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Data Structures

Data Structures. -- Data processing often involves in processing huge volumes of data. Many Companies handle million records of data stored in database. Many ways are formulated to handle data efficiently.

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Data Structures

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  1. Data Structures -- Data processing often involves in processing huge volumes of data. Many Companies handle million records of data stored in database. Many ways are formulated to handle data efficiently. -- An User-defined data type is a combination of different primary data types, which represents a complex entity. -- An Abstract Data Type ( A D T ) not only represents a set of complex data objects, but also includes a set of operations to be performed on these objects, defines that how the data objects are organized. -- The group of methods implements a set rules, which defines a logical way of handling data. -- The complex entity along with its group of methods is called Abstract Data Type ( A D T ) . -- Data structure is described as an instance of Abstract Data Type ( ADT ). -- We can define that Data structure is a kind of representation of logical relationship between related data elements. In data structure, decision on the operations such as storage, retrieval and access must be carried out between the logically related data elements. Data Structure Some Data structures Arrays Strings Lists StacksQueues Trees Graphs Dictionaries Maps Hash Tables Sets Lattice Neural-Nets Linear Non-Linear Linear Lists Stacks Queues Trees Graphs Some Common Operations on Data structures Insertion : adding a new element to the collection. Deletion : removing an element from a collection. Traversal : access and examine each element in collection. Search : find whether an element is present or not. Sorting : rearranging elements in a particular order. Merging : combining two collections into one collection.

  2. Arrays – Linked Lists What is a Linked List The elements of a linked list are not constrained to be stored in adjacent locations. The individual elements are stored “somewhere” in memory, rather like a family dispersed, but still bound together. The order of the elements is maintained by explicit links between them. • Limitations of Arrays • Fixed in size : • Once an array is created, the size of array cannot be increased or decreased. • Wastage of space : • If no. of elements are less, leads to wastage of space. • Sequential Storage : • Array elements are stored in contiguous memory locations. At the times it might so happen that enough contiguous locations might not be available. Even though the total space requirement of an array can be met through a combination of non-contiguous blocks of memory, we would still not be allowed to create the array. • Possibility of overflow : • If program ever needs to process more than the size of array, there is a possibility of overflow and code breaks. • Difficulty in insertion and deletion : • In case of insertion of a new element, each element after the specified location has to be shifted one position to the right. In case of deletion of an element, each element after the specified location has to be shifted one position to the left. The Linked List is a collection of elements called nodes, each node of which stores two items of information, i.e., data part and link field. -- The data part of each node consists the data record of an entity. -- The link field is a pointer and contains the address of next node. -- The beginning of the linked list is stored in a pointer termed as head which points to the first node. -- The head pointer will be passed as a parameter to any method, to perform an operation. -- First node contains a pointer to second node, second node contains a pointer to the third node and so on. -- The last node in the list has its next field set to NULL to mark the end of the list.

  3. struct node { int rollno; struct node *next; }; int main() { struct node *head,*n1,*n2,*n3,*n4; /* creating a new node */ n1=(struct node *) malloc(sizeof(struct node)); n1->rollno=101; n1->next = NULL; /* referencing the first node to head pointer */ head = n1; /* creating a new node */ n2=(struct node *)malloc(sizeof(struct node)); n2->rollno=102; n2->next = NULL; /* linking the second node after first node */ n1->next = n2; /* creating a new node * / n3=(struct node *)malloc(sizeof(struct node)); n3->rollno=104; n3->next=NULL; /* linking the third node after second node */ n2->next = n3; /* creating a new node */ n4=(struct node *)malloc (sizeof (struct node)); n4->rollno=103; n4->next=NULL; /* inserting the new node between second node and third node */ n2->next = n4; n4->next = n3; Creating a Singly Linked List /* deleting n2 node */ n1->next = n4; free(n2); } 150 head 150 n1-node 150 720 150 n2-node n1-node 150 910 720 150 n3-node n2-node n1-node 150 head 150 400 910 n1-node n2-node n3-node 720 n4-node 150 head 150 910 720 n3-node n1-node n4-node 400 n2-node

