Chapter 4: Lists 2004 년가을학기. 강경란 정보및컴퓨터공학부, 아주대학교

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1 Chapter 4: Lists 2004 년가을학기 강경란 정보및컴퓨터공학부, 아주대학교

2 1. Pointers 2. Singly Linked Lists Chapter 4 Lists 3. Dynamically Linked Stacks and Queues 4. Polynomials 5. Additional List Operations 6. Equivalence Relations 7. Sparse Matrices 8. Doubly Linked Lists -2/60-

3 1. List Terminology A collection of items accessible one after another beginning at the head and ending at the tail 2. Linked list head 3. Doubly linked list tail bat mat cat pat head 4. Circular list tail bat mat cat pat head tail bat mat cat pat -3/60-

4 List Example 1 - Single Node Case typedef struct list_node *list_pointer; typedef struct list_node { char data[4]; list_pointer link; (= list_node *link;) ; #define IS_EMPTY(ptr) (!(ptr)) list_pointer list_head = NULL; list_head = (list_pointer) malloc(sizeof(list_node)); strcpy(list_head ->data, bat ); list_head ->link=null; list_head head->data list_head Address of the first node b a t \0 0 list_head head->link -4/60-

5 1. Create a list 2. Insert a node 3. Delete a node 4. Print the list Operations onto the Lists typedef struct list_node *list_pointer; typedef struct list_node { int data; list_pointer link; list_node; -5/60-

6 Create a List list_pointer create2(int data1, int data2) { /* create a list of two nodes */ list_pointer first, second; first = (list _p pointer) malloc(sizeof(list ( _ node)); second = (list_pointer) malloc(sizeof(list_node)); second->link = NULL; second->data = data2; first->data = data1; first->link = second; second 20 return first; first 10 list_head = create2(10, 20); list_head -6/60-

7 Insert a Node (1/2) #define IS_FULL(ptr) (!(ptr)) Head of the list Insertion position void insert(list_pointer *ptr, list_pointer node, int key) Key value of the new node { list_pointer temp; temp = (list_pointer) malloc(sizeof(list_node)); if (IS_FULL(temp)){ fprintf(stderr, "The memory is full\n"); exit(1); temp->data = key; if (*ptr) { temp->link = node->link; node->link = temp; else { temp->link = NULL; *ptr = temp; -7/60-

8 Insert a Node (2/2) 1. Insert a node which has 10 as data into a null list list_head = NULL; insert(&list_head, list_head, 10); list_head Insert a node which has 50 as data at the back of the first node insert(&list_head, list_head, 50); list_head /60-

9 deleted node Delete a Node (1/2) void delete(list_pointer *ptr, list_pointer trail, list_pointer node) { Head of the list Preceding node /* trail is the preceding node. ptr is the head of the list */ if (trail) trail->link = node->link; else *ptr = (*ptr)->link; free(node); To delete the head node What if the list is empty, i.e. *ptr is NULL? How should the function be changed if ptr is just list_pointer? -9/60-

10 Delete a Node (2/2) 1. Example 1 list lst_head To be deleted delete(&list_head, list_head, list_head->link); 2. Example 2 list_head To be deleted delete(&list_head, NULL, list_head); -10/60-

11 Erasing a List void erase(poly_pointer *ptr) { /* erase the polynomial pointed to by ptr */ poly_pointer temp; while (*ptr) { temp = *ptr; *ptr = (*ptr)->link; free(temp); list_head erase(&list_head); -11/60-

12 Dynamically Linked Stacks and Queues Stack top bat mat cat pat Queue front bat mat cat pat rear -12/60-

13 Stacks #define MAX_STACKS 10 /* maximum number of stacks */ typedef struct { int key; /* other fields */ element; typedef struct stack *stack_pointer; typedef struct stack { element item; stack_pointer link; ; stack_pointer top[max_stacks]; 1. Initialization top[i]=null, 0 i<max_stacks 2. Boundary conditions IS_EMPTY(top[i]): no item is available in i-th stack IS_FULL(temp) : no memory space is available -13/60-

