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Linear Data structures

- Linear form a sequence
- Linear relationship b/w the elements
- represented by means of sequential memory location
- Link list and arrays are linear relationship
- Non-Linear Structure are Trees and Graphs

Operation performed by Linear Structure

- Traversal: Processing each element in the list
- Search : Find the location of the element with a given value or the record with a given key
- Insertion : Adding new element to the list
- Deletion : Removing an element from the list
- Sorting : Arranging the elements in some type of order
- Merging : Combining two list into single list

Linear Array

- List of finite number N of homogenous data elements (i.e. data elements of same type) such that
- The elements of the array are referenced respectively by an index set consisting of N consecutive number
- The elements of the array are stored respectively in successive memory location

Length of Array

- N = length of array

Length = UB – LB + 1

- UB = Upper Bound or Largest Index
- LB= Lower Bound or smallest Index

Representation in Memory

- Address of any element in Array =

LOC(LA[k])=Base (LA) + w (k - LB)

- LOC(LA[k]) =Address of element LA[k] of the Array LA
- Base (LA) = Base Address of LA
- w = No. of words per memory cell for the Array LA
- k = Any element of Array

Multidimensional Arrays

- Two Dimensional Arrays
- Matrices in Mathematics
- Tables in Business Applications
- Matrix Arrays

1 2 3

1 A[1,1] A[1,2] A[1,3]

2 A[2,1] A[2,2] A[2,3]

3 A[3,1] A[3,2] A[3,3]

Column and Row Major Order 2 Dimension

Loc(A[J,K])= Base(A) + w [M(K-1)+(J-1)] (Column Major Order)

Loc(A[J,K])= Base(A) + w [N(J-1)+(K-1)] (Row Major Order)

Column and Row Major Order 3 Dimension

Length = Upper Bound – Lower Bound +1

Effective Index = Index Number – Lower Bound

Column and Row Major Order 3 Dimension

Length = Upper Bound – Lower Bound +1

Effective Index = Index Number – Lower Bound

Row Major Order:

Loc = Base + w(E1L2+E2)L3+E3)

Column Major Order:

Loc = Base + w(E3L2+E2)L1+E1)

Operations on Array

- Traversing a Linear Array

TraverseArray (LA, LB, UB)

Function: This algorithm traverse LA applying an operation PROCESS to each element of LA

Input: LA is a Linear Array with Lower Bound LB and Upper bound UB

Algorithm:

- [Initialize Counter] Set K:=LB
- Repeat Steps 3 and 4 while K≤UB
- [Visit element] Apply PROCESS to LA[K]
- [Increase counter] Set K:=K+1

[End of Step 2 loop]

5. Exit

Operations Cont….

- Insert an element in Linear Array

InsertElement (LA, ITEM, N, K)

Function: This algorithm insert an element in a Linear Array at required position

Input: LA is a Linear Array having N elements

ITEM is the element to be inserted at given position K

Precondition: K≤N where K is a +ve integer

Algorithm:

- [Initialize Counter] Set J:=N
- Repeat Steps 3 and 4 while J≥K
- [Move Jth element downward] Set LA[J+1] := LA[J]
- [Decrease counter] Set J:=J-1

[End of Step 2 loop]

5. [Insert element] Set LA[K]:=ITEM

6. [Reset N] N:= N+1

7. Exit

Operation Cont….

- Delete an element from a Linear Array

DeleteElement (LA, ITEM, N, K)

Function: This algorithm delete an element from a given position in Linear Array

Input: LA is a Linear Array having N elements

K is the position given from which ITEM needs to be deleted

Output: ITEM is the element deleted from the given position K

Precondition: K≤N where K is a +ve integer

Algorithm:

- Set ITEM:=LA[K]
- Set J:= K
- Repeat Steps 4 and 5 while J<N
- [Move Jth element upward] Set LA[J] := LA[J+1]
- [Increase counter] Set J:=J+1

[End of Step 3 loop]

6. [Reset N] N:= N-1

7. Exit

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