1. CSCE 3110 Data Structures & Algorithm Analysis 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. typedef struct poly_node *poly_pointer; typedef struct poly_node { int coef; int expon; poly_pointer next; }; poly_pointer a, b, c; coef expon link Representation Polynomials

5. 3 14 2 8 1 0 a 8 14 -3 10 10 6 b null Example

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

7. 3 14 2 8 1 0 a 8 14 -3 10 10 6 b 11 14 a->expon > b->expon -3 10 d 2 8 Adding Polynomials (cont’d)

8. 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)

9. case -1: /* a->expon 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->link; 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; }

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

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

12. 3 14 2 8 1 0 ptr circular Circularly linked lists

13. X 1  X 2  X 3  a What happens when we insert a node to the front of a circular linked list? Problem: move down the whole list. Operations in a circular list X 1  X 2  X 3  a Keep a pointer points to the last node. A possible solution:

14. 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 1  X 2  X 3  (1) (2) ptr Insertion

15. 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

16. 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; }

17. 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 ?

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

19. Doubly Linked List insertFirst swapElements

20. 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

21. down right value row col a ij ij entry node a ij Nodes in the Sparse Matrix

22. 4 4 1 0 12 2 1 -4 0 2 11 3 3 -15 1 1 5 Circular linked list Linked Representation

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

24. Operations on Sparse Matrices Transpose Addition Multiplication