1. Outline lecture Revise arrays Entering into an array
Totalling values in an array
Sequential search

2. 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

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

4. 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?

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. Target ? ?

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

15. 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

16. 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 )
A simple search method is as follows: p193

17. Flowchart for Sequential Search P193
While
Target
Array(R ) and
R<=N
R= R+1 If
R > N F T
Print
Element Not Found
Print
Array(R )

18. Flowchart for Sequential Search using for loopJ 10 1
If target not found
J= J+1 If
Target
found F T
Print
Element Not Found
Print
Array(R )

19. Task :- in pairs Draw an array with 10 integer values
Populate the array with 10 elements
Write an algorithm using the sequential search technique to find the target 6 in the array
Draw a flowchart

20. Demonstration
The more comparisons he longer it takes – time!

21. 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

22. 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

23. 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

24. Task :- in pairs – how many comparisons ?
An iterative sequential search of an array that {a) finds its target; (b) does not find its target
(a) A search for (b) A search for 6
Look at 9
Look at 9
8 <> 9 , so continue searching …
6 <> 9 , so continue searching …
Look at 5
Look at 5

25. 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

26. 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