14 Stacks Insert an Item (1/2) void add(stack_pointer *top, element item) { /* insert an item at the top of a stack */ stack_pointer temp = (stack_pointer) malloc(sizeof (stack)); if (IS_FULL(temp)) { fprintf(stderr,"the memory is full\n"); exit(1); temp->item = item; temp->link = *top; *top = temp; What if top is just stack_pointer? -14/60-

15 Stacks Insert an Item (2/2) top[0] element new_item; new_ item.key=20; add(&top[0], new_item); top[0] /60-

16 Stacks Delete an Item (1/2) element delete (stack_pointer *top) { /* delete an item from a stack */ stack_pointer temp = *top; element item; if (IS_EMPTY(temp)) { fprintf(stderr,"the stack is empty\n"); exit(1); item = temp->item; *top = temp->link; free(temp); return item; -16/60-

17 Stacks Delete an Item (2/2) top[0] item = delete(&top[0]); printf( %d\n, item.key); top[0] /60-

18 Queues #define MAX_QUEUE 10 /* Maximum Number of Queues */ typedef struct queue *queue_pointer; typedef struct queue { element item; queue_pointer e link; ; queue_pointer front[max_queues], rear[max_queues]; 1. Initial condition front[i]=null, 0 i < MAX_QUEUES 2. Boundary conditions IS_EMPTY(front[i]): no item is available in i-th queue IS_FULL(temp): no memory space is available -18/60-

19 Queues Insert an Item (1/2) void addq (queue_pointer *front, queue_pointer *rear, element item) { /* insert an item at the rear of a queue */ queue_pointer temp = (queue_pointer) malloc(sizeof (queue)); if (IS_FULL(temp)) { fprintf(stderr,"the memory is full\n"); exit(1); temp->item = item; temp->link = NULL; if (*front) (*rear)->link = temp; else *front = temp; Queue was empty *rear = temp; -19/60-

20 Queues Insert an Item (2/2) front[0] rear[0] element item; item.key=50; addq(&front[0], &rear[0], item); front[0] rear[0] /60-

21 Queues Delete an Item (1/2) element deleteq (queue_pointer *front) { /* Delete an item from a queue */ queue_pointer temp = *front; element item; if (IS_EMPTY(*front)) { fprintf(stderr,"the queue is empty\n"); exit(1); item = temp->item; *front = temp->link; free(temp); return item; -21/60-

22 Queues Delete an Item (2/2) front[0] rear[0] item=deleteq(&front[0]); printf( %d\n, item.key); front[0] rear[0] /60-

23 Polynomials - Representation typedef struct poly_node *poly_pointer; typedef struct poly_node { int coef; int expon; poly y_p pointer link; coef expon link ; poly_pointer a,b,d; A(x) = 3x x a B(x) = 8x 14-3x x 6 b /60-

24 Polynomials Addition (1/3) 1. if (a-> expon == b->expon) a b front rear -24/60-

25 Polynomials Addition (2/3) 2. if (a-> expon < b->expon) a b front rear -25/60-

26 Polynomials Addition (3/3) 3. if (a-> expon > b->expon) a b front rear -26/60-

27 A Function for Polynomial Addition (1/4) poly_pointer padd (poly_pointer a, poly_pointer b) { /* return a polynomial which is the sum of a and b */ poly_pointer pointer front, rear, temp; int sum; rear = (poly y_p pointer)malloc(sizeof(poly (p y_ node)); if (IF_FULL(rear)) { fprintf(stderr, "The memory is full\n"); exit(1); front = rear; -27/60-

28 A Function for Polynomial Addition (2/4) while(a && b) { switch (COMPARE(a->expon, b->expon)) { case -1: /* a->expon < b->expon */ attach(b->coef,b->expon,&rear); b = b->link; break; case 0: /* a->expon = b->expon */ sum = a->coef + b->coef; if (sum) attach(sum,a->expon,&rear); a = a->link; b->link; break; case: 1 /* a->expon > a->expon */ attach(a->coef,a->expon,&rear); a = a->link; -28/60-

