©brooks/cole, 2003 chapter 8 algorithms. ©brooks/cole, 2003 conceptconcept 8.1

©Brooks/Cole, 2003

Chapter 8

Algorithms

©Brooks/Cole, 2003

CONCEPTCONCEPT

8.18.1

©Brooks/Cole, 2003

Figure 8-1

Informal definition of an algorithm used in a computer

©Brooks/Cole, 2003

Figure 8-2

Example: Finding the largest integer

• We want to find the largest integer among a list positive integers.

• This task cannot be done in one step.

• This algorithm is called FindLargest

©Brooks/Cole, 2003

Figure 8-3

Defining actions in FindLargest algorithm1. The action is not the same as the other steps

2. The wording is not the same

The Algorithm needs to be refined

©Brooks/Cole, 2003

Figure 8-4

FindLargest RefinementStep 0 initializes the largest to zero

The wording is the same

©Brooks/Cole, 2003

Figure 8-5

Generalization of FindLargest

• This is a generalized form of the FindLargest algorithm.• N is the number of integers.

©Brooks/Cole, 2003

THREE CONSTRUCTSTHREE CONSTRUCTS

8.28.2

©Brooks/Cole, 2003

Figure 8-6

Three constructs to a structured program

• It has been proven there is no need for any other construct.• Those three constructs makes a program or an algorithm easy to understand, debug and change.

If the result of the test is true follow a sequence of instructions, if false, follow different instructions

The same sequence of instructions are repeated

sequence of instructions

©Brooks/Cole, 2003

ALGORITHMALGORITHMREPRESENTATIONREPRESENTATION

8.38.3

©Brooks/Cole, 2003

Figure 8-7Flowcharts for three constructs

(Pictorial Representation)

©Brooks/Cole, 2003

Figure 8-8

Pseudocode for three constructs(Englishlike Representation)

©Brooks/Cole, 2003

Example 1Example 1

Write an algorithm in pseudocode that finds the average of two numbers

SolutionSolution

See Algorithm 8.1 on the next slide.

©Brooks/Cole, 2003

AverageOfTwoInput: Two numbers

1. Add the two numbers2. Divide the result by 23. Return the result by step 2

End

Algorithm 8.1:Algorithm 8.1: Average of twoAverage of two

©Brooks/Cole, 2003

Example 2Example 2

Write an algorithm to change a numeric grade to a pass/no pass grade.

SolutionSolution


©Brooks/Cole, 2003

Pass/NoPassGradeInput: One number

1. if (the number is greater than or equal to 70)then 1.1 Set the grade to “pass”else 1.2 Set the grade to “nopass”End if

2. Return the gradeEnd

Algorithm 8.2:Algorithm 8.2: Pass/no pass GradePass/no pass Grade

©Brooks/Cole, 2003

Example 3Example 3

Write an algorithm to change a numeric grade to a letter grade.

SolutionSolution


©Brooks/Cole, 2003

LetterGradeInput: One number

1. if (the number is between 90 and 100, inclusive)then 1.1 Set the grade to “A”End if

2. if (the number is between 80 and 89, inclusive)then 2.1 Set the grade to “B”End if

Algorithm 8.3:Algorithm 8.3: Letter gradeLetter grade

Continues on the next slide

©Brooks/Cole, 2003

3. if (the number is between 70 and 79, inclusive)then 3.1 Set the grade to “C”End if

4. if (the number is between 60 and 69, inclusive)then 4.1 Set the grade to “D”End if

Algorithm 8.3:Algorithm 8.3: Letter grade (continued)Letter grade (continued)

Continues on the next slide

©Brooks/Cole, 2003

5. If (the number is less than 60)then 5.1 Set the grade to “F”End if

6. Return the gradeEnd

Algorithm 8.3:Algorithm 8.3: Letter grade (continued)Letter grade (continued)

©Brooks/Cole, 2003

Example 4Example 4

Write an algorithm to find the largest of a set of numbers. You do not know the number of numbers.

