CMPT 120

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CMPT 120

• Introduction to Computer Science and Programming
  I
• Chris Schmidt

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Algorithms

• What is an algorithm?
• An algorithm is a set of instructions on how to
  accomplish something
• The basic idea can be applied to many typical
  activities
• Recipes, assembly instructions, directions on how
  to get somewhere could all be viewed as types of
  algorithms

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Algorithms

• Recipe Example from Study Guide
• Combine the room-temperature butter and the
  sugar. Mix until light and fluffy.
• Add the eggs to the creamed butter and mix to
  combine.
• In another bowl, combine the liquid ingredients
  and mix to combine.
• Sift together the flour and other dry
  ingredients.
• Alternately add the dry and liquid ingredients to
  the butter-egg mixture. Mix just enough to
  combine.

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Algorithms

• Aspects of a proper algorithm
• Solves a problem
• How to make muffins
• Unambiguous instructions
• Step 5 isnt entirely clear
• Completes in a finite amount of time given proper
  input
• This clearly does

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Algorithms

• What sort of problems are algorithms created for?
• Sorting and searching
• Well be looking at some well known algorithms
  for this later in the semester
• Encryption and Decryption
• Mathematical factoring, finding prime numbers
• Idea can be applied to any problem you want to
  write code to solve

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Algorithms

• Check if a user entered number is prime
• Ask the user for a number to check the primeness
  of.
• Start with divisor equal to 2.
• If the users number is divided evenly by the
  divisor, it is not prime. You are done.
• If the divisor squared is less than the users
  number, increase it by one and go to step 3.
• If youve reached this step, the users number is
  prime.

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Algorithms

• Aspects of a proper algorithm
• Solves a problem
• Tests if a user entered number is prime
• Unambiguous instructions
• Completes in a finite amount of time given proper
  input
• What if step 4 didnt compare the divisor with
  the square root of the users number?

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Pseudocode

• So far weve used natural language to describe
  algorithms
• It is helpful to describe algorithms in
  pseudocode (almost code)
• An algorithm written in pseudocode is then easily
  coded in any give programming language

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Pseudocode

• Digital Clock Example from Study Guide
• set hour to 0
• set minute to 0
• set second to 0
• repeat forever
• set second to second 1
• if second is more than 59, then
• set second to 0
• set minute to minute 1
• if minute is more than 59, then
• set minute to 0
• set hour to hour 1
• if hour is more than 23, then
• set hour to 0
• write hour minutesecond
• wait for 1 second

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Pseudocode

• Pseudocode for prime number example
• set divisor to 2
• write Enter an integer greater than 2
• read userNumber
• repeat while divisor2 lt userNumber
• if userNumber divisor is equal to 0
• write The number is not prime, it is divisible
  by
• write divisor
• exit program
• set divisor to divisor 1
• write The number is prime.

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Writing a Program

• Define the problem
• Create a plan (algorithm) to solve the problem
• Translate your algorithm into code
• Test and make adjustments to your code and
  algorithm as neede

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Creating an Algorithm

• What to keep in mind when creating your algorithm
• Read in all needed input
• Proper output
• What are the normal cases (possibilities) based
  on the input?
• Are there any special cases?

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Algorithm Example

• Problem Find the roots (real) of a quadratic
  equation.
• Quadratic Equation ax2 bx c
• The roots are where this formula is equal to 0,
  ax2 bx c 0
• Ex. a1,b0,c-1 x2 1 (x-1) (x1) 0
  roots at x1,x-1

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Algorithm Roots of Quadratic Formula

• How do we find the roots?
• Quadratic equation
• Does this formula always work?

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Algorithm Roots of Quadratic Formula

• Input the coefficients a,b,c
• Output the roots of ax2 bx c
• What cases do we need to handle?

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Algorithm Roots of Quadratic Formula

• What cases do we need to handle?
• Normal
• Two distinct roots
• One root
• But what special cases do we need to be careful
  of?
• No roots 4ac gt b2
• a0 (straight line bxc0 root at c/b)
• a0,b0 (horizontal line, no roots unless c 0)
• a0,b0,c0 (infinite roots)

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Algorithm Roots of Quadratic Formula Pseudocode

• write Enter the coefficients of the formula
• read a,b,c
• if a,b,and c equal 0
• write infinite roots
• exit
• if a and b equal 0
• write no roots
• exit
• if a equals 0
• root -c/b
• write One root at x, root
• exit
• .
• .
• .

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Testing

• Remember once youve translated your pseudocode
  into actual code that you need to test every
  possible case