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

2. Applications of Linked Lists
Stacks and Queues Implemented with Linked Lists
Polynomials Implemented with Linked Lists
Remember the array based implementation?
Hint: two strategies, one efficient in terms of space, one in terms of running time

3. Operations on Linked Lists
Running time?
insert, remove
traverse, swap
How to reverse the elements of a list?

4. Polynomials Representation typedef struct poly_node *poly_pointer;
int coef;
int expon;
poly_pointer next; };
poly_pointer a, b, c;
coef expon link

5. Example a
null b
-3 10
null

6. Adding Polynomials 3 14 2 8 1 0 a 8 14 -3 10 10 6 b 11 14
2 8
1 0 a
-3 10 b
11 14
a->expon == b->expon d
2 8
1 0 a
-3 10 b
11 14
-3 10
a->expon < b->expon d

7. Adding Polynomials (cont’d)
2 8
1 0 a
-3 10 b
11 14
-3 10
2 8 d
a->expon > b->expon

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)) {

9. 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;
case 1: /* a->expon > b->expon */
attach(a->coef, a->expon, &rear);
a = a->next; }
for (; a; a = a->next)
for (; b; b=b->next)
rear->next = NULL;
temp = front; front = front->next; free(temp);
return front;

10. Analysis (1) coefficient additions 0  additions  min(m, n)
where m (n) denotes the number of terms in A (B).
(2) exponent comparisons
extreme case
em-1 > fm-1 > em-2 > fm-2 > … > e0 > f0
m+n-1 comparisons
(3) creation of new nodes
m + n new nodes
summary O(m+n)

11. Attach a Term 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;

12. Other types of lists:
Circular lists
Doubly linked lists

13. Circularly linked lists
circular list vs. chain
ptr
2 8
1 0
avail
ptr
temp
avail
...

14. Operations in a circular list
What happens when we insert a node to the front of a circular
linked list?
X 
X 
X  a
Problem: move down the whole list.
A possible solution:
X 
X 
X  a
Keep a pointer points to the last node.

15. Insertion ptr (2) (1) 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)
X 
X 
X 
ptr
(2)
(1)

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

17. Doubly Linked List
Keep a pointer to the next and the previous element in the list
typedef struct node *pnode; typedef struct node { char data [4]; pnode next;
pnode prev; }

18. Doubly Linked List
Keep a header and trailer pointers (sentinels) with no content
header.prev = null; header.next = first element
trailer.next = null; trailer.prev = last element
Update pointers for every operation performed on the list
How to remove an element from the tail of the list ?

19. Doubly Linked List – removeLast()
Running time?
How does this compare to simply linked lists?

20. Doubly Linked List
insertFirst
swapElements

21. Revisit Sparse Matrices
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

22. Nodes in the Sparse Matrix
down
col
row
right
entry node
value i j
aij
aij

23. Linked Representation4 4 2 11 1 1 1 12 5 2 1 -4 3 3
-15
Circular linked list

24. Sparse Matrix Implementation
#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