Lecture 1: Course Overview

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Lecture 1 Course Overview

• Course CSE 360
• Instructor Dr. Eric Torng
• TA Huamin Chen

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Topics

• Course Overview
• Algorithms
• Models of Computation
• Problems
• Functions or Program Specification
• What we will be doing in this course

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What do people do with computers?

• One answer
• Run programs on them.

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What is a program?

• Algorithm
• define difference later
• List of instructions
• finite
• definite no ambiguity

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Examples

• Dough recipe
• Maximum program

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Dough recipe

• Ingredients
• 3 cups flour
• 1 cup water
• Instructions
• bring water to boil
• thoroughly mix flour and boiling water
• refrigerate overnight

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Maximum program

• Variables
• integer array A100
• integer max, i
• Instructions
• max A0
• for (i1ilt100i)
• IF Ai gt max THEN max Ai
• return max

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Models of Computation

• A model of computation is a programming language
• Defines concept of legal programs
• Dough recipe is not a legal computer program
• Main constraints
• available resources
• possible operations
• (also other parameters)

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Difference between program and algorithm

• Algorithm
• high level idea
• Program
• implementation of algorithm in a specific
  programming language/computational model
• Different programs can implement the same high
  level algorithm

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Initial Model of Computation

• C programming language
• Modified Churchs Thesis
• C is a general model of computation
• Any algorithm can be expressed as a C program
• If some algorithm cannot be expressed by a C
  program, it cannot be expressed in any reasonable
  programming language

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What does an algorithm do?

• A specific program/algorithm is written to solve
  a specific problem.

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What is a problem?

• A problem is a mapping or function between a set
  of inputs and a set of outputs
• Example
• Sorting problem
• Input x 4 2 3 1
• Output f(x) 1 2 3 4

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Sorting problem
(4,2,3,1)
(1,2,3,4)
(3,1,2,4)
(7,5,1)
(1,5,7)
(1,2,3)
(1,2,3)
Inputs
Outputs
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How to specify a problem

• Input
• Describe what an input instance looks like
• Output
• Describe what task should be performed on the
  input
• In particular, describe what output should be
  produced

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Example Problems

• Sorting Problem
• Input
• Integers n1, n2, ..., nk
• Output
• n1, n2, ..., nk in nondecreasing order
• Find element problem
• Input
• Integers n1, n2, , nk
• Search key S
• Output
• yes if S is in n1, n2, , nk, no otherwise

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Observation

• A problem is a SPECIFICATION for a program
• In our case, a problem is very cleanly defined
  and thus there should be little ambiguity in what
  is being requested
• This is not always true in real life

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What a computer programmer does

• 1) Client gives a problem description to the
  programmer
• often unclear
• ask questions!
• 2) You design an algorithm/program to solve the
  problem.

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What do people do with problems?

• In programming courses
• Develop programs to solve these problems
• In this course
• 1) We will show there exist problems which cannot
  be solved by any C program
• Churchs Thesis
• What is it and why is it important in this
  context?
• Techniques used
• Diagonalization technique
• Reduction technique

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What will we do in this course?

• 2) We then will study restricted computational
  models
• Study what can be done
• Study what cannot be done

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Quick Review

• Group work
• What is a model of computation?
• What is a problem?
• How do we specify a problem?
• What do programming courses teach you to do with
  problems?
• What is one thing we are going to teach you about
  problems in this course?

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Key Concepts

• Algorithms and programs
• models of computation/programming languages
• Problems
• function
• program specification
• Unsolvable problems