  4. Implementing Singly Linked List struct node { int data; struct node *next; }; struct node *createnode() { struct node *new; new = (struct node *)malloc(sizeof(struct node)); printf("\nEnter the data : "); scanf("%d",&new->data); new->next = NULL; return new; } void append(struct node **h) { struct node *new,*temp; new = createnode(); if(*h == NULL) { *h = new; return; } temp = *h; while(temp->next!=NULL) temp = temp->next; temp->next = new; } void display(struct node *p) { printf("\nContents of the List : \n\n"); while(p!=NULL) { printf("\t%d",p->data); p = p->next; } } void insert_after(struct node **h) { struct node *new,*temp; int k; if(*h == NULL) return; printf("\nEnter data of node after which node : "); scanf("%d",&k); temp = *h; while(temp!=NULL && temp->data!=k) temp = temp->next; if(temp!=NULL) { new=createnode(); new->next = temp->next; temp->next = new; } } void insert_before(struct node **h) { struct node *new,*temp,*prev ; int k; if(*h==NULL) return; printf("\nEnter data of node before which node : "); scanf("%d",&k); if((*h)->data == k) { new = createnode(); new->next = *h; *h = new; return; } temp = (*h)->next; prev = *h;

  5. Implementing Singly Linked List ( continued ) while(temp!=NULL && temp->data!=k) { prev=temp; temp=temp->next; } if(temp!=NULL) { new = createnode(); new->next = temp; prev->next = new; } } void delnode(struct node **h) { struct node *temp,*prev; int k; if(*h==NULL) return; printf("\nEnter the data of node to be removed : "); scanf("%d",&k); if((*h)->data==k) { temp=*h; *h=(*h)->next; free(temp); return; } temp=(*h)->next; prev=*h; while(temp!=NULL && temp->data!=k) { prev=temp; temp=temp->next; } if(temp!=NULL) { prev->next = temp->next; free(temp); } } void search(struct node *h) { struct node *temp; int k; if(h==NULL)return; printf("\nEnter the data to be searched : "); scanf("%d",&k); temp=h; while(temp!=NULL && temp->data!=k) temp=temp->next; (temp==NULL)? printf("\n\t=>Node does not exist") : printf("\n\t=>Node exists"); } void destroy(struct node **h) { struct node *p; if(*h==NULL) return; while(*h!=NULL) { p = (*h)->next; free(*h); *h=p; } printf("\n\n ******Linked List is destroyed******"); }

  6. Implementing Singly Linked List ( continued ) int main() { struct node *head=NULL; int ch; while(1) { printf("\n1.Append"); printf("\n2.Display All"); printf("\n3.Insert after a specified node"); printf("\n4.Insert before a specified node"); printf("\n5.Delete a node"); printf("\n6.Search for a node"); printf("\n7.Distroy the list"); printf("\n8.Exit program"); printf("\n\n\tEnter your choice : "); scanf("%d",&ch); switch(ch) { case 1:append(&head);break; case 2:display(head);break; case 3:insert_after(&head);break; case 4:insert_before(&head);break; case 5:delnode(&head);break; case 6:search(head);break; case 7:destroy(&head);break; case 8:exit(0);break; default : printf( "Wrong Choice, Enter correct one : "); } } } /* function to sort linked list */ void sort(struct node *h) { struct node *p,*temp; int i, j, n, t, sorted=0; temp=h; for(n=0 ; temp!=NULL ; temp=temp->next) n++; for(i=0;i<n-1&&!sorted;i++) { p=h; sorted=1; for(j=0;j<n-(i+1);j++) { if ( p->data > ( p->next )->data ) { t=p->data; p->data =(p->next)->data; (p->next)->data = t; sorted=0; } p=p->next; } } } /* function to count number of node in the list */ int count ( struct node *h) { int i; for( i=0 ; h!=NULL ; h=h->next) i++; return i; }

  7. Algorithm for adding two polynomials in linked lists Add_Polynomial( list p, list q ) set p, q to point to the two first nodes (no headers) initialize a linked list r for a zero polynomial while p != null and q != null if p.exp > q.exp create a node storing p.coeff and p.exp insert at the end of list r advance p else if q.exp > p.exp create a node storing q.coeff and q.exp insert at the end of list r advance q else if p.exp == q.exp if p.coeff + q.coeff != 0 create a node storing p.coeff + q.coeff and p.exp insert at the end of list r advance p, q end while if p != null copy the remaining terms of p to end of r else if q != null copy the remaining terms of q to end of r

  8. Doubly Linked List • Pitfalls encountered while using singly linked list : • A singly linked list allows traversal of the list in forward direction, but not in backward direction. • Deleting a node from a list requires keeping track of the previous node,. • In the list any node gets corrupted, the remaining nodes of the list become unusable. • These problems of singly linked lists can be overcome by doubly linked list. A Doubly Linked List is a data structure having an ordered list of nodes, in which each node consists of two pointers. One pointer is to store the address of next node like in singly linked list. The second pointer stores the address of previous node. It is also known as two-way list. The specialty of DLL is that the list can be traversed in forward as well as backward directions. The concept of DLL is also used to representing tree data structures. head tail A B C /* a node in doubly linked list */ struct node { struct node *prev; int data ; struct node *next; } Tree structure using Doubly Linked List

