CH 6 : VECTORS, LISTS AND SEQUENCES ACKNOWLEDGEMENT: THESE SLIDES ARE ADAPTED FROM SLIDES PROVIDED WITH DATA STRUCTURES AND ALGORITHMS IN C++, GOODRICH, TAMASSIA AND MOUNT (WILEY 2004) AND SLIDES FROM JORY DENNY AND MUKULIKA GHOSH 1

ITERATORS AND POSITION (CH 6.2.1) 2

LISTS  List ADT (Ch )  Doubly linked list (Ch ) 3

LIST ADT (CH 6.2.2) 4

INSERT(P,E) 5 ABXC ABC p ABC p X q p q

ERASE(P) 6 ABCD p ABC D p ABC

EXERCISE: LIST PERFORMANCE AND SPACE (BEST, WORST, AVERAGE) Singly-linked ListDoubly-linked List Worst case Average case Best case 7 Singly-linked ListDoubly-linked List Space usage for list of n elements

LIST PERFORMANCE AND SPACE SUMMARY Singly-linked ListDoubly-linked List Worst case Average case Best case 8 Singly-linked ListDoubly-linked List Space usage for list of n elementsO(n)

VECTORS (CH 6.1)  The Vector ADT (Ch )  Array-based implementation (Ch ) 9

VECTOR ADT (CH 6.1.1)  The Vector ADT extends the notion of array by storing a sequence of arbitrary objects  An element can be accessed, inserted or removed by specifying its rank (number of elements preceding it)  An exception is thrown if an incorrect rank is specified (e.g., a negative rank) 10

APPLICATIONS OF VECTOR  Direct applications  Sorted collection of objects (elementary database)  Indirect applications  Auxiliary data structure for algorithms  Component of other data structures 11

EXERCISE 12

ARRAY-BASED VECTOR (CH 6.1.2) STORAGE 012n i 0 13

ARRAY-BASED VECTOR (CH 6.1.2) INSERTION 14 V 012n i V 012n i V 012n e i

ARRAY-BASED VECTOR (CH 6.1.2) DELETION 15 V 012n r V 012n e i V 012n i

EXERCISE: ARRAY-BASED VECTOR PERFORMANCE (BEST, WORST, AVG) 16 Array based Vector (Fixed) Array-based Vector (Growable) Space used by Vector at(i) Set(i,e) insert(i,e) erase(i) size() empty()

EXERCISE: ARRAY-BASED VECTOR PERFORMANCE 17 Array based Vector (Fixed) Array-based Vector (Growable) Doulbly-linked List Vector Space used by Vector ? at(i), set(i,e) ? insert(i,e) ? erase(i) ? size(), empty() ?

SEQUENCES  Sequence ADT (Ch )  Implementations of the sequence ADT (Ch ) 18

SEQUENCE ADT (CH 6.3.1) 19

APPLICATION OF SEQUENCES  The Sequence ADT is a basic, general-purpose, data structure for storing an ordered collection of elements  Direct applications:  Generic replacement for stack, queue, vector, or list  Small database (e.g., address book)  Indirect applications:  Building block of more complex data structures 20

ARRAY BASED IMPLEMENTATION OF SEQUENCE (CH 6.3.3) positions elements S lf

EXERCISE: SEQUENCE PERFORMANCE (BEST,WORST, AVG) Circular Array based SequenceDoubly-linked List based Sequence 22 Circular Array based SequenceDoubly-linked List based Sequence Space usage

SEQUENCE SUMMARY Circular Array based SequenceDoubly-linked List based Sequence 23 Circular Array based SequenceDoubly-linked List based Sequence Space usage O(N)O(n)