Lecture 2 Arrays

1. Lecture 2Arrays

2. 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

3. 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

4. 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

5. Length of Array • N = length of array Length = UB – LB + 1 • UB = Upper Bound or Largest Index • LB= Lower Bound or smallest Index

6. 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

7. 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]

8. 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)

9. Column and Row Major Order 3 Dimension Length = Upper Bound – Lower Bound +1 Effective Index = Index Number – Lower Bound

10. 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)

11. Column and Row Major Order 3 Dimension

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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