  9. Insertion of node in Doubly Linked List q A B D C p q A B C D Deletion of node in Doubly Linked List A B C p D A B C

  10. Implementing Doubly Linked List struct node { struct node *prev; int data; struct node *next; }; struct node *createnode() { struct node *new; new = (struct node *)malloc(sizeof(struct node)); printf("\nEnter the data : "); scanf("%d",&new->data); new->prev = NULL; new->next = NULL; return new; } void append(struct node **h) { struct node *new,*temp; new = createnode(); if(*h == NULL) { *h = new; return; } temp = *h; while(temp->next!=NULL) temp = temp->next; temp->next = new; new->prev = temp; } void forward_display(struct node *p) { printf("\nContents of the List : \n\n"); while(p!=NULL) { printf("\t%d",p->data); p = p->next; } printf("\n"); } void insert_after(struct node **h) { struct node *new,*temp; int k; if(*h == NULL) return; printf("\nEnter data of node after which node : "); scanf("%d",&k); temp = *h; while(temp!=NULL && temp->data!=k) temp = temp->next; if(temp!=NULL) { new=createnode(); new->next = temp->next; temp->next = new; new->prev = temp; if(new->next != NULL) new->next->prev = new; } }

  11. Implementing Doubly Linked List ( continued ) void insert_before(struct node **h) { struct node *new,*temp; int k; if(*h==NULL) return; printf("\nEnter data of node before which node : "); scanf("%d",&k); if((*h)->data == k) { new = createnode(); new->next = *h; new->next->prev=new; *h = new; return; } temp = *h; while(temp!=NULL && temp->data!=k) { temp=temp->next; } if(temp!=NULL) { new = createnode(); new->next = temp; new->prev = temp->prev; new->prev->next = new; temp->prev = new; } } void delnode(struct node **h) { struct node *temp; int k; if(*h==NULL) return; printf("\nEnter the data of node to be removed : "); scanf("%d",&k); if((*h)->data==k) { temp=*h; *h=(*h)->next; (*h)->prev=NULL; free(temp); return; } temp=*h; while(temp!=NULL && temp->data!=k) { temp=temp->next; } if(temp!=NULL) { temp->next->prev = temp->prev; temp->prev->next = temp->next; free(temp); } }

  12. Implementing Doubly Linked List ( continued ) void search(struct node *h) { struct node *temp; int k; if(h==NULL) return; printf("\nEnter the data to be searched : "); scanf("%d",&k); temp=h; while(temp!=NULL && temp->data!=k) temp=temp->next; if (temp==NULL) printf("\n\t=>Node does not exist") else printf("\n\t=>Node exists"); } void destroy(struct node **h) { struct node *p; if(*h==NULL) return; while(*h!=NULL) { p = (*h)->next; free(*h); *h=p; } printf("\n\n ******Linked List is destroyed******"); } int main() { struct node *head=NULL; int ch; while(1) { printf("\n1.Append"); printf("\n2.Display All"); printf("\n3.Insert after a specified node"); printf("\n4.Insert before a specified node"); printf("\n5.Delete a node"); printf("\n6.Search for a node"); printf("\n7.Distroy the list"); printf("\n8.Exit program"); printf("\n\n\tEnter your choice : "); scanf("%d",&ch); switch(ch) { case 1:append(&head);break; case 2:forward_display(head);break; case 3:insert_after(&head);break; case 4:insert_before(&head);break; case 5:delnode(&head);break; case 6:search(head);break; case 7:destroy(&head);break; case 8:exit(0);break; default : printf("Wrong Choice, Enter correct choice : "); } } }

  13. prev prev prev prev data data data data next next next next 910 Circular Singly Linked List tail 150 400 720 910 n3-node n4-node n2-node n1-node -- Singly Linked List has a major drawback. From a specified node, it is not possible to reach any of the preceding nodes in the list. To overcome the drawback, a small change is made to the SLL so that the next field of the last node is pointing to the first node rather than NULL. Such a linked list is called a circular linked list. -- Because it is a circular linked list, it is possible to reach any node in the list from a particular node. -- There is no natural first node or last node because by virtue of the list is circular. -- Therefore, one convention is to let the external pointer of the circular linked list, tail, point to the last node and to allow the following node to be the first node. -- If the tail pointer refers to NULL, means the circular linked list is empty. Circular Doubly Linked List -- A Circular Doubly Linked List ( CDL ) is a doubly linked list with first node linked to last node and vice-versa. -- The ‘ prev ’ link of first node contains the address of last node and ‘ next ’ link of last node contains the address of first node. -- Traversal through Circular Singly Linked List is possible only in one direction. -- The main advantage of Circular Doubly Linked List ( CDL ) is that, a node can be inserted into list without searching the complete list for finding the address of previous node. -- We can also traversed through CDL in both directions, from first node to last node and vice-versa.

