Problems Solving with Programming

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Problems Solving with Programming

• What is programming ?
• Algorithms Properties
• Algorithms Specification
• Algorithms Design
• Algorithms Construction
• Algorithms Description

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Problems Solving with Programming

• Programming means solving problems with the help
  of a computer
• PROBLEM ? COMPUTER ?
• 
  SOLUTION

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Problems Solving with Programming

• Designing an algorithm
• Writing the problem
• Feeding the program and data into the computer

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Problems Solving with Programming

• Algorithms are instructions for the solving of
  problems
• Examples from everyday life -cooking recipes
  calculation of formulas rules of a game.
• An instruction is called an algorithm, when the
  following applies

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Problems Solving with Programming

• Condition 1 The description is of finite
  length.
• Condition 2 The process will come to an end
  after the execution of a finite number of
  operations. (Counterexample Repeat the steps 1
  to 3 until you have won 1 Million (1) Fill in a
  lottery coupon (2) hand it in at a lottery
  agency (3) wait for the next draw and collect
  your winnings).

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Problems Solving with Programming

• Condition 3 The sequence in which the
  operations have to be applied must be determined
  unambiguously.
• Prepare the soup according to the
  instructions on the can. At the end add some
  asparagus pieces. Cut the ham in strips (It is
  not quite clear when the operation Put in some
  pieces of esparagus has to be executed.

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Problems Solving with Programming

• Condition 4 The effect of each operation has
  been defined unambiguously.
• Otherwise there could be unwelcome results.
• Important properties of an algorithm - Finite
  description , - Efficiency , - Definite effect
  , - Termination.

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Problems with Solving Programming

• The inner structure of an algorithm can be
  described by listing the steps that have to be
  done
• ALGORITHM Inner structure Do this then
  do that
• A so-called outer behaviour of an algorithm
  takes only the effect of algorithm into account.
  It is also called the specification of an
  algorithm.

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Problems Solving with Programming

• Algorithm
• Input Data (Outer behaviour)
• Do this data do that (Inner structure) BLACK
  BOX
• Output Data (Outer behaviour)
• The outer behaviour of an algorithm has to be
  described before the inner structure.
• The relation between input and output data is
  important for the specification. There are two
  conditions for the specification precondition V
  and postcondition N.

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Problems Solving with Programming

• Consider the following example of a specification
  
• (LIST is a list of 100 numbers) Outer
  behaviour
• SORT
• (for all I between 1 and 99 LISTI lt
  LISTI1) Outer behaviour .
• SORT The specification indicates that the
  algorithm SORT no matter what is looks like
  will sort a list of 100 numbers into ascending
  order.

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Problems Solving with Programming

• General form of specification V A N
  with
• V precondition
• A desired algorithm
• N postcondition

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Problems Solving with Programming

• Algorithms Design Of all the steps of
  programming, the first is the most difficult.
• Designing an algorithm
• Writing the program
• Feeding the program and data into the computer.

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Problems Solving with Programming

• How do you find an algorithm for a given problem
  ?
• Phase 1 A problem is reduced to simple
  subproblems.
• Phase 2 Searching for algorithms for the
  simple problems and putting them together to form
  the whole algorithm.
• Example for the reduction of problems You Have
  invited guests for dinner and are planning a
  menu.
• The first question What is the menu to consist
  of ?
• Menu appetizers --- main course ---
  dessert.
• appetizers grapefruit cocktail salmon
  sandwiches.

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Problems Solving with Programming

• Algorithms design
• Counterpart for the Top-Down-Strategy is called
  Bottom-Up-Strategy.
• The Bottom-Up-Strategy deals with putting smaller
  problems together

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Problems Solving with Programming

• Algorithms are usually made up of three
  constructs of smaller partial algorithms
• Composition sequential execution
• Selection alternative execution
• Iteration repeated execution .
• By nesting these constructs even complicated
  algorithms can be represented.

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Problems Solving with Programming

• Composition A1 and A2 are two algorithms.
  With composition, A1 is started first. When A1
  is finished, A2 is them started.
• It is important that A1 terminates (finishes)
  after a finite amount of time, otherwise A2
  cannot ever be started.
• Selection (alternative execution)
• Selection A1, A2 and A3 are algorithms. A1 is
  executed first, depending on the result either A2
  or A3 is started.

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Problems Solving with Programming

• Iteration repeated execution.
• A1 and A2 are algorithms. A1, A2 are repeated
  until A1 becomes FALSE.

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Problems Solving with Programming

• Algorithm description An algorithm can be
  presented
• In colloquial form
• As a graphical representation
• Using programming languages .
• Colloquial language is not quite suitable for the
  presentation of algorithms, because of the
  following problems
• Ambiguities
• Incompleteness
• inaccuracy

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Problems Solving with Programming

• 2. Graphical presentation by means of
• Flows charts are nets of individual symbols
  with definite meanings
• Structograms consists of nestings of
  individual symbols with definite meanings.
• 3. If algorithms are to be executed by computers
  they have to be represented in a certain
  programming language.