fundamentals of algorithms

• computational thinking


  the thought process involved in formulating a problem and expressing its solution in such a way that a computer can effectively carry out
• decomposition


  breaking down the problem into smaller sub-problems, so that each sub-problem accomplishes an identifiable task
• pattern recogntition 


  finding repeating patterns that could be solved quickly
• abstraction

  removing unnecessary detail from a problem
• algorithm creation


  creating a step by step set of instructions to solve the problem
• algorithm


  a step-by-step solution to solve a problem ina finite number of steps
• three parts to an algorithm:

  • input - the values that are put into the algorithm
  • process - what happens in the algorithms
  • output - the value that the algorithm produces
• flowcharts


  a graphical way of displaying an algorithm
• flow chart symbols

  A) start/stop

  B) beginning

  C) end

  D) process

  E) assign

  F) do something

  G) decision

  H) calculation

  I) direction

  J) 1

  K) answers

  L) input/output

  M) input

  N) output

  O) connector

  P) connectors

  Q) direction

  R) flow

  S) travel

  
• comparing flowcharts to pseudocode

  • pseudocode is much easier to create accurate and detailed algorithms
  • flow charts are an easier way to see the flow of a program and how it runs from start to finish
• pseudocode


  text that is written programmatically but designed to be read by humans and not a machine
• variable assignment in pseudocode

  IDENTIFIER <- value
• user input in pseudocode

  variable <- USERINPUT
• output(print) in pseudocode

  OUTPUT StringExp
• random integer in pseudocode

  RANDOM_INT(IntExp, IntExp)
• commentsin pseudocode

  # comment
• trace tables


  a way for us to track the value of a variable through a program, they are very useful for helping to identify logic errors
• we can compare how efficient algorithms are by calculating how much time they take to complete a task and we can do that by working out how many calculations are required for the algorithm to be completed