CSCE 3110 Data Structures & Algorithm Analysis Rada Mihalcea rada/CSCE3110 More on lists. Circular lists. Doubly linked lists.

CSCE 3110Data Structures & Algorithm Analysis

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

More on lists. Circular lists. Doubly linked lists.

Applications of Linked Lists

Stacks and Queues Implemented with Linked ListsPolynomials Implemented with Linked Lists

Remember the array based implementation?

• Hint: two strategies, one efficient in terms of space, one in terms of running time

Operations on Linked Lists

Running time?insert, removetraverse, swap

How to reverse the elements of a list?

typedef struct poly_node *poly_pointer; typedef struct poly_node { int coef; int expon; poly_pointer next; }; poly_pointer a, b, c;

A x a x a x a xm

e

m

e em m( ) ...

1 2 01 2 0

coef expon link

Representation

Polynomials

3 14 2 8 1 0a

8 14 -3 10 10 6b

a x x 3 2 114 8

b x x x 8 3 1014 10 6

null

null

Example

3 14 2 8 1 0a

8 14 -3 10 10 6b

11 14d

a->expon == b->expon

3 14 2 8 1 0a

8 14 -3 10 10 6b

11 14d

a->expon < b->expon-3 10

Adding Polynomials

3 14 2 8 1 0a

8 14 -3 10 10 6b

11 14

a->expon > b->expon

-3 10d

2 8

Adding Polynomials (cont’d)

poly_pointer padd(poly_pointer a, poly_pointer b){ poly_pointer front, rear, temp; int sum; rear =(poly_pointer)malloc(sizeof(poly_node)); if (IS_FULL(rear)) { fprintf(stderr, “The memory is full\n”); exit(1); } front = rear; while (a && b) { switch (COMPARE(a->expon, b->expon)) {

Adding Polynomials (cont’d)

case -1: /* a->expon < b->expon */ attach(b->coef, b->expon, &rear); b= b->next; break; case 0: /* a->expon == b->expon */ sum = a->coef + b->coef; if (sum) attach(sum,a->expon,&rear); a = a->next; b = b->next; break; case 1: /* a->expon > b->expon */ attach(a->coef, a->expon, &rear); a = a->next; } } for (; a; a = a->next) attach(a->coef, a->expon, &rear); for (; b; b=b->next) attach(b->coef, b->expon, &rear); rear->next = NULL; temp = front; front = front->next; free(temp); return front;}

(1) coefficient additions0 additions min(m, n)where m (n) denotes the number of terms in A (B).

(2) exponent comparisonsextreme caseem-1 > fm-1 > em-2 > fm-2 > … > e0 > f0

m+n-1 comparisons(3) creation of new nodes

extreme casem + n new nodessummary O(m+n)

Analysis

void attach(float coefficient, int exponent, poly_pointer *ptr){/* create a new node attaching to the node pointed to by ptr. ptr is updated to point to this new node. */

poly_pointer temp; temp = (poly_pointer) malloc(sizeof(poly_node)); if (IS_FULL(temp)) { fprintf(stderr, “The memory is full\n”); exit(1); } temp->coef = coefficient; temp->expon = exponent; (*ptr)->next = temp; *ptr = temp;}

Attach a Term

Other types of lists:

Circular listsDoubly linked lists

3 14 2 8 1 0ptr

ptr

avail ...

avail

temp

circular list vs. chain

Circularly linked lists

X1 X2 X3 a

What happens when we insert a node to the front of a circularlinked list?

Problem: move down the whole list.

Operations in a circular list

X1 X2 X3 a

Keep a pointer points to the last node.

A possible solution:

void insertFront (pnode* ptr, pnode node){ /* insert a node in the list with head (*ptr)->next */ if (IS_EMPTY(*ptr)) { *ptr= node; node->next = node; /* circular link */ } else { node->next = (*ptr)->next; (1) (*ptr)->next = node; (2) }}

X1 X2 X3

(1)(2) ptr

Insertion

int length(pnode ptr){ pnode temp; int count = 0; if (ptr) { temp = ptr; do { count++; temp = temp->next; } while (temp!=ptr); } return count;}

List length

Doubly Linked List

Keep a pointer to the next and the previous element in the listtypedef struct node *pnode;

typedef struct node { char data [4]; pnode next;

pnode prev; }

Doubly Linked List

Keep a header and trailer pointers (sentinels) with no content

header.prev = null; header.next = first elementtrailer.next = null; trailer.prev = last element

Update pointers for every operation performed on the listHow to remove an element from the tail of the list ?

Doubly Linked List – removeLast()

Running time?How does this compare to simply linked lists?

Doubly Linked List

insertFirstswapElements

15000

0040

00012

01100

Previous scheme: represent each non-NULL element as a tuple(row, column, value)

New scheme:each column (row): a circular linked list with a head node

Revisit Sparse Matrices

down right

value

row col

aij

i j

entry node

aij

Nodes in the Sparse Matrix

4 4

1 012

2 1-4

0 211

3 3-15

1 15

Circular linked list

Linked Representation

#define MAX_SIZE 50 /* size of largest matrix */typedef struct mnode *pmnode;typedef struct mnode { int row; int col; int value; pmnode next, down; };

Operations on sparse matrices

Sparse Matrix Implementation