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# Data structures

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### Data structures

1. 1. Data Structures
2. 2. Abstract Data TypeA collection of related data is known as an abstract data type (ADT)Data Structure = ADT + Collection of functions that operate on the ADT
3. 3. Data Structure• Consist of the data structure definition and a collection of functions that operate on the struct – We will never access the struct directly!
4. 4. • Separate what you can do with data from how it is represented• Other parts of the program interacts with data through provided operations according to their specifications• Implementation chooses how to represent data and implement its operations
5. 5. Multiple Implementations• An ADT can have several implementations• Interface functions are the same• Application programs will not see any difference
6. 6. ADT: Linear list• A sequence of elements• There is first and last element• Each element has previous and next – Nothing before first – Nothing after last
7. 7. Why linked lists ?• A linked list is a dynamic data structure. – It can grow or shrink in size during the execution of a program. – It can be made just as long as required. – It does not waste memory space.• Linked lists provide flexibility in allowing the items to be rearranged efficiently. – Insert an element. – Delete an element.
8. 8. • What we can do with a linear list? – Delete element – Insert element – Find element – Traverse list
9. 9. Illustration: InsertionA B C Item to be X insertedA B C X
10. 10. Illustration: DeletionA B CA B C
11. 11. In essence ...• For insertion: – A record is created holding the new item. – The next pointer of the new record is set to link it to the item which is to follow it in the list. – The next pointer of the item which is to precede it must be modified to point to the new item.• For deletion: – The next pointer of the item immediately preceding the one to be deleted is altered, and made to point to the item following the deleted item.
12. 12. Traverse: list  elements in order• get_first(list) - – returns first element if it exists• get_next(list) - – returns next element if it exists• Both functions return NULL otherwise• Calling get_next in a loop we will get one by one all elements of the list
13. 13. How we can implement a list?• Array?• Search is easy (sequential or binary)• Traversal is easy: for(i = first; i <= last; ++i) process(a[i]);• Insert and delete is not easy – a good part of the array has to be moved!• Hard to guess the size of an array
14. 14. A linked list implementation• Linked list is a chain of elements• Each element has data part and link part pointing to the next element
15. 15. Main operations• Create list• Add node – beginning,middle or end• Delete node – beginning,middle or end• Find node• Traverse list
16. 16. Conceptual IdeaInsert List implementationDelete and the related functionsTraverse
17. 17. Example: Working with linked list• Consider the structure of a node as follows: struct stud { int roll; char name[25]; int age; struct stud *next; }; /* A user-defined data type called “node” */ typedef struct stud node; node *head;
18. 18. Creating a List• To start with, we have to create a node (the first node), and make head point to it. head = (node *) malloc (sizeof (node)); head roll name next age
19. 19. Contd.• If there are n number of nodes in the initial linked list: – Allocate n records, one by one. – Read in the fields of the records. – Modify the links of the records so that the chain is formed.
20. 20. void create_list (node *list){ int k, n; node *p; printf (“n How many elements?”); scanf (“%d”, &n); To be called from the main() list = (node *) malloc (sizeof (node)); function as: p = list; for (k=0; k<n; k++) node *head; { ……. create_list (head); scanf (“%d %s %d”, &p->roll, p->name, &p->age); p->next = (node *) malloc (sizeof (node)); p = p->next; } free (p->next); p->next = NULL;}
21. 21. Traversing the List• Once the linked list has been constructed and head points to the first node of the list, – Follow the pointers. – Display the contents of the nodes as they are traversed. – Stop when the next pointer points to NULL.
22. 22. void display_list (node *list){ int k = 0; node *p; p = list; while (p != NULL) { printf (“Node %d: %d %s %d”, k, p->roll, p->name, p->age); k++; p = p->next; }}
23. 23. Inserting a Node in the List• The problem is to insert a node before a specified node. – Specified means some value is given for the node (called key). – Here it may be roll.• Convention followed: – If the value of roll is given as negative, the node will be inserted at the end of the list.
24. 24. • When a node is added at the beginning, – Only one next pointer needs to be modified. • head is made to point to the new node. • New node points to the previously first element.• When a node is added at the end, – Two next pointers need to be modified. • Last node now points to the new node. • New node points to NULL.• When a node is added in the middle, – Two next pointers need to be modified. • Previous node now points to the new node. • New node points to the next node.
25. 25. void insert_node (node *list){ int k = 0, rno; node *p, *q, *new; new = (node *) malloc (sizeof (node)); scanf (“%d %s %d”, &new->roll, new->name, &new->age); printf (“nInsert before roll (-ve for end):”); scanf (“%d”, &rno); p = list; if (p->roll == rno) /* At the beginning */ { new->next = p; list = new; }
26. 26. while ((p != NULL) && (p->roll != rno)) { q = p; p = p->next; } The pointers q and p if (p == NULL) /* At the end */ always point to { consecutive nodes. q->next = new; new->next = NULL; } if (p->roll == rno) /* In the middle */ { q->next = new; new->next = p; }}
27. 27. Deleting an Item• Here also we are required to delete a specified node. – Say, the node whose roll field is given.• Here also three conditions arise: – Deleting the first node. – Deleting the last node. – Deleting an intermediate node.
