1. Chapter 2: Design of Algorithms
Representing algorithms
How to express algorithms the best?
Possible solutions:
Natural language
Programming language
Pseudo-Code
+ Known by everyone (that speaks it)
-- Hides the structure of the algorithm
-- Allows ambiguity in expressions
+ Language that computer understands (e.g. Fortran, C, Pascal)
+ Very exact and well structured
-- Very restrictive particularly in early design phases

2. Representing Algorithms
Pseudo-Code: golden medium
Bases on a natural language (e.g. English)
Uses “programming-language”-like notation (e.g. statements, conditions etc.)
Examples
Set x to the value 45
Return
Go to step 100 if condition is satisfied
Types of pseudo-code instructions
Sequential operations
Conditional operations
Iterative operations

3. Representing Algorithms
Sequential operations
Input/Output:
Communication with the outside
Input:
Get the value for “variable1” “variable2” …
Example: Get the value of x y z
Output
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:
Set the value of “variable” to “arithmetic operation”
Example: Set the value of Area to p*r2

4. Representing Algorithms
Conditional operations:
If “condition” is true then
Set of algorithmic operations
Else
Example:
If denominator = 0 then Print the message ‘Operation cannot be done’
Else Set fraction to numerator/denominator

5. Representing Algorithms
Iterative operations
Repeat Step i to j until “condition” becomes true
Step i: …
Step j:
Repeat until “condition” becomes true
Set of operations
End of loop
While “condition” remains true do
End of the loop

6. Representing Algorithms
Examples of iterative operations
Printing squares of 1 to n:
Get the value of n
While n > 0 do
Print n2
Set n to n-1
The same algorithm with a repeat loop:
If n > 0 then
Repeat until n < 1 becomes true
Difference between while and repeat:
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, …)

7. Representing Algorithms
Are the three types of operations (sequential, conditional, iterative) sufficient to represent ANY possible valid algorithm?
 Y E S !
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.

8. Algorithmic Problem Solving
Sequential Search Algorithm
Problem Statement:
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:
1. Get N, N1,…,N1000, T1, …T1000
2. If N = N1 then Print the value T1 …
If N = N1000 then Print the value T1000
Stop

9. Sequential Search Algorithm
Assessment of the first solution
+: 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

10. Sequential Search Algorithm
Second solution:
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
4. If N = Ni then
5. Print the Phone number is Ti
6. Mark N as found
Else
7. Add 1 to i
8. Stop

11. Sequential Search Algorithm
Assessment of the second solution
+: 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:
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
4. If N = Ni then
5. Print the Phone number is Ti
6. Mark N as found
Else
7. Add 1 to i
8. If N is not marked as found then Print message ‘Name is not in the directory’
9. Stop

12. Finding the Maximum Given a list of n numbers
Task: find the largest number in the list
Solution:
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
7. If Ai > maximum then
8. Set maximum to Ai
9. Set location to I
10. Add 1 to I
End of the loop
11. Print maximum and location
12. Stop

13. Pattern Matching
Given a text T (sequence of letters) and a pattern (e.g. word) p
Find the occurrence of p in T
Example:
Text: let me know whether or not to go
Pattern: no
Output: Match starting at position 9
Pattern: no
Output: Match starting at position 24
Example: Genome research
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: A A A (a match)

14. Pattern Matching Solution:
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)
5. Try to match the pattern P1…Pm at position k
6. If there was a match then
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

15. Pattern Matching
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: P1 P2 … Pm
Algorithm for Step 5
Set i to 1 and mismatch to no
Repeat until (i > m) or mismatch = yes
If Pi not equal Tk+i-1 then
Set mismatch to yes
Else
Set i to i+1
End of loop