Algorithms III

1
Algorithms III

• Problem Solving
• and
• Pseudocode

2
Methods of Problem Solving

• Decode this sentence
• Pdeo eo pda yknnayp wjosan.

3
Problem Solving

• Now that we know what algorithms are, we are
  going to try some problem solving and write
  algorithms for the problems.
• Well start with step-by-step instructions that
  solve a particular problem and then write a
  generic algorithm that will solve any problem of
  that type.

4
Someone stole a cookie from the cookie jar

• Momma had just filled the cookie jar when the
  three children went to bed. That night one child
  woke up, ate half the cookies and went back to
  bed. Later the second child woke up, ate half
  the remaining cookies, and went back to bed.
  Still later the third child woke up, ate half the
  remaining cookies, leaving 3 cookies in the jar.
  How many cookies were in the jar to begin with?

5
Solve the Problem

• 3 cookies left X 2 6 cookies left after
  2nd child
• 6 X 2 12 cookies left after 1st child
• 12 X 2 24 original number of cookies

6
A Generic Algorithm

• Whats a generic algorithm for this problem?
• An algorithm that will work with any number of
  remaining cookies
• AND
• that will work with any number of children

7
Generic Algorithm for Cookie Problem

• Get number of children as input from the user.
• Get number of remaining cookies as input from the
  user.
• While there are still children that have not
  raided the cookie jar, multiply the number of
  cookies by 2 and reduce the number of children by
  1.
• Print the original number of cookies.

8
Pseudocode

• When we broke down the previous problem into
  steps, we expressed each step as an English
  phrase.
• We can think of this as writing pseudocode for
  the problem.
• Typically, pseudocode is a combination of English
  phrases and formulas.
• If we know the programming language that well be
  using, it can also include code fragments.

9
Brians Shopping Trip

• Brian bought a belt for 9 and a shirt that cost
  4 times as much as the belt. He then had 10.
  How much money did Brian have before he bought
  the belt and shirt?

10
Brians Shopping Trip

• First we solve the problem to help us identify
  the steps.
• 9 4 X 9 START -10
• 9 36 START - 10
• 45 START -10
• 55 START

11
Generic Algorithm

• Now, well make a generic algorithm to solve any
  problem of this type.
• Instead of using actual amounts or a description
  of items, well use variable names.

12
Brians Clothing Purchases

• Brians belt cost 9. Well call this item1.
• Brians shirt cost 4 times item1. So, well call
  4 the multiplier .
• Brians shirt will be called item2. It can be
  calculated by item2 multiplier X item1.
• Since Brian had 10 left over, well call that
  amountLeft.

13
Brians Clothing Purchases Cont.

• Brian started with start dollars.
• item1 item2 start - amountLeft
• start item1 item 2 amountLeft

14
Pseudocode for Brians Clothing Problem Algorithm

• Get price of item1 from user
• Get multiplier from user
• Get amountLeft from user
• Calculate item2 (item2 multiplier X item1)
• Calculate start (start item1 item2
  amountLeft)
• Print The starting amount start

15
Uses of Pseudocode

• Used in designing algorithms.
• Used in communicating to users.
• Used in implementing algorithms as programs.
• Used in debugging logic errors in programs.

16
Uses of Pseudocode Cont.

• Must have a limited vocabulary.
• Must be easy to learn.
• Must produce simple, English-like narrative
  notation.

17
Control Structures

• Sequence
• Selection
• Repetition

18
Sequence

• Series of steps or statements that are executed
  in the order they are written.
• ExampleGet num1 from user
• Get num2 from user
• sum num1 num2
• Print sum sum

19
Selection

• Defines one or two courses of action depending on
  the evaluation of a condition.
• A condition is an expression that is either true
  or false.
• Example if condition (is true) do this
• else do that end_if

20
Repetition

• Many times there will be a group of statements
  that should be repeated.
• These statements will make up what is known as
  the body of a loop.
• Example
• while condition (is true)
• loop-body end_while

21
Pseudocode for Cookie Problem

• Get number of children as input from the user,
  numChild.
• Get number of remaining cookies as input from the
  user, cookiesLeft.
• while (numChild gt 0 )
• cookiesLeft cookiesLeft X 2
• numChild numChild - 1
• Print Original number of cookies cookiesLeft