1. Linked Lists

2. Outline Why linked lists? Linked lists basics Implementation Basic primitives ­Searching ­Inserting ­Deleting

3. 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

4. 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

5. 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

6. 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

7. 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.

8. Array vs. linked lists Array – int v[4]; List – ???? 2 5 3 v[0] v[1] v[2] v[3] v 2 5 3 ?

9. 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()

10. Arrays vs. linked lists ArraysLists 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)

11. 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

12. 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)

13. Array vs. linked lists Array – int v[4]; List – List* Head; 2 5 3 v[0] v[1] v[2] v[3] v 2 5 3 Head

14. Lists - (cont.) Primitives ­Insert ( at the head of the list ) ­Search ­Delete ­InsertSorted NOTE: The ordering of a list is not immediate ­It requires double pointers or auxiliary lists

15. 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

16. 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 */

17. Lists - list.c (1) #include List* Insert( List* head, int val) { List* p; p = newE(); p->key = val; /* più vari campi */ p->next = head; head = p; return head; }

18. 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); }

19. Lists - list.c (3) void Display(List* head) { List* p; p = head; while( p != NULL) { printf(“%5d\n”,p->val); p = p->next; }

20. 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; }

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

22. Lists: Deleting an element Deleting an element q (after element p) After p->next = q->next; free(q); Before p q p->next q->next p q

23. 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; }

24. Lists: Inserting an element Insertion of node q after node p Before After 3 6 p 5 q p->next 3 6 p 5 qq->next q->next = p->next; p->next = q;

25. 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; }

26. 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

27. Lists - list.c (4) /* tail insertion: q->next is null here */ p = newE(); p->key = val; p->next = NULL; q->next = p; return head; }

28. Stacks and Queues

29. 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: ­Push ­Pop ­Top ­Empty

30. Dynamic stacks and queues To overcome this limitation: ­Use the function realloc in case of overflow ­To implement as a list The second solution is particularly advantageous for queues

31. 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; }

32. 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

33. 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

34. Linear queues with lists Dynamic EnqueueDynamic 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.

35. 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

36. Queues and lists - (cont.) Dynamic EnqueueDynamic 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; }