Linked ListsLinked Lists

Outline

• Why linked lists?• Linked lists basics• Implementation• Basic primitives

Searching Inserting Deleting

Why linked lists?

• The default implementation for storing a set of objects is an array int v[10];

denotes the allocation of 10 int variables

• Arrays are efficient for many purposes (e.g., fast access to elements), but have several limitations

Limitations of arrays (1)

• Their size must be fixed in advance

At compile time (statically allocated)int mydata[100];

At run time (dynamically allocated)int *mydata;mydata = (int*)malloc(sizeof(int)*100);

• In theory it is possible, for a dynamically allocated array to resize it using realloc but it tends to be quite inefficient E.g., reallocate a large array to add 1 element

Limitations of arrays (2)

• Because of first limitation, arrays are often over-sized

• To deal with dynamically changing sets of data, programmers usually allocate arrays which seem "large enough“.

• Problems: Low utilization of arrays (you allocate a size X but use at

most a fraction of it) and the space is wasted If the program ever needs to process more than X data,

the code breaks

Limitation of arrays (3)

• Inserting elements to keep a given order is inefficient

• Example: If elements of the array represent an order of arrival

(a[0] is last arrived) inserting a new element implies moving all elements one position ahead

Array vs. linked lists

• Linked lists solve limitations of arrays by paying in terms of efficiency of access of elements

• Arrays: allocate memory for all its elements stored in contiguous

memory locations (appears as one block of memory)

• Linked lists: allocate space for each element separately in its own

block of memory called a "linked list element" or "node". The list gets is overall structure by using pointers to

connect all its nodes together like the links in a chain.

Array vs. linked lists

• Array– int v[4];

• List– ????

253-1

v[0]v[1]v[2]v[3]

v2

5

3

-1

?

Linked lists

• Each list node contains two fields: a "data" field to store whatever element type the list

holds and a "next" field which is a pointer used to link one

node to the next node.

• Each node is allocated with malloc() and it continues to exist until it is explicitly deallocated with free()

Arrays vs. linked lists

Arrays Lists

Access time

+ (independent of

array size – random access)

-(proportional to list

size – sequential access)

Utilization

- (over allocation

typical)

+ (allocate what you

need)

Modification of element order

- (requires

movement of elements)

+ (insert where

needed by moving pointers)

Lists (cont.)

• Variants: Double linked lists

• The element possesses a pointer also to the previous element

Circular lists• The last element in the list is linked to the head

Lists (cont.)

• Variants: Lists with sentinel

• Head or tail or both exist as fictitious elements to manage special cases at the boundary

Ordered Lists• Starting from the head the elements (i.e., the keys)

have an order (increasing or decreasing)

Array vs. linked lists

• Array– int v[4];

• List– List* Head;

253-1

v[0]v[1]v[2]v[3]

v2

5

3

-1

Head

Lists - (cont.)

• Primitives­Insert (at the head of the list)­Search­Delete­InsertSorted

• NOTE: The ordering of a list is not immediate It requires double pointers or auxiliary lists

Lists: Basic operations

•Different from vector based data structures, operation on a list requires pointer manipulation

•Element creation: Using malloc()

•Initialization of a list A pointer to list initialized to NULL

•Insertion/deletion of an element Movement of pointers

Lists - list.h

typedef struct e{ int key; List* next;

} List;

List* Insert(List*,int); /* modifies the head */List* Search(List*, int);void Display(List*);List* Delete(List*,int, int*); /* modifies the head */

List* InsertSorted(List*,int); /* modifies the head*/

Lists - list.c (1)

#include <stdio.h>

List* Insert( List* head, int val){List* p;

p = newE();

p->key = val; /* più vari campi */p->next = head;head = p;return head;

}

Lists - list.c (2)

List* Search( List* head, int val){List* p;

p = head;while(p != NULL){

if( p->key == val) return(p);

else p = p->next;

}return(NULL);

}

Lists - list.c (3)

void Display(List* head){List* p;

p = head;

while( p != NULL){

printf(“%5d\n”,p->val);p = p->next;

}}

Lists - list.c (4)

•The previous examples are in fact two applications of a generic “visit” function that does something on ALL list elements

void Visit (List* head){List* p;

p = head;while( p != NULL){

/* do something on p->key */p = p->next;