28. 28. void delete_node (node *list){ int rno; node *p, *q; printf (“nDelete for roll :”); scanf (“%d”, &rno); p = list; if (p->roll == rno) /* Delete the first element */ { list = p->next; free (p); }
29. 29. while ((p != NULL) && (p->roll != rno)) { q = p; p = p->next; } if (p == NULL) /* Element not found */ printf (“nNo match :: deletion failed”); if (p->roll == rno) /* Delete any other element */ { q->next = p->next; free (p); }}
30. 30. Doubly linked list A B CAssignment :Insertion, deletion in a doublylinked list
31. 31. A First-in First-out (FIFO) List Out In B A C B A Also called a QUEUE
32. 32. A Last-in First-out (LIFO) List In Out C B A B C Also called a STACK
33. 33. Stack
34. 34. Stacks in Our Life
35. 35. More Stacks• A stack is a LIFO structure: Last In First Out
36. 36. Basic Operations with Stacks• Push – Add and item • Overflow• Pop – Remove an item • Underflow• Stack Top – What’s on the Top • Could be empty
37. 37. Push• Adds new data element to the top of the stack
38. 38. Pop• Removes a data element from the top of the stack
39. 39. Stack Top• Checks the top element. Stack is not changed
40. 40. push pop create STACKisempty isfull
41. 41. Assume:: stack contains integer elementsvoid push (stack s, int element); /* Insert an element in the stack */int pop (stack s); /* Remove and return the top element */void create (stack s); /* Create a new stack */int isempty (stack s); /* Check if stack is empty */int isfull (stack s); /* Check if stack is full */
42. 42. • We shall look into two different implementations of stack: – Using arrays – Using linked list
43. 43. Stack Implementation
44. 44. Stack Implementation Using Arrays• Basic idea. – Declare an array of fixed size (which determines the maximum size of the stack). – Keep a variable which always points to the “top” of the stack.
45. 45. Declaration#define MAXSIZE 100struct lifo { int st[MAXSIZE]; int top; };typedef struct lifo stack;
46. 46. Stack Creationvoid create (stack s){ s.top = 0; /* Points to last element pushed in */}
47. 47. Pushing an element into the stack void push (stack s, int element) { if (s.top == (MAXSIZE-1)) { printf (“n Stack overflow”); break; } else { s.top ++; s.st [s.top] = element; }
48. 48. Removing/Popping an element from the stack int pop (stack s) { if (s.top == 0) { printf (“n Stack underflow”); break; } else { return (s.st [s.top --]); } }
49. 49. Checking for stack full / empty int isempty (stack s) { if (s.top == 0) return 1; else return (0); }int isfull (stack s) { if (s.top == (MAXSIZE – 1)) return 1; else return (0); }
50. 50. Stack Implementation Using Linked List• Very similar to the linked list implementation discussed earlier. struct lifo { int element; struct lifo *next; }; typedef struct lifo stack; stack *top;
51. 51. Contd.• Basic concept: – Insertion (push) and deletion (pop) operations take place at one end of the list only. – For stack creation / push operation • Required to call malloc function – How to check stack underflow? • Easy. Simply check if top points to NULL. – How to check overflow? • Check is malloc returns –1.
52. 52. Sample Usagestack A, B;create (A); create (B);push (A, 10); push (A, 20); push (A, 30);push (B, 5); push (B, 25); push (B, 10);printf (“n%d %d %d”, pop(A), pop(A), pop(A));printf (“n%d %d %d”, pop(B), pop(B), pop(B));if (not isfull (A)) 30 20 10 push (A, 50); 10 25 5if (not isempty (A)) k = pop (A);
53. 53. Queues
54. 54. Queues in Our Life• A queue is a FIFO structure: Fast In First Out
55. 55. Basic Operations with Queues• Enqueue - Add an item to the end of queue • Overflow• Dequeue - Remove an item from the front • Could be empty• Queue Front - Who is first? • Could be empty• Queue End - Who is last? • Could be empty
56. 56. Enqueue
57. 57. Dequeue
58. 58. Queue Front
59. 59. Queue Rear
60. 60. Queue implementation with arrays
61. 61. Queue will overgrow the array • Should we use VERY L A R G E ARRAYS?
62. 62. Array implementation of queues queueAry maxsize count front rear 7 4 1 5 front rear 11 37 22 15 3 -7 1
63. 63. Structure for a queue arraystruct intqueue { int *queueArray; int maxSize; int count; int front; int rear;};
64. 64. Queue Implementation Using Linked List • Basic idea: – Create a linked list to which items would be added to one end and deleted from the other end. – Two pointers will be maintained: • One pointing to the beginning of the list (point from where elements will be deleted). • Another pointing to the end of the list (point where new elements will be inserted). RearFront
65. 65. Assume:: queue contains integer elementsvoid enqueue (queue q, int element); /* Insert an element in the queue */int dequeue (queue q); /* Remove an element from the queue */queue *create (); /* Create a new queue */int isempty (queue q); /* Check if queue is empty */int size (queue q); /* Return the number of elements in queue */
66. 66. Creating a queuefront = NULL;rear = NULL;
67. 67. Inserting an element in queuevoid enqueue (queue q, int x){ queue *ptr; ptr = (queue *) malloc (sizeof (queue)); if (rear == NULL) /* Queue is empty */ { front = ptr; rear = ptr; ptr->element = x; ptr->next = NULL; } else /* Queue is not empty */ { rear->next = ptr; ptr ->element = x; ptr->next = NULL; }}
68. 68. Deleting an element from queueint dequeue (queue q) { queue *old; if (front == NULL) /* Queue is empty */ printf (“n Queue is empty”); else if (front == rear) /* Single element */ { k = front->element; free (front); front = rear = NULL; return (k); } else { k = front->element; old = front; front = front->next; free (old); return (k); } }
69. 69. Checking if emptyint isempty (queue q){ if (front == NULL) return (1); else return (0);}
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