29 A Function for Polynomial Addition (3/4) /* copy the rest of list a and list b */ for (; a; a = a->link) attach(a->coef,a->expon,&rear); for (; b; b = b->link) attach(b->coef,b->expon,&rear); rear->link = NULL; /* delete the useless initial node */ temp = front; front = front->link; free(temp); return front; -29/60-

30 Polynomial Attachment (4/4) void attach(float coefficient, int exponent, poly_pointer *ptr) { /* create a node and attach it to the node pointed to by ptr */ 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)->link = temp; *ptr = temp; -30/60-

31 Analysis of padd m A( x ) + a ( m e 1 = am 1x +... n B( x) + b f 1 = b 1 x +... n where a i, b i 0, e m-1 > > e 0 0, f n-1 > > f 0 0, 0 0 x x e f number of coefficient additions min{m, n number of terms m + n number of exponent comparisons m + n f(m,n) = O(m+n) -31/60-

32 1. Zero polynomial Polynomial : Circularly Linked List a x x a /60-

33 A(x) = 3x x Polynomial Addition Circular List a B(x) = 8x 14-3x x b -1 D(x) = 11x 14-3x x x d /60-

34 Polynomial Addition Circular List (1/2) poly_pointer cpadd (poly_pointer a, poly_pointer b) { poly y_p pointer starta, d, lastd; int sum, done = FALSE; starta = a; a = a->link; b = b->link; d = get_node(); d->expon = -1; lastd = d; -34/60-

35 Polynomial Addition Circular List (2/2) do { switch (COMPARE(a->expon, b->expon)) { case -1: /* a->expon < b->expon */ attach(b->coef,b->expon,&lastd); b = b->link; break; case 0: /* a->expon == b->expon */ if (starta == a) done = TRUE; else { sum = a->coef + b->coef; if (sum) attach(sum,a->expon,&lastd); a = a->link; b = b->link; break; case: 1 /* a->expon > a->expon */ while (!done); lastd->link =d; return d; attach(a->coef,a->expon,&lastd); a = a->link; -35/60-

36 Additional Operations on Lists (1/5) 1. Base data structure typedef struct list_node *list_pointer; Typedef struct list_node { int data; list_pointer link; ; list_pointer list_head, list_head2; list_head list_head /60-

37 Additional Operations on Lists (2/5) 2. Finding the length (circular list) int length (list_pointer ptr) { list_pointer temp; int count = 0; if (ptr) { temp = ptr; do { count++; temp = temp->link; while (temp!= ptr); return count; printf( %d, length(list_head)); head)); printf( %d, length(list_head2)); -37/60-

38 Additional Operations on Lists (3/5) 3. Inverting list_pointer invert(list_pointer lead) { list_pointer middle, trail; middle = NULL; while (lead) { trail = middle; middle = lead; lead = lead->link; middle->link = trail; return middle; list_pointer list_head3 = invert(list_head); -38/60-

39 Additional Operations on Lists (4/5) 4. Concatenating list_pointer concatenate (list_pointer ptr1, list_pointer ptr2) { list_pointer temp; if (IS_EMPTY(ptr1)) return ptr2; else { if (!IS_EMPTY(ptr2)) { for (temp = ptr1; temp->link; temp = temp-> link); temp->link = ptr2; return ptr1; -39/60-

40 Additional Operations on Lists (5/5) 5. Inserting at the front (circular list) void insert_ front (list_pointer *ptr, list_pointer node) { /* ptr points to the last node in the list */ if (IS_EMPTY(*ptr)) { *ptr = node; node->link = node; else { node->link = (*ptr)->link; (*ptr)->link = node; list_pointer i t node_p=malloc(sizeof(list_node)); d insert(&list_head, node_p); list_head is assumed to point to the last node of the list -40/60-

