Chapter 2: Design of Algorithms

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Chapter 2 Design of Algorithms

• Representing algorithms
• How to express algorithms the best?
• Possible solutions
• Natural language
• Programming language
• Pseudo-Code
• Natural language
• Known by everyone (that speaks it)
• -- Hides the structure of the algorithm
• -- Allows ambiguity in expressions
• Programming language
• 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

• 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

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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 pr2

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Representing Algorithms

• Conditional operations
• If condition is true then
• Set of algorithmic operations
• Else
• Set of algorithmic operations
• Example
• If denominator 0 then Print the message
  Operation cannot be done
• Else Set fraction to numerator/denominator

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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
• Set of operations
• End of the loop

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Representing Algorithms

• Examples of iterative operations
• Printing squares of 1 to n
• Get the value of n
• While n gt 0 do
• Print n2
• Set n to n-1
• The same algorithm with a repeat loop
• Get the value of n
• If n gt 0 then
• Repeat until n lt 1 becomes true
• Print n2
• Set n to n-1
• 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, )

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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.

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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
• 1001. If N N1000 then Print the value T1000
• 1002. Stop

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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

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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

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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 gt
  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

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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 lt n do
• 7. If Ai gt 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

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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
• Text let me know whether or not to go
• 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)

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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 gt n-m1 (until we treated the
  entire text)
• 5. Try to match the pattern P1Pm 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

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Pattern Matching

• Step 5 ???
• 5. Try to match the pattern P1Pm at position k
• Situation
• Text T1 T2 Tk Tk1Tkm-1 Tkm Tn
• Pattern P1 P2 Pm
• Algorithm for Step 5
• Set i to 1 and mismatch to no
• Repeat until (i gt m) or mismatch yes
• If Pi not equal Tki-1 then
• Set mismatch to yes
• Else
• Set i to i1
• End of loop