SolutionSolution


©Brooks/Cole, 2003

FindLargestInput: A list of positive integers

1. Set Largest to 02. while (more integers)

2.1 if (the integer is greater than Largest) then 2.1.1 Set largest to the value of the

integer End ifEnd while

3. Return LargestEnd

Algorithm 8.4:Algorithm 8.4: Find largestFind largest

©Brooks/Cole, 2003

Example 5Example 5

Write an algorithm to find the largest of 1000 numbers.

SolutionSolution


©Brooks/Cole, 2003

FindLargestInput: 1000 positive integers

1. Set Largest to 02. Set Counter to 03. while (Counter less than 1000)

3.1 if (the integer is greater than Largest) then 3.1.1 Set Largest to the value of the integer

End if 3.2 Increment CounterEnd while


Algorithm 8.5:Algorithm 8.5: Find largest of 1000 numbersFind largest of 1000 numbers

©Brooks/Cole, 2003

MORE FORMALMORE FORMALDEFINITIONDEFINITION

8.48.4

©Brooks/Cole, 2003

Algorithm

• Algorithm is an ordered set of unambiguous steps that produces a result and terminate in a finite time.

• Ordered set; must be ordered set of instructions.• Unambiguous; each step must be clearly defined.• Produces result; if not the algorithm is useless.• Terminate in finite time; if it doesn’t, then it is

not an algorithm.

©Brooks/Cole, 2003

SUBALGORITHMSSUBALGORITHMS

8.58.5

©Brooks/Cole, 2003

Figure 8-9

Concept of a subalgorithm

• The principle of structured programming requires breaking the algorithm into smaller units called subalgorithms.

• Each subalgorithm is then divided into smaller units until the subalgorithm become intrinsic (understood immediately)

©Brooks/Cole, 2003

FindLargestInput: A list of positive integers

1. Set Largest to 02. while (more integers)

2.1 FindLargerEnd while


Algorithm 8.6:Algorithm 8.6: Find largestFind largest

FindLargerInput: Largest and current integer

1. if (the integer is greater than Largest)then 1.1 Set Largest to the value of the integerEnd ifEnd

©Brooks/Cole, 2003

Structure Chart

• Is a tool that shows the relationship between different modules in an algorithm.

• It is mostly used at design level.• See Appendix E

©Brooks/Cole, 2003

BASICBASICALGORITHMSALGORITHMS

8.68.6

©Brooks/Cole, 2003

Figure 8-10Summation

©Brooks/Cole, 2003

Figure 8-11Product

Exercise;XN ?

©Brooks/Cole, 2003

Finding the Smallest

• Finding the smallest is similar to finding the largest with two differences. First, the decision is to find the smallest. Second, initialized with a very large number.

©Brooks/Cole, 2003

Sorting

• Is the process by which data are arranged according to their value.

• There are three sorting algorithms;1.Selection sort2.Bubble sort3.Insertion sort

©Brooks/Cole, 2003

Figure 8-12

Selection sort

©Brooks/Cole, 2003

Search Algorithm

• Searching is the process of finding a location of a target in a list of objects.

• There are two basic searches for lists:1.Sequential Search.2.Binary Search.

©Brooks/Cole, 2003

Figure 8-20: Part II

Example of a sequential sort

• Used for small and unsorted lists• Sequential sort is very slow

©Brooks/Cole, 2003

Figure 8-23

Iterative and Recursive Algorithms

• An Algorithm is iterative whenever the definition doesn’t involve the algorithm itself.

• An Algorithm is recursive whenever it appears in the definition itself.

©Brooks/Cole, 2003

FactorialInput: A positive integer num

1. Set FactN to 02. Set i to 13. while (i is less than or equal to num)

3.1 Set FactN to FactN x I 3.2 Increment iEnd while

4. Return FactNEnd

Algorithm 8.7:Algorithm 8.7: Iterative factorialIterative factorial

©Brooks/Cole, 2003

FactorialInput: A positive integer num

1. if (num is equal to 0)then 1.1 return 1else1.2 return num x Factorial (num – 1) End ifEnd

Algorithm 8.8:Algorithm 8.8: Recursive factorialRecursive factorial

Much easier, more elegant and simple for creator and reader.

©brooks/cole, 2003 chapter 8 algorithms. ©brooks/cole, 2003 conceptconcept 8.1

Documents