41 1. Equivalence relations 1) For any polygon x, x x Equivalence Relations 2) For any two polygons, x and y, if x y then y x 3) For any three polygons, x, y and z, if x y and y z, x z 2. Problem 1) To partition a set S into equivalent classes such that two members x and y of S are in the same equivalence class iff x y 2) Example 0 4, 3 1, 6 10, 8 9, 7 4, 6 8, 3 5, 2 11, 11 0 {0,2,4,7,11; {1,3,5; {6,8,9,10-41/60-

42 Equivalence Relations Algorithm Assume that m is the number of pairs, n is the number of objects void equivalence () { initialize seq to NULL and out to TRUE; while (there are more pairs) { read the next pair <i,j>; put j on the seq[i] list; put i on the seq[j] list; for (i = 0; i < n; i++) if (out[i]) { out[i] = FALSE; output this equivalence class; -42/60-

43 Example of Equivalence Relations 0 4, 3 1, 6 10, 8 9, 7 4, 6 8, 3 5, 2 11, 11 0 seq /60-

44 Implementation of Equivalence Relations (1/3) typedef struct node *node_pointer; typedef struct node { int data; node_pointer link; ; void main (void) { short int out[max_size]; node_pointer seq[max_size]; node_pointer x,y,top; int i,j,n; printf("enter the size (<= %d) ", MAX_ SIZE); scanf("%d", &n); for (i=0; i<n; i++) { out[i]=true; seq[i]=null; printf("enter a pair of numbers (-1-1 to quit): "); scanf("%d%d", &i, &j); -44/60-

45 Implementation of Equivalence Relations (2/3) /* phase 1: input the equivalence class */ while (i >= 0) { x = (node_pointer)malloc(sizeof(node)); if (IS_FULL(x)) { fprintf(stderr, "The memory is full\n"); exit(1); x->data = j; x->link = seq[i]; seq[i] = x; x = (node_pointer)malloc(sizeof(node)); if (IS _ FULL(x)) { fprintf(stderr, "The memory is full\n"); exit(1); x->data = i; x->link = seq[j]; seq[j] = x; printf("enter a pair of numbers (-1-1 to quit): "); scanf("%d%d", &i, &j); -45/60-

46 Implementation of Equivalence Relations (3/3) /* phase 2: print out the equivalent classes */ for (i = 0; i < n; i++) if (out[i]) { printf("\nnew class: %5d", i); out[i] = FALSE; x = seq[i]; top = NULL; for (;;) { while (x) { j = x->data; if (out[j]) { printf(%5d", j); out[j] = FALSE; y = x->link; x->link = top; top = x; x = y; else x = x->link; if (!top) break; x = seq[top->data]; top = top->link; -46/60-

47 Sparse Matrix Circular List Representation 1. Node structure typedef enum {head, entry tagfield; typedef struct matrix_node *matrix_pointer; typedef struct entry_node { int row; Head node int col; int value; ; typedef struct matrix_node { down right next 0 matrix_pointer down; matrix_pointer right; Entry node tagfield tag; union { down right 1 matrix_pointer next; entry_node entry; u; row col value ; -47/60-

48 Example of Circular Representation of Sparse Matrix hdnode[0] hdnode[1] hdnode[2] hdn ode[0] hdnode e[1] hdn node[2] /60-

49 Reading a Sparse Matrix (1/3) matrix_pointer hdnode[max_size]; matrix_pointer mread (void) { int num_rows, num_cols, num_terms, num_heads, i; int row, col, value, current_row; matrix_pointer temp,last,node; printf("enter the number of rows, columns, and number of nonzero terms: "); scanf("%d%d%d", &num_rows, &num_cols, &num_terms); num_heads = (num_cols > num_rows)? num_cols : num_rows; node = new_node(); node->tag = entry; node->u.entry.row = num_rows; node->u.entry.col = num cols; -49/60-

