Lecture 2 Arrays

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# Lecture 2 Arrays - PowerPoint PPT Presentation

Lecture 2 Arrays. 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.

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### Lecture 2Arrays

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
• 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