}}

Example of usage

int val;List* head, p;…val = 1;p = Search (head, val);if (p == NULL)printf(“Value not found!\n”);

elseprintf(“Value found!\n”);

Lists: Deleting an element

• Deleting an element q (after element p)

After

p->next = q->next;free(q);

Beforep q

p->next q->next

p q

Delete it

Search where is it

Delete from head

Lists - list.c (3)

List* Delete( List* head, int val, int* status){List *p, *q;

p = q = head;if (head != NULL){ if (p->key == val) { /* found */

head = p->next;free(p);*status = SUCCESS;return head;

} else {while(q->next != NULL) {

p = q;q = q->next;if (q->key == val) {

p->next = q->next;free(q);*status = SUCCESS;return head;}}}}

*status = FAILURE;return head;

}

Lists: Inserting an element

• Insertion of node q after node p

Before

After

3 6p

5q

p->next

3 6p

5p->next q q->next

q->next = p->next;p->next = q;

Lists - list.c (4)

List* InsertSorted(List* head, int val){List *p, *q=head;

/* head insertion */if( (q == NULL) || (q->key > val)){

p = newE();

p->key = val;p->next = head;head = p;

return head;}

Lists - list.c (4)

/* search where to insert */while( q->next != NULL) { if( q->next->key > val) {

p = newE(); p->key = val; p->next = q->next; q->next = p; return head;

} q = q->next;}

q is != NULL, so q->next is defined

Lists - list.c (4)

/* tail insertion: q->next is null here*/

p = newE();p->key = val;p->next = NULL;q->next = p;return head;

}

Stacks and Queues

Stack

•Use a LIFO (Last In First Out) policy The last element inserted is the first that will be

deleted Eg.: a stack of books

•Implementation in terms of lists•Primitives:­Push­Pop­Top­Empty

Stack and queues

•Dynamic Push Insertion in head

•Dynamic Pop Deletion from head

List* head=NULL; //init.

head = Push (head, val); //call List* Push (List*,int val){ List* p; p = newE(); p->next = head; p->key = val; head = p;

}

List* Pop(List* head, int* val){ List* p;

if (head==NULL) { printf(“Stack Underflow\n”); } else {

*val­=­head->key;p­=­head;head­=­p->next;free(p);

return head; }}

Queues

• Implements a FIFO (First In First Out) policy First inserted item is the first to be extracted (deleted) E.g., a queue of persons to be served

Queues and lists

•Dynamic Enqueue Insert in tail

•Dynamic Dequeue Extract from the head

• Given the huge number of accesses to the tail of the list, it is convenient to use an explicit pointer tail for the queues

Linear queues with lists

• Dynamic Enqueue • Dynamic Dequeue

Function call:pTail = enqueue (&head, pTail, val);

List* enqueue(List** head,List* pTail,int val)

{ List* p; p = newE(); p->key = val; if (pTail==NULL) { //first elem

*head = p;p->next = NULL;

} else {pTail->next = p;}

pTail = p; return pTail;}

head = dequeue (head, &pTail, &val);

List* dequeue(List* head,List** pTail,int* val)

{ List* p;

if (head==NULL) {printf(“Queue underflow\n”);

} else {*val = head->key;p = head;if (head == *pTail) {/* one-element queue */

*pTail=NULL; head=NULL;} else { head = head->next;}

free (p); } return head;}

List* head=NULL, tail; //init.

Circular queues

•Dynamic Enqueue Insert in tail

•Dynamic Dequeue Extract from the head

• Usage of pointer pTail for insertion and deletion: last element points to first one

pTailpTail->next

Queues and lists - (cont.)

• Dynamic Enqueue • Dynamic Dequeue

Function call:pTail = enqueue(pTail, val);

List* enqueue(List* pTail, int val){ List* pNew; pNew = newE(); p->key = val; /* ……. */ if (pTail==NULL) {

pTail = pNew; pTail->next = pTail;

} else { pNew->next = pTail->next; pTail->next = pNew; pTail = pNew;}

return pTail;}

Function call:pTail = dequeue(pTail, val);

List* dequeue(List* pTail, int* val,int* status)

{ List* pOld; if (pTail=!=NULL) {

*status = SUCCESS;if (pTail == pTail->next){

*val = pTail->key;free(pTail);pTail = NULL;}

else{pOld = pTail->next;*val = pOld->key;pTail->next = pOld->next;free(pOld);}}

return pTail;}