More Algorithms
2008/09/24: Lecture 6b
CMSC 104, Section 0101
John Y. Park
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More Algorithms
Topics
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Algorithms: Elements in Depth
In-Class Project: Euclid’s Algorithm
In-Class Project: Student Voluteerizer
Reading
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None
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Pseudocode:
Control Structures
Any problem can be solved using only three
logical control structures:
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Sequence
Selection
Repetition
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Sequence
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A series of steps or statements that are
executed in the order they are written.
Example:
Display “Enter two numbers: “
Read <number1>
Read <number2>
<sum> = <number1> + <number2>
Display “sum = “, <sum>
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Sequence
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Some languages…
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Have line numbers
Allow a set of sequenced steps to be grouped as
a “statement block”
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Explicitly bracketed (e.g., with “begin…end” or {…}
Allow “goto”s
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Evil-evil-evil!!!!!
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Sequence

Goto e.g.:
<a> = 0
goto Label3:
Label1:DISPLAY “Hello”
DISPLAY “bye”
Label2:<a> = <a> + 1
DISPLAY <a>
goto Label1:
DISPLAY “Never get here…”
Label3:DISPLAY “Starting up”
goto Label2:
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Sequence
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You should try to avoid the “goto” like the
plague!
In this class, you will never need to use a
“goto”
DON’T USE GOTOs!!!
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Why did I even mention it?
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It is a vehicle for explaining what other control
structures are doing, in a more logical manner
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Selection
 Defines one or more courses of action
depending on the evaluation of a condition.
 Synonyms: conditional, branching,
decision
 Examples:
If (condition is true)
do this
End_if
If (condition is true)
do this
Else
do that
End_if
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Selection
 More complex examples:
 DISPLAY “Enter number to invert”
READ <my_num>
If (<my_num> < 0)
DISPLAY “Don’t like negative numbers”
if (<my_num> < -999)
DISPLAY “… but I guess you really do!”
End_if
Else_if (<my_num> == 0)
<result> = 0
Else
<result> = 1 / <my_num>
End_if
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Repetition
 Allows one or more statements to be
repeated as long as a given condition is true.
 Synonyms: looping, iteration
 Example:
While (condition is true)
do this
End_while
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Repetition
 More complex example (with mistakes)
 DISPLAY “Enter number to compute factorial for”
READ <my_num>
While (<my_num> > 0)
<factorial> = <factorial> * <my_num>
<my_num> = <my_num> - 1
End_while
DISPLAY “The factorial of”, <my_num>, “ is “, <factorial>
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Repetition
 More complex example (with mistakes)
 DISPLAY “Enter number to compute factorial for”
READ <my_num>
<factorial> = 0
While (<my_num> > 0)
<factorial> = <factorial> * <my_num>
<my_num> = <my_num> - 1
End_while
DISPLAY “The factorial of”, <my_num>, “ is “, <factorial>
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Repetition
 More complex example (with mistakes)
 DISPLAY “Enter number to compute factorial for”
READ <my_num>
<factorial> = 0
<saved_my_num> = <my_num>
While (<my_num> > 0)
<factorial> = <factorial> * <my_num>
<my_num> = <my_num> - 1
End_while
<my_num> = <saved_my_num>
DISPLAY “The factorial of”, <my_num>, “ is “, <factorial>
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Pseudocode Style
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Any user prompts should appear exactly as you
wish the programmer to code them.
The destination of any output data should be stated,
such as in “Display”, which implies the screen.
Make the data items clear (e.g., surround them by <
and > ) and give them descriptive names.
Use formulas wherever possible for clarity and
brevity.
Use keywords (such as Read and While) and use
them consistently. Accent them in some manner.
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Pseudocode (con’t)
[Review]
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Use indentation for clarity of logic.
Avoid using code. Pseudocode should not be
programming language-specific.
Always keep in mind that you may not be the person
translating your pseudocode into programming
language code. It must, therefore, be unambiguous.
You may make up your own pseudocode guidelines,
but you MUST be consistent.
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Euclid’s Algorithm
Problem: Find the largest positive integer that divides
evenly into two given positive integers (i.e., the
greatest common divisor).
Algorithm:
1.
2.
3.
Assign M and N the values of the larger and smaller of
the two positive integers, respectively.
Divide M by N and call the remainder R.
If R is not 0, then assign M the value of N, assign N the
value of R, and return to Step 2. Otherwise, the greatest
common divisor is the value currently assigned to N.
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Finding the GCD of 24 and 9
M
N
R
24
9
6
9
6
3
6
3
0
So, 3 is the GCD of 24 and 9.
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Euclid’s Algorithm
Tips about problem # 1 :
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The user should specify the two numbers to factor. She may enter
them in any order (i.e., don't assume first is greater).
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You will need a new arithmetic operation for computing
remainders: the '%' operator. E.g.:
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"24 % 7" equals "3"
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“-5 % 2” equals “-1”, and "18 % -8" equals "+2"
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"7 % 0" equals "the end of the world as we know it."
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The user may input one or both values as negative numbers. You
must either:
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explicitly test for and reject negative numbers

make sure your algorithm computes the correct answer with
them
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Student Voluteerizer
Problem: Write a generic algorithm for helping
call on student “volunteers” in a “fair” manner
<obviously underspecified…>
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