CS107:
Introduction to Computer Science
Lecture 2
Jan 29th
• Last time
– What is not Computer Science
– What is Computer Science
– Algorithms, properties and examples
• Today
– Expressing algorithms: Pseudocode
– Examples
• Algorithm for adding two m-digit numbers
• Algorithm for computing miles-per-gallon
What is Computer Science?
The study of algorithms:
– their formal properties
• correctness, limits
• efficiency/cost (Chapters 2, 3, 10)
– their hardware realizations
• computer design (Chapters 4-6)
– their linguistic realizations
• programming languages (Chapters 7-9)
– their applications
• network design, ocean modeling, bioinformatics, ...
What is an algorithm?
Algorithm = well-defined procedure that allows an agent
to solve a problem.
Algorithms must:
1. Be well-ordered and unambiguous
2. Be executable (understandable),
3. Solve the problem, and
4. Terminate.
Note: often the agent is a computer or a robot…
Example Algorithms
•
•
•
•
•
•
Cooking a dish
Making a peanut-butter jelly sandwich
Shampooing hair
Adding two numbers (p 7)
Programming a VCR (p 6)
Making a pie (p 13)
Designing Algorithms
We need:
• A problem for which an effective algorithm can be
written (i.e., one that is tractable),
• A language (e.g., “pseudocode” or C++),
A methodology for translating the problem into an
algorithm, and
• A computing “agent” that can understand and
execute such algorithms.
Expressing algorithms
• Is natural language good?
– For daily life, yes…but for CS is lacks structure and
would be hard to follow
– Too rich, ambiguous, depends on context
• How about a programming language?
– Good, but not when we try to solve a problem..we want
to think at an abstract level
– It shifts the emphasis from how to solve the problem to
tedious details of syntax and grammar.
Pseudocode
• Pseudocode = English but looks like programming
• Good compromise
– Simple, readable, no rules, don’t worry about
punctuation. Lets you think at an abstract level about
the problem.
– Contains only instructions that have a well-defined
structure and resemble programming languages
Pseudocode elements
Basic (primitive) operations
– Read the input from user
– Print the output to the user
– Cary out basic arithmetical computations
• Conditional operations
– Execute an operation if a condition is true
• Sequential operations
• Repeat operations
– Execute a block of operation multiple times until a certain
condition is met
Variables
Variable
– A named memory location that can store a value
– Think of it as a box into which you can store a value,
and from which you can retrieve a value
Examples:
i
carry
– List variables: used when the input comes as a list of
elements
am-1 am-2
…
…
a1 a0
a 1 a2
a m-1 am
…
…
Expression and assignment statements
Function: change the value of a variable by evaluating
arithmetic expressions
• can use any arithmetic expression, just like on a typical
calculator: +. -. *, /, …
Examples
set the value of m to 2
set the value of i to 6.
set the value of carry to i+2*m
set the value of ai to 0
a 1 a2
a m-1 am
…
…
Input/Output Statements
Function: transfer values from the user to a variable, or viceversa
get values for <variable>
print value of <variable>
• Examples
– Get the value of n from the user
– Get value of the list of elements a1, a2, …,am from
the user
– Print the value of result to the user
Sequential statements
The steps of an algorithm are carried out in the order they are
written.
Conditional statements
Function: specifying a statement that may or may not be done:
if <condition> then
<statement to be done>
else <statement to be done otherwise>
Example
if the value of carry is 0 then set the value of a to
else set the vale of a to a+1
0
Loop statements
Function: specify a group of statements that may be done
several times (repeated):
repeat until <condition>
< statements to be repeated >
• How does this work?
– Condition is evaluated
– If it is true than the loop terminates and the next instruction to be
executed will be the instruction immediately following the loop
– If it is false, then the algorithm executes the <statements to be
repeated> in order, one by one
Example
Step 1: set count to 1
Step 2: repeat step 3 to step 5 until count is > 10
Step 3: set square to count *count
Step 4: print value of square and value of count
Step 5: add 1 to count
Step 6: end
• What does this algorithm do?
• Note: indentation
– Not necessary, but makes reading/understanding algorithms easier
An example pseudocode algorithm (Fig 1.2)
Given: m ≥ 1 and two positive numbers a and b, each
containing m digits, compute the sum c = a + b.
0 Get values for m, am-1 … a0 and bm-1 … b0
1 Set the value of carry to 0.
2 Set the value of i to 0.
3 Repeat steps 4-6 until i > m-1
4 Set the value of ci to ai + bi + carry
5 if ci ≥ 10 then
subtract 10 from ci and set the value of carry
to 1
else set the value of carry to 0
6 Add 1 to i
7 Set the value of cm to carry
So, how does this work???
For example, the input is m = 4, a = 3276, and b = 7345.
After step 0, the variables m, a, and b have those values:
m
4
3 2
a3 a2
7 6
a1 a0
7 3
b3 b2
4 5
b1 b0
After steps 1 and 2, the variables i and carry are initialized.
i
0
carry
0
Next, steps 4-6 are repeated until the value of i > 3. Each
repetition computes a single digit of c.
c4 c3 c2
c1 c0
A model for visualizing an algorithm’s behavior
Computer
Algorithm
Input
(keyboard)
Output
(screen)
Variables
E.g., Visualizing Fig 1.2
Computer
Input
(keyboard)
4
3276
7345
0 Get values for …
…
8 Print value of …
m
4
i
0
carry
3 2
a3 a2
7 3
7 6
a1 a 0
4 5
b3 b2
b1 b0
c4 c3 c2
c1 c0
Output
(screen)
0
Another example: computing MPG (Fig 2.5)
Set response to “Yes”
Repeat steps 2-10 until response = “No”
2 Get gallons, start, end
3 Set distance to end - start
4 Set mpg to distance ÷ gallons
5 Print mpg
6 if mpg > 25.0 then
7
print “You are getting good gas mileage”
8 else print “You are NOT getting good gas
mileage”
9 Print “Do you want to do this again, Yes or No?”
10 Get response
11 Stop
0
1
So, how does this work???
For example, suppose we use 25 gallons, beginning at 12000
and ending at 13000 on the odometer. Then, after step 2,
some variables have the following values:
Yes
25
12000
13000
response
gallons
start
end
After step 4, the variables distance and mpg are computed.
distance
1000
mpg
40
Steps 5-9 displays these results on the output screen:
40
You are getting good gas mileage
Do you want to do this again, Yes or No?
Visualizing Fig 2.5
Computer
Input
(keyboard)
25
12000
13000
0 Set response …
…
11 Stop
response Yes gallons
start
distance
end
mpg
Output
(screen)
Summary
• Pseudocode
–
–
–
–
Get/print statements (input/output statements)
Conditional statements
Sequential statements
Loops
• Algoritms
– Compute sum of two m-digit numbers
– Compute miles-per-gallon
Over the weekend…
1. Get the textbook.
2. Read Chapter 1, 2.1 and 2.2
3. Discuss and solve the problems in the Lab 1
(in groups or individually).
Lab 1 is due on Monday in class.
If you have questions we’ll discuss them in class on Monday.
4.
Bring a digital picture for the lab tomorrow. You will
need it for your website.