50 Reading a Sparse Matrix (2/3) if (!num_heads) node->right = node; else { for (i = 0; i < num_heads; i++) { temp = new_node(); hdnode[i] = temp; hdnode[i]->tag = head; hdnode[i]->right = temp; hdnode[i]->u.next = temp; current_row = 0; last = hdnode[0]; for (i = 0; i < num_terms; i++) { printf("enter row, column and value: "); scanf("%d%d%d", &row,&col,&value); if (row > current_row) { last->right t = hdnode[current e t_ row]; current_row = row; last = hdnode[row]; -50/60-

51 Reading a Sparse Matrix (3/3) temp = new_node(); temp->tag = entry; temp->u.entry.row = row; temp->u >u.entry.col = col; temp->u.entry.value = value; last->right = temp; last = temp; hdnode[col]->u.next->down=temp; >down temp; hdnode[col]->u.next = temp; last->right = hdnode[current _ row]; for (i = 0; i < num_cols; i++) hdnode[i]->u.next->down = hdnode[i]; for (i = 0; i < num_heads-1; i++) hdnode[i]->u.next = hdnode[i+1]; hdnode[num_heads-1]->u.next = node; node->right = hdnode[0]; return node; -51/60-

52 Writing a Sparse Matrix void mwrite (matrix_pointer *node) { int i; matrix_pointer temp, head = node->right; printf("\n num_rows = %d, num_cols = %d \n", node->u.entry.row, node->u.entry.col); printf(" The matrix by row, column, and value: \n\n"); for (i = 0; i < node->u.entry.row; i++) { for (temp = head->right; temp!= head; temp = temp->right){ printf("%5d%5d%5d \n", temp->u.entry.row, temp->u.entry.col, temp->u.entry.value); head = head->u.next; -52/60-

53 Writing a Sparse Matrix - Example hd dnode[0] hdnode e[1] hdno ode[2] /

54 Erasing a Sparse Matrix void merase (matrix_pointer *node) { matrix_pointer x,y, head = (*node)->right; int i, num_heads; /* free the entry and head nodes by row */ for (i = 0; i < (*node)->u.entry.row; i++) { y = head->right; while (y!= head) { x = y; y = y->right; free(x); x = head; head = head->u.next; free(x); /* free remaining head nodes */ y = head; while (y!= *node) { x = y; y = y->u.next; free(x); free(*node); *node = NULL; -54/60-

55 Erasing a Sparse Matrix - Example hdnode e[0] hdn node[1] hdnode[2 2] /60-

56 Doubly Linked Lists 1. Node structure typedef struct node *node_pointer; typedef struct node { node_pointer llink; element item; node_pointer rlink; ptr = ptr->llink->rlink l k = ptr->rlink->llink ll k ptr llink item rlink -56/60-

57 Doubly Linked Circular Lists (DLCL) 1. Doubly linked circular list with head nodes Head node list_head llink item rlink 2. Empty list list_head -57/60-

58 Inserting a Node to a DLCL list_head a b c d void dinsert (node_pointer node, node_pointer newnode) { /* insert newnode to the right of the node */ newnode->llink = node; newnode->rlink = node->rlink; node->rlink->llink = newnode; node->rlink = newnode; -58/60-

59 Deleting a Node from DLCL list_head a b c void ddelete (node_p pointer node, node_pointer deleted) { /* delete from the DLCL pointed to by node */ if (node == deleted) printf("deletion of head node not permitted.\n"); else { deleted->llink->rlink = deleted->rlink; deleted->rlink->llink = deleted->link; free(deleted); -59/60-

60 1. Singly linked list 1) Stack 2) Queue 3) Polynomials 4) Equivalence class 2. Circularly linked list 1) Polynomials l 2) Sparse matrix Summary 3. Doubly linked circular list 1) Insertion 2) Deletion -60/60-

Chapter 4. LISTS. 1. Pointers

Chapter 4. LISTS. 1. Pointers Chap 4: LIST (Page 1) Chapter 4. LISTS TABLE OF CONTENTS 1. POINTERS 2. SINGLY LINKED LISTS 3. DYNAMICALLY LINKED STACKS AND QUEUES 4. POLYNOMIALS 5. ADDITIONAL LIST OPERATIONS 6. EQUIVALENCE RELATIONS