Fall, 2015 Prof. Jungkeun Park

Transcription

1 Data Structures t and Algorithms Circular lists / Doubly linked lists Fall, 2015 Prof. Jungkeun Park Copyright Notice: This material is modified version of the lecture slides by Prof. Rada Mihalcea in Univ. of North Texas.

2 Applications of Linked Lists Stacks and Queues Implemented e 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 2

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

4 Polynomials A ( x ) a Representation m 1 x e m 1 a m 2 x e m 2 typedef struct poly_node *poly_pointer; typedef struct poly_node { int coef; int expon; poly_pointer next; }; poly_pointer a, b, c;... a 0 x e 0 coef expon link 4

5 Example 14 8 a 3x 2x 1 a null b 8 x 3 x 10 x b null 5

6 Adding Polynomials a b a->expon == b->expon d a b a->expon < b->expon d 6

7 Adding Polynomials (cont d) a a->expon > b->expon 2 8 b d 7

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, td The memory is full\n ); exit(1); } front = rear; while (a && b) { switch (COMPARE(a->expon, b->expon)) { 8

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; 9

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 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 summary O(m+n) 10

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; 11

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

13 Circularly linked lists circular list vs. chain ptr ptr avail temp avail... 13

14 Operations in a circular list What happens when we insert a node to the front of a circular linked list? a 1 X 1 X 2 X 3 Problem: move down the whole list. A possible solution: X 1 X 2 X 3 Keep a pointer points to the last node. a 14

15 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) X 1 X 2 X 3 (2) ptr (1) 15

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; } 16

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

18 Doubly Linked List Keep a header and trailer tae pointers (sentinels) e s) 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

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

20 Doubly Linked List insertfirst st swapelements 20

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 21

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

23 Linked Representation 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 24