1. Arrays

2. Linear Arrays
A linear array is a list of a finite number n of homogeneous data elements (i.e., data elements of the same type) such that:
The elements of the array are referenced respectively by an index set consisting of n consecutive numbers.
The elements of the array are stored respectively in successive memory locations.
The length or the number of data elements of the array can be obtained from the index set by the following formula:
Length = UB - LB + 1

3. Representation of Linear Arrays in Memory
Let LA be a linear array in the memory of the computer.
The computer calculates the address of kth Element of the array by the following formula:
LOC(LA[K]) = Base(LA) + w(K – LB)
Here, W is the number of words per memory cell for the array LA.
1000
1001
1002 .
LA[1]
LA[2]
LA[3] .

4. Traversing a linear array
Algorithm 4.1:
Set K := LB
Repeat step 3 and 4 while K <= UB
Apply PROCESS to LA[K]
Set K := K + 1
Exit

5. Inserting into a linear array
Algorithm 4.2:
INSERT( LA, N, K, ITEM)
Set J := N
Repeat Steps 3 and 4 while J >= K
Set LA[J+1] := LA[J]
Set J := J – 1
Set LA[K] := ITEM
Set N := N + 1
Exit

6. Deleting From a Linear Array
Algorithm 4.3:
DELETE( LA, N, K, ITEM)
Set ITEM := LA[K]
Repeat for J := K to N – 1
Set LA[J] := LA[J+1]
3. Set N := N - 1
4. Exit

7. Searching
Searching refers to the operation of finding an item from a list of items based on some key value.
Two Searching Methods
Linear Search
Binary Search

8. Algorithm: Linear-Search (LA, N, Key)
A linear search is a technique for finding a particular value in a unsorted or sorted list.
Search each item of list using key value, one at a time, until finding the item
from the list.
Algorithm: Linear-Search (LA, N, Key)
Set k := 1 and Loc := 0
Repeat Steps 3 and 4 while k <= N
If Key = LA[k], then Set Loc := k, print: Loc and exit.
Set k := k+1
If Loc = 0 then Write: Item is not in List
Exit
Here
L - The list of data items
N – Total no. of items in L
Key – Item to be searched.

9. Example of Linear Search
List : 10, 6, 222, 44, 55, 77, 24
Key: 55
Steps:
K=1
K=2
K=3
K=4
K=5
So, Item 55 is in position 5. 55 10 6
222 44

10. Complexity Analysis of Linear Search
Worst Case
The worst case occurs when Item is the last element in the List or is not in
the List.
So, C(n) = n = O(n).
(2) Average Case
The average case occurs when the availability of the Item in the List is
equally likely to occur at any position in the List.
So, C(n) = =
= 0(n)