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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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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

slide13
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

slide15
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

slide17
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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