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Algorithms II

Problem Solving

and

Pseudocode

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Methods of Problem Solving

Decode this sentence:

Pdeo eo pda yknnayp wjosan.

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Problem Solving

Now that we know what algorithms are, we are going to try some problem solving and write algorithms for the problems.

We’ll 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.

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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?

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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

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A Generic Algorithm

What’s 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

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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.

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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 we’ll be using, it can also include code fragments.

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Brian’s 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?

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Brian’s 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$

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Generic Algorithm

Now, we’ll make a generic algorithm to solve any problem of this type.

Instead of using actual amounts or a description of items, we’ll use variable names.

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Brian’s Clothing Purchases

Brian’s belt cost $9. We’ll call this item1. Brian’s shirt cost 4 times item1. So, we’ll

call 4 the multiplier . Brian’s shirt will be called item2. It can be

calculated by item2 = multiplier X item1. Since Brian had $10 left over, we’ll call that

amountLeft.

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Brian’s Clothing Purchases Cont.

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

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Pseudocode for Brian’s 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

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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.

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Uses of Pseudocode Cont.

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

narrative notation.

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Control Structures

• Sequence• Selection• Repetition

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Sequence

• Series of steps or statements that are executed in the order they are written.

• Example:Get num1 from user

Get num2 from user

sum = num1 + num2

Print “sum = “ sum

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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

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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-bodyend_while

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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 > 0 )

cookiesLeft = cookiesLeft X 2

numChild = numChild - 1 Print “Original number of cookies =”

cookiesLeft