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Outline lecture

- Revise arrays
- Entering into an array
- Totalling values in an array
- Sequential search

What is an Array

- We are interested in one-dimensional arrays
- An array has a fixed number of elements and all elements are of the same type
- Each box has an index which in java and C++ starts with 0
- Here is an array which holds the ages of 10 people

0 1 2 3 4 5 6 7 8 9

32 34 56 32 12 67 21 34 21 45

0 1 2 3 4 5 6 7 8 9

32 34 56 32 12 67 21 34 21 45

- Lets look at this array in detail
- What do you notice about the array ?
- Is the data organised in any particular way?

Examples of Arrays

- Draw an array of 20 elements which contains student marks – what type will it be ?
- Draw an array of 15 elements which contains student grades ranging form A-E – what type will it be?

Entering data into an array

- When you enter data into an array we use a loop
- What type of loop do you think we will use?
- Hint – we know the number of elements there are in the array
- Use a counter to keep track of how many elements are entered into the array

Entering data into an array

Read

- Algorithm
- Loop : R = 1 to 10
- Enter A( R)
- Loop end
- The number of elements in array is 10
- The counter of loop (R ) allows the computer to increase the element number by 1 each time a piece of data is entered into a memory location
- The computer can find a particular element in the array by using the reference number index represented by R
- R = loop counter
- A(R ) = element R in the A array

- R
- 10
- 1

Enter

A(R )

R

B

Accumulating the elements of array

Calc

- You may need to sum the elements of an array
- Initialise the sum variable which contains the total to zero
- The instruction Sum = Sum + A(R ) tells the computer to add the valve of element A(R ) to the old valve of the sum (Sum) and to store the result into sum memory location (Sum)
- Algorithm
- Loop : R = 1 to 10
- sum = Sum + A( R)
- Loop end
- The number of elements in array is 10
- The counter of loop (R ) allows the computer to increase the element number by 1 each time a piece of data is entered into a memory location
- Sum = Sum of the elements of A
- A(R ) = element R in the A array

- R
- 5
- 1

Sum = Sum +

A(R )

R

B

Why Search ?

- Everyday life -We always Looking for something – builder yellow pages, universities, hairdressers
- Computers can search
- World wide web –
- Spreadsheet –
- Databases –
- Large records – 1000s takes time - many comparison slow system – user wont wait long time

Search Algorithms

- Different types – Sequential Search, Binary Search
- Discuss - search algorithms - analyze them
- Analysis of the algorithms enables programmers to decide which algorithm to use for a specific application

Some observations – Key

- each item in a data set - special member that uniquely identifies the item in the data set
- For e.g University - a data set which contains student records – student ID uniquely identifies each student
- This unique member of the item is called Key of the item

Some observations - Key

- Where can Keys of the item in a data set be used in ?
- When searching the data set - for a particular item, what do we do ?
- compare the key of the item for which we are searching - with the keys of the items in the data set – e.g if we looking particular student id in a list of student id exam results

Analysis of Algorithms

- In addition to describing the algorithms – analyse them
- What does analysis of algorithms involve ?
- key comparisons
- Moreover – the number of key comparisons refers to - the number of times the key of the item (in search & sort algorithms) is compared with the keys of the items in the list

Sequential search (linear search)

- Problem :- we want to search for a given element in a list.
- Do we know where the target element occurs?.

Sequential search (linear search)

- We can have no guarantees about the order of elements in the list if (for example) insertions have been under a user’s control.
- Search starts at the first element in the list and continues until either the item is found in the list - or entire list is searched

A simple search method is as follows: p193

- Algorithm
- R = 1
- While Array(R ) <> Target
- R = R + 1
- WhileEnd
- If R > N
- Then
- Print “Element Not Found”
- Else
- Print Array (R )

Flowchart for Sequential Search P193Print

Print

R = 1

While

Target

Array(R ) and

R<=N

R= R+1

If

R > N

F

T

Element Not Found

Array(R )

Flowchart for Sequential Search using for loopPrint

Print

- J
- 10
- 1

If target not found

J= J+1

If

Target

found

F

T

Element Not Found

Array(R )

Task :- in pairs

- Draw an array with 10 integer values
- Populate the array with 10 elements

1 5 6 3 7 8 9 5 2 3

- Write an algorithm using the sequential search technique to find the target 6 in the array
- Draw a flowchart

Demonstration

- http://www.cosc.canterbury.ac.nz/people/mukundan/dsal/LSearch.html

The more comparisons he longer it takes – time!

Sequential search (linear search)

- If the search item is found, its index (that is its location in array) is returned. If search is unsuccessful, -1 is returned
- Note the sequential search does not require the list elements to be in any particular order

Sequential Search Analysis : Task – in pairs

- For each iteration in the loop, the search item is compared with an element in the list,and a few other statements are executed. Loop terminates when search item is found in list
- Therefore the execution of the other statement in loop is directly related to the outcome of the key comparisons

Sequential Search Analysis

- When analysing a search algorithm, - count the number of key comparisons –why ?
- because this number gives us the most useful information,
- this criterion for counting the number of key comparisons can be applied equally well to other search algorithms

An iterative sequential search of an array that {a) finds its target; (b) does not find its targetTask :- in pairs – how many comparisons ?

(a) A search for 8 (b) A search for 6

Look at 9

Look at 9

9 5 8 4 7

9 5 8 4 7

8 <> 9 , so continue searching …

6 <> 9 , so continue searching …

Look at 5

Look at 5

9 5 8 4 7

9 5 8 4 7

Sequential Search Analysis

- Suppose the search item is in the list
- Then number of key comparisons depends on where in the list the search item is located.
- If search item is first element of L – make one key comparison – best case
- Worst case search item is the last item – algorithm makes n comparisons

Sequential Search Analysis

- If the search item Target , is the first element in list, how many one comparisons are needed?
- if target is second, how many one comparisons are needed?
- So if the target is the kth element in the list k comparisons are made

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