Algorithms, Programs,
and Computers
CS 110
Fall 2005
Problem Solving

You want to make money and you
have some simpletons who are
willing to help
• Devise a plan that will make money
(write a business plan for starting a
restaurant)
• Tell the simpletons to execute the
business plan
Problem Solving

The simpletons can make mistakes
• Refine the communication of
instructions to them


Use time cards, tables, flow charts, pictures
Develop a bullet proof “process”
Problem Solving

You want to make money and you
have a computer to help you
• Devise an algorithm (plan)
• Make the algorithm very detailed so a
simpleton can do it (program)
• Execute the program (computer)
Hardware / Software

A program is a sequence of
instructions that tell the computer
what to do
• What language do computers speak?
• What language do people speak?
Computer Language

Assembly Language
• ADD R1, R2
• MOV [R5], R1
• IF (R4 < R2) JMP A:



Very sequential
Like a flow chart
Not the language of human users
It Gets Worse

Computer logic is even more
primitive
• AND
• OR
• NOT

All programs (nearly every electronic
device you use) operates with only
these three logical operations
It Gets Much Better


Computer software exists to create
an abstraction between AND/OR/NOT
and human language/logic
Programming Languages
• C++, Java, C#, Perl
C++
void main (int argc, char **argv) {
printf (“Hello, world\n”);
}
Java
class program
{
public static void main(String args[]) {
System.out.println("Hello World!");
}
}
Why So Many Languages?

Each has strengths and weaknesses
• Error protection

Syntax in English vs. syntax in German
• Expressiveness

Eskimo words for snow
Multipurpose Computers

How can computers interpret so
many different languages?
• Translate them all into a common
language (machine language)

Compilers!
Recap: Problem Solving



Computers execute machine
language
Programs are a sequence of
instructions in some language
Compilers transform programs from
one language to another, usually a
simpler one
Algorithms

The way one solves a problem
• Divide and conquer
• Top-down or bottom-up
• Simplify
• Deduction
• Trial and error
Dealing Out Cards

Poker: deal five cards to everyone at
the table
How?
(step by step)
Draw a Square
Draw a Triangle
Recap: Algorithms



An approach to solving a problem
A sequence of steps
Break a complex problem into
simpler pieces
The first step in making computers
work for you!
Complexity

There’s a danger here
• Time is scarce
• Simple algorithms may entail inordinate
time and resources
• Computers are simpletons

We must think about an algorithm’s
complexity before using it
Complexity of Cards

Consider dealing five cards
• One second per deal
• How long to finish dealing five cards to:
2 players
Complexity of Cards

Consider dealing five cards
• One second per deal
• How long to finish dealing five cards to:
3 players
Complexity of Cards

Consider dealing five cards
• One second per deal
• How long to finish dealing five cards to:
4 players
Complexity of Cards

Consider dealing five cards
• One second per deal
• How long to finish dealing five cards to:
100 players
Complexity of Cards

It takes 5 * num_players time
time
Number of players
A Linear Time Algorithm
Complexity of Other Problems

Many problems are polynomial (n2)
• Execution time grows as the square of
the problem size (sorting names)
time
Problem size
Complexity of Other Problems

Many problems are exponential (2n)
• Execution time grows as to the nth with
increase in problem size (Traveling
Salesperson Problem)
time
Problem size
Complexity of Other Problems

Some problems are intractable
• There are 1079 atoms in Universe
• It would be impossible to solve an
algorithm this complex
Complexity of Other Problems

Some problems are not computable
• Literally no end to computation to be
donw
Recap: Algorithms


Algorithms have different
complexities
Complexity is important to
understand
• What is knowable?
• How difficult is it to acquire?