

01-1

Problem Solving & Algorithm Design

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SLIDE 2

01-2

Problem solving

  • The act of finding a solution to a perplexing,

distressing, vexing, or unsettled question

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SLIDE 3

01-3

How to Solve it

  • Written by George Polya in 1945
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SLIDE 4

01-4

How to Solve it

  • Written by George Polya in 1945

» It is written in a mathematical context for

mathematical problems

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SLIDE 5

01-5

How to Solve it

  • Written by George Polya in 1945

» It is written in a mathematical context for

mathematical problems

> With simple wording changes his list of

suggestions are applicable to all types

  • f problems
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SLIDE 6

01-6

Ask Questions

  • To understand a problem
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SLIDE 7

01-7

Ask Questions

  • To understand a problem

» What do I know about the problem?

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SLIDE 8

01-8

Ask Questions

  • To understand a problem

» What do I know about the problem?

» What is the information that I have to

process in order to find the solution?

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SLIDE 9

01-9

Ask Questions

  • To understand a problem

» What do I know about the problem? » What is the information that I have to process in

  • rder to find the solution?

» What does the solution look like?

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SLIDE 10

01-10

Ask Questions

  • To understand a problem

» What do I know about the problem? » What is the information that I have to process in

  • rder to find the solution?

» What does the solution look like?

» What sort of special cases exist?

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SLIDE 11

01-11

Ask Questions

  • To understand a problem

» What do I know about the problem? » What is the information that I have to process in

  • rder to find the solution?

» What does the solution look like? » What sort of special cases exist?

» How will I recognize that I have found the

solution?

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SLIDE 12

01-12

Look for Familiar Things

» You should never “reinvent the wheel”

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SLIDE 13

01-13

Look for Familiar Things

» You should never “reinvent the wheel”

» In computing, you see certain problems

again in different guises

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SLIDE 14

01-14

Look for Familiar Things

» You should never “reinvent the wheel” » In computing, you see certain problems again in

different guises

» A good programmer sees a task, or

perhaps part of a task (subtask), that has been solved before and plugs in the solution.

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SLIDE 15

01-15

Divide and conquer

» Break up a large problem into smaller units

that can be handled more easily

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SLIDE 16

01-16

Divide and conquer

» Break up a large problem into smaller units that

can be handled more easily

» Abstraction plays an important role

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SLIDE 17

01-17

Divide and conquer

» Break up a large problem into smaller units that

can be handled more easily

» Abstraction plays an important role

» The divide-and-conquer approach can be

applied over and over

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SLIDE 18

01-18

Abstraction

An explanation, idea or model that
 removes complex details This is a key concept Abstraction will reappear
 throughout the course

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SLIDE 19

01-19

Algorithm

A technical term for a set of instructions for solving a problem or sub-problem

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01-20

Algorithm

A technical term for a set of instructions for solving a problem or sub-problem Desirable Properties Use a finite amount of time

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SLIDE 21

01-21

Algorithm

A technical term for a set of instructions for solving a problem or sub-problem Desirable Properties Use a finite amount of time Use a finite amount of data, material

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SLIDE 22

01-22

Algorithm

A technical term for a set of instructions for solving a problem or sub-problem Desirable Properties Use a finite amount of time Use a finite amount of data, material Instructions are unambiguous

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SLIDE 23

01-23

Who writes algorithms?

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SLIDE 24

01-24

Who writes algorithms?

Anyone who wants to write a set of instructions for solving a problem

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SLIDE 25

01-25

An Example Algorithm

How to prepare Hollandaise sauce

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01-26

Algorithm Written in Pseudocode

A mixture of English and formatting to make the steps in the algorithm explicit

Put butter in a pot
 Turn on burner (low heat)
 Put pot on the burner
 While (not bubbling)
 Leave pot on the burner
 Turn off burner
 Put other ingredients in the blender
 Turn on blender
 While (more butter needed)
 Pour butter into blender in a slow stream
 Turn off blender

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01-27

Developing an Algorithm

  • Implementing an algorithm involves making

it computer-readable

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01-28

Developing an Algorithm

  • Implementing an algorithm involves making

it computer-readable

» Must be in a suitable form for a computer

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SLIDE 29

01-29

Developing an Algorithm

  • Implementing an algorithm involves making

it computer-readable

» Must be in a suitable form for a computer

  • The methodology (set of working methods)

used to make the plan must

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SLIDE 30

01-30

Developing an Algorithm

  • Implementing an algorithm involves making

it computer-readable

» Must be in a suitable form for a computer

  • The methodology (set of working methods)

used to make the plan must

» Begin with a problem statement

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SLIDE 31

01-31

Developing an Algorithm

  • Implementing an algorithm involves making

it computer-readable

» Must be in a suitable form for a computer

  • The methodology (set of working methods)

used to make the plan must

» Begin with a problem statement » Conclude with a plan that can be easily

coded