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CSCE 3110 Data Structures & Algorithm Analysis

CSCE 3110 Data Structures & Algorithm Analysis. Rada Mihalcea http://www.cs.unt.edu/~rada/CSCE3110 More on lists. Circular lists. Doubly linked lists. . Applications of Linked Lists. Stacks and Queues Implemented with Linked Lists Polynomials Implemented with Linked Lists

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CSCE 3110 Data Structures & Algorithm Analysis

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  1. CSCE 3110Data Structures & Algorithm Analysis Rada Mihalcea http://www.cs.unt.edu/~rada/CSCE3110 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. coef expon link Polynomials Representation typedef struct poly_node *poly_pointer; typedef struct poly_node { int coef; int expon; poly_pointer next; }; poly_pointer a, b, c;

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

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

  7. Adding Polynomials (cont’d) 2 8 1 0 3 14 a -3 10 10 6 8 14 b -3 10 11 14 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; 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. 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 extreme case 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 3 14 avail ptr temp avail ...

  14. X3 X2 X2 X1 X1 Operations in a circular list What happens when we insert a node to the front of a circular linked list? a Problem: move down the whole list. A possible solution: X3 a Keep a pointer points to the last node.

  15. X2 X1 Insertion 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) } } X3 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 col down right row entry node value i j aij aij

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

  24. #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

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