CSCE 3110Data Structures & Algorithm Analysis

Rada Mihalceahttp://www.cs.unt.edu/~rada/CSCE3110

Growable Arrays. Lists.Reading: Chap. 3 Weiss

Linked Lists

Avoid the drawbacks of fixed size arrays with

Growable arraysLinked lists

Growable arrays

Avoid the problem of fixed-size arraysIncrease the size of the array when needed (I.e. when capacity is exceeded)Two strategies:

tight strategy (add a constant): f(N) = N + cgrowth strategy (double up): f(N) = 2N

Tight Strategy

Add a number k (k = constant) of elements every time the capacity is exceeded

123456789101112131415

C0 + (C0+k) + … (C0+Sk) =

S = (N – C0) / k

Running time?

C0 * S + S*(S+1) / 2 O(N2)

Tight Strategy

void insertLast(int rear, element o) {if ( size == rear) {

capacity += k;element* B = new element[capacity];for(int i=0; i<size; i++) { B[i] = A[i];}

A = B; } A[rear] = o;

rear++; size++; }

Growth Strategy

Double the size of the array every time is needed (I.e. capacity exceeded)1

23456789101112131415

C0 + (C0 * 2) + (C0*4) + … + (C0*2i) =

i = log (N / C0)

Running time?

C0 [1 + 2 + … + 2 log(N/C0) ] O(N)

How does the previous code change?

Linked Lists

Avoid the drawbacks of fixed size arrays with

Growable arraysLinked lists

int i, *pi;float f, *pf;pi = (int *) malloc(sizeof(int));pf = (float *) malloc (sizeof(float));*pi =1024;*pf =3.14;printf(”an integer = %d, a float = %f\n”, *pi, *pf);free(pi);free(pf);

request memory

return memory

Using Dynamically Allocated Memory (review)

bat cat sat vat NULL

Linked Lists

bat cat sat vat NULL

mat

Insertion

Compare this with the insertion in arrays!

bat cat sat vat NULL mat

danglingreference

Deletion

List ADT

ADT with position-based methodsgeneric methods size(), isEmpty()query methods isFirst(p), isLast(p)accessor methods first(), last()

before(p), after(p)update methods swapElements(p,q),

replaceElement(p,e)insertFirst(e), insertLast(e)insertBefore(p,e),

insertAfter(p,e)removeAfter(p)

typedef struct node, *pnode;typedef struct node { char data [4]; pnode next; };Creationpnode ptr =NULL; Testing#define IS_EMPTY(ptr) (!(ptr))Allocationptr=(pnode) malloc (sizeof(node));

Declaration

Implementation

b a t \0 NULL

address offirst node

ptr data ptr link

ptr

e name (*e).namestrcpy(ptr data, “bat”);ptr link = NULL;

Create one Node

pnode create2( ){/* create a linked list with two nodes */ pnode first, second; first = (pnode) malloc(sizeof(node)); second = ( pnode) malloc(sizeof(node)); second -> next= NULL; second -> data = 20; first -> data = 10; first ->next= second; return first;} 10 20 NULL

ptr

Example: Create a two-nodes list

void insertAfter(pnode node, char* data){/* insert a new node with data into the list ptr after node */ pnode temp; temp = (pnode) malloc(sizeof(node)); if (IS_FULL(temp)){ fprintf(stderr, “The memory is full\n”); exit (1); }

Insert (after a specific position)

strcpy(temp->data, data); if (node) { noempty list temp->next=node->next; node->next= temp; } else { empty list temp->next= NULL; node =temp; }}

50

10 20 NULL

temp

node

10 20 NULL 50 20 NULL 50

node trail = NULL node

(a) before deletion (b)after deletion

Deletion

Delete node other than the first node

10 20 NULL 50 20 NULL 10

head node head

void removeAfter(pnode node){/* delete what follows after node in the list */ pnode tmp; if (node) { tmp = node -> next; node->next = node->next->next; free(tmp); }}

10 20 NULL 50

20 NULL 10

node

void traverseList(pnode ptr){ printf(“The list contains: “); for ( ; ptr; ptr = ptr->next) printf(“%4d”, ptr->data); printf(“\n”); }

Traverse a list

Where does ptr point after this function call?

Other List Operations

swapElementsinsertFirstinsertLastdeleteBeforedeleteLast

Running Time Analysis

insertAfter O(?)deleteAfter O(?)deleteBefore O(?)deleteLast O(?)insertFirst O(?)insertLast O(?)