# C and Data Structures Baojian Hua

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C and Data Structures Baojian Hua bjhua@ustc.edu.cn
Linked List C and Data Structures Baojian Hua

Recap The extensible array-based implementation of linear list:
may be too slow insert or delete operations involve data movement may be too space waste only a small portion of the allocated space is occupied with data General computer science idea “pay as you go”

Polymorphic Abstract Data Types in C
// recall the poly ADT: #ifndef LIST_H #define LIST_H typedef void *poly; typedef struct listStruct *list; list newList (); int length (list l); poly nth (list l, int n); void insert (list l, poly x, int i); poly delete (list l, int i); void foreach (list l, void (*f)(poly)); #endif

// Turn the above figure into C, we have: // in file “linkedList.c” #include <stdlib.h> #include “list.h” struct listStruct { poly data; list next; }; data next head

Operation: “newList” // “new” returns an empty list, which consists of
// a single head node. list newList () { list l = (list)malloc (sizeof (*l)); l->data = NULL; // Why this? l->next = NULL; return l; } /\ l

Operation: “length” int length (list l) { list p = l->next;
int n = 0; while (p) { p = p->next; n++; } return n; n==0 data next l p

Operation: “length” int length (list l) { list p = l->next;
int n = 0; while (p) { p = p->next; n++; } return n; n==1 data next l p

Operation: “length” int length (list l) { list p = l->next;
int n = 0; while (p) { p = p->next; n++; } return n; n==2 data next l p

Operation: “length” int length (list l) { list p = l->next;
int n = 0; while (p) { p = p->next; n++; } return n; n==3 data next l p

Operation: “nth” poly nth (list l, int n) { list p = l->next;
int i = 0; if (n<0 || n>=length(l)) error (“invalid index”); while (i!=n) { p = p->next; i++; } return p;

Operation: “nth” n==2 i==0 l … p data next n==2 i==1 l … data p next

Operation: “insert” void insert (list l, poly x, int n) {
// 1. change the “next” field of pointer t; // 2. change the “next” field of element (n-1) …; } n==2 we’d search pointer p l data next data next data next x next t

Operation: “insert” void insert (list l, poly x, int n) { list p;
if (n<0 || n>length(l)) error (“invalid index”); // search pointer p points to position n-1 p = n? (nth (l, n-1)) : l;

Operation: “insert” // continued… // Step #1: cook list node:
list temp = (list)malloc (sizeof (*temp)); temp->data = x; // Step #2: temp points to n-th data item temp->next = p->next; // Step #3: link temp onto list p->next = temp; return; }

Operation: “delete” poly delete (list l, int n) {
// The key step is to search pointer p // Leave this as exercise. // See Lab #3. …; } n==2 we’d search pointer p l data next data next data next

Operation: “foreach” void foreach (list l, void (*f)(poly)) {
list p = l->next; while (p) { f (p->data); p = p->next; } l data next data next data next

better space usage---no waste good time complexity insert or delete take linear time but have to search the data sequential, :-( Can be further generalized: circular linked list doubly linked list doubly circular linked list

Circular Linked List All the pointers forms a circle
Note that the first node has two fields head: points to the head of the list tail: points to the tail of the list l head tail data next data next data next

// in file “clist.c” struct listStruct { struct node *head; struct node *tail; }; struct node poly data; struct node *next; } head tail data next l

Linear List Application #1: Polynomials
where ciR and n Nat uniquely determined by a linear list: For this representation, all the list operations apply

Linear List Application: Polynomials
Space waste: Consider this: 20001 items with 3 non-zeros A refined representation: ci<>0 for 0<=i<=m Ex:

Abstract data type: polyn represent the polynomial data type operations: polyn newPolyn (); // an empty polyn polyn add (polyn p1, polyn p2); real value (polyn p, real x0); // p(x0) polyn mult (polyn p1, polyn p2); // add an item c*x^n, which does not appear in p void insert (polyn p, real c, int n);

// in file “polyn.h” #ifndef POLYN_H #define POLYN_H typedef struct polynStruct *polyn; polyn newPolyn (); polyn add (polyn p1, polyn p2); real value (polyn p, real x0); polyn mult (polyn p1, polyn p2); void insert (polyn p, real c, int n); #endif

// in file “polyn.c” #include “linkedList.h” #include “polyn.h” struct polynStruct { linkedList coefExps; }; // where “coefExps” is a list of tuples: (c, n) // one way to read “list coefExps” is: // list<tuple<double, nat>> coefExps // However, C does not support this style of // declaration… :-(

Operation: “newPolyn”
polyn newPolyn () { polyn p = (polyn)malloc (sizeof (*p)); // use a linked list internally p->coefExps = newLinkedList (); return p; }

Operation: “insert” void insert (polyn p, real c, nat n) {
// could we use “double” and “int”, instead of // “real” and “nat”? tuple t = newTuple (c, n); linkedListInsertAtTail (p->coefExps, t); return; } // Leave other functions as exercises.

#include “tuple.h” #include “polyn.h” struct polyn { linkedList coefExps; };

Linear List Application#2: Dictionary
Dictionay: where ki are keys and vi are value all ki are comparable and distinct How can dict’ be represented in computers? many ideas (we’d discuss some in future) for now, we make use of a linear list

Abstract data type: dict represent the dictionary data type operations: dict newDict (); // an empty dict void insert (dict d, poly key, poly value); poly lookup (dict d, poly key); poly delete (dict d, poly key);

// in file “dict.h” #ifndef DICT_H #define DICT_H typedef struct dictStruct *dict; dict newDict (); void insert (dict d, poly key, poly value); poly lookup (dict d, poly key); poly delete (dict d, poly key); #endif

// in file “dict.c” #include “linkedList.h” #include “dict.h” struct dictStruct { linkedList l; };

Operations: “new” dict newDict () {
dict d = (dict)malloc (sizeof (*d)); d->l = newLinkedList (); return d; }

Operations: “insert” void insert (dict d, poly key, poly value) {
tuple t = newTuple (key, value); linkedListInsertAtHead (d->l, t); return; } // Leave other functions as programming // exercises.