Chapter 2: Design of Algorithms
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Representing algorithms
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How to express algorithms the best?
Possible solutions:
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Natural language
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Natural language
Programming language
Pseudo-Code
+ Known by everyone (that speaks it)
-- Hides the structure of the algorithm
-- Allows ambiguity in expressions
Programming language
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+ Language that computer understands (e.g. Fortran, C, Pascal)
+ Very exact and well structured
-- Very restrictive particularly in early design phases
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Representing Algorithms
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Pseudo-Code: golden medium
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Bases on a natural language (e.g. English)
Uses “programming-language”-like notation (e.g.
statements, conditions etc.)
Examples
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Set x to the value 45
Return
Go to step 100 if condition is satisfied
Types of pseudo-code instructions
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Sequential operations
Conditional operations
Iterative operations
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Representing Algorithms
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Sequential operations
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Input/Output:
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Communication with the outside
Input:
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Output
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Get the value for “variable1” “variable2” …
Example: Get the value of x y z
Print the value for “variable1” “variable2” …
Example: Print the value of x y z
Print the message ‘message content’
Example: Print the message ‘An error has been detected’
Computation:
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Set the value of “variable” to “arithmetic operation”
Example: Set the value of Area to p*r2
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Representing Algorithms
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Conditional operations:
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If “condition” is true then
Set of algorithmic operations
Else
Set of algorithmic operations
Example:
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If denominator = 0 then Print the message ‘Operation cannot
be done’
Else Set fraction to numerator/denominator
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Representing Algorithms
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Iterative operations
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Repeat Step i to j until “condition” becomes true
Step i:
…
Step j:
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Repeat until “condition” becomes true
Set of operations
End of loop
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While “condition” remains true do
Set of operations
End of the loop
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Representing Algorithms
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Examples of iterative operations
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Printing squares of 1 to n:
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Get the value of n
While n > 0 do
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The same algorithm with a repeat loop:
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Get the value of n
If n > 0 then
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Print n2
Set n to n-1
Repeat until n < 1 becomes true
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 Print n
 Set n to n-1
Difference between while and repeat:
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While: pre-check (continuation) condition then perform work (# of
times 0, 1, 2, …)
Repeat: perform work then post-check (termination) condition (# of
times 1, 2, …)
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Representing Algorithms
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Are the three types of operations (sequential,
conditional, iterative) sufficient to represent ANY
possible valid algorithm?
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YES!
Even the most complex algorithms used in e.g.
international switching systems can be represented
using said operations
Compare: We only need few letters (26 in English) to
write the most marvelous novels.
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Algorithmic Problem Solving
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Sequential Search Algorithm
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Problem Statement:
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Given a name N and a telephone book including names
N1 to N1000 and phone numbers T1 to T1000
Task: Find the phone number T of the name N
First solution:
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1.
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…
1001.
1002.
Get N, N1,…,N1000, T1, …T1000
If N = N1 then Print the value T1
If N = N1000 then Print the value T1000
Stop
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Sequential Search Algorithm
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Assessment of the first solution
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+: Algorithm prints all phone numbers of the
given name N
--: Too long listing (1001 lines)
--: Slow: it checks always all entries even
after the phone number has been already
found
--: No error message if the name is not in the list
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Sequential Search Algorithm
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Second solution:
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1. Get N, N1, …, N1000, T1, …, T1000
2. Set i to 1 and mark the N as not yet found
3. Repeat 4 to 7 until N is found
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If N = Ni then
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Print the Phone number is Ti
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Mark N as found
Else
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Add 1 to i
8. Stop
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Sequential Search Algorithm
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Assessment of the second solution
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+: Very short listing (only 8 lines)
+: Quick if N is in the list, it does not check all entries in all cases
--: Big problem: Endless loop if N is not in the list
Final solution:
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1. Get N, N1, …, N1000, T1, …, T1000
2. Set i to 1 and mark the N as not yet found
3. Repeat 4 to 7 until either N is found or i > 1000
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If N = Ni then
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Print the Phone number is Ti
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Mark N as found
Else
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Add 1 to i
8. If N is not marked as found then Print message ‘Name is not in
the directory’
9. Stop
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Finding the Maximum
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Given a list of n numbers
Task: find the largest number in the list
Solution:
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1. Get the value n
2. Get the values A1, A2, …, An
3. Set the value of maximum to A1
4. Set the value of location to 1
5. Set the value of i to 2
6. While i <= n do
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If Ai > maximum then
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Set maximum to Ai
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Set location to I
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Add 1 to I
End of the loop
11. Print maximum and location
12. Stop
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Pattern Matching
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Given a text T (sequence of letters) and a pattern (e.g. word) p
Find the occurrence of p in T
Example:
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Text:
Pattern:
Output:
Text:
Pattern:
Output:
let me know whether or not to go
no
Match starting at position 9
let me know whether or not to go
no
Match starting at position 24
Example: Genome research
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Genome: … T C G A T T G T C C C A G T G C A A A C T G C A T …
Probe:
AAA
(a match)
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Pattern Matching
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Solution:
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1. Get values n and m the size of the text and the pattern
2. Get T1,…,Tn and P1,…,Pm
3. Set k to 1
4. Repeat until k > n-m+1 (until we treated the entire text)
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5. Try to match the pattern P1…Pm at position k
6. If there was a match then
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7. Print the value of k the starting location of the match
8. Add 1 to k (slides to the right)
End of loop
9. Stop
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Pattern Matching
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Step 5 ???
5. Try to match the pattern P1…Pm at position k
Situation:
Text: T1 T2 … Tk Tk+1…Tk+m-1 Tk+m …Tn
Pattern:
P 1 P2 … Pm
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Algorithm for Step 5
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Set i to 1 and mismatch to no
Repeat until (i > m) or mismatch = yes
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If Pi not equal Tk+i-1 then
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Else
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Set mismatch to yes
Set i to i+1
End of loop
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