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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 2 arrays

Lecture 2Arrays


Linear data structures
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
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
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
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
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
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
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
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 dimension1
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
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
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
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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