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Lecture#2: Arrays

Lecture#2: Arrays. Course Teacher: Syed Ahmed Hasan. 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. Operation performed by Linear Structure.

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Lecture#2: Arrays

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  1. Lecture#2: Arrays Course Teacher: Syed Ahmed Hasan

  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

  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) or as an ADT any data 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. 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

  8. 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

  9. Alternative Algorithm: • Repeat for K:=LB to UB Apply PROCESS to LA[K] [End of loop] 2. Exit

  10. Example: Home Work Consider the array AUTO which records the number of automobile sold each ear from 1932 through 1984. • Find the NUM of years during which more than 300 automobiles were sold • Print each year and the number of automobile sold in that year (This is a book example # 4.4)

  11. Operations Cont • Insert an element in Linear Array • NOTE : This Algorithm consist of minimal steps. For more detail add appropriate steps as discussed in class

  12. Operations Cont 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 he element to be inserted at given position K Precondition: K≤N where K is a +ve integer

  13. 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

  14. Operation Cont • Delete an element from a Linear Array • NOTE : This Algorithm consist of minimal steps. For more detail add appropriate steps as discussed in class

  15. 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

  16. Algorithm: • Set ITEM:=LA[K] • Repeat for J:=K to N-J • [Move Jth element upward] Set LA[J] := LA[J+1] [End of Step 2 loop] 4. [Reset N] N:= N-1 5. Exit

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