  14. Implementing Circular Singly Linked List struct node { int data; struct node *next; }; struct node *createnode() { struct node *new; new = (struct node *)malloc(sizeof(struct node)); printf("\nEnter the data : "); scanf("%d",&new->data); new->next = NULL; return new; } void append(struct node **t) { struct node *new,*head; new = createnode(); if(*t == NULL) { *t = new; new->next = *t; return; } head = (*t)->next; (*t)->next = new; new->next = head; *t = new; } void display(struct node *t) { struct node *temp = t->next, *head=t->next; printf("\nContents of the List : \n\n"); do { printf("\t%d",temp->data);temp = temp->next; }while(temp!=head); printf(“\n”); } void insert_after(struct node **t) { struct node *new,*temp; int k, found=0; if(*t == NULL) return; printf("\nEnter data of node after which node : "); scanf("%d",&k); if((*t)->data==k) { new = createnode(); new->next = (*t)->next; (*t)->next = new; *t=new; return; } temp=(*t)->next; while(temp!=*t) { if(temp->data == k) { new = createnode(); new->next = temp->next; temp->next = new; found=1; break; } temp=temp->next; } if(found==0) printf("\nNode does not exist.."); }

  15. Implementing Circular Singly Linked List ( continued ) void insert_before(struct node **t) { struct node *new,*temp,*prev,*head; int k,found=0; if(*t==NULL) return; printf("\nEnter data of node before which node : "); scanf("%d",&k); head=(*t)->next; if(head->data == k) { new = createnode(); new->next = head; (*t)->next = new; return; } temp = head->next; prev = head; while(temp!=head) { if(temp->data==k) { new = createnode(); prev->next = new; new->next = temp; found=1; break; } else { prev=temp; temp=temp->next; } } if(found==0) printf("\nNode does not exist.."); } void delnode(struct node **t) { struct node *temp,*prev,*head; int k,found=0; if(*t==NULL) return; printf("\nEnter the data of node to be removed : "); scanf("%d",&k); head=(*t)->next; if(head->data==k) { temp=head; if(temp->next!=head) (*t)->next=head->next; else *t = NULL; free(temp); return; } temp=head->next; prev=head; while(temp!=head) { if(temp->data == k) { prev->next = temp->next; if(temp==*t) *t = prev; free(temp); found=1; break; } else { prev=temp; temp=temp->next; } } if(found==0) printf("\nNode does not exist.."); }

  16. Implementing Circular Singly Linked List ( continued ) int main() { struct node *tail=NULL; int ch; while(1) { printf("\n1.Append"); printf("\n2.Display All"); printf("\n3.Insert after a specified node"); printf("\n4.Insert before a specified node"); printf("\n5.Delete a node"); printf("\n6.Exit program"); printf("\n\n\tEnter your choice : "); scanf("%d",&ch); switch(ch) { case 1:append(&tail);break; case 2:display(tail);break; case 3:insert_after(&tail);break; case 4:insert_before(&tail);break; case 5:delnode(&tail);break; case 6:exit(0);break; default : printf(“\n\tWrong Choice… “); } } } Types of Data Structures Data structures are classified in several ways : Linear : Elements are arranged in sequential fashion. Ex : Array, Linear list, stack, queue Non-Linear : Elements are not arranged in sequence. Ex : trees, graphs Homogenous : All Elements are belongs to same data type. Ex : Arrays Non-Homogenous : Different types of Elements are grouped and form a data structure. Ex: classes Dynamic : Memory allocation of each element in the data structure is done before their usage using D.M.A functions Ex : Linked Lists Static : All elements of a data structure are created at the beginning of the program. They cannot be resized. Ex : Arrays

  17. Stacks -- Stack is an ordered collection of data elements into which new elements may be inserted and from which elements may be deleted at one end called the “TOP” of stack. -- A stack is a last-in-first-out ( LIFO ) structure. -- Insertion operation is referred as “PUSH” and deletion operation is referred as “POP”. -- The most accessible element in the stack is the element at the position “TOP”. -- Stack must be created as empty. -- Whenever an element is pushed into stack, it must be checked whether the stack is full or not. -- Whenever an element is popped form stack, it must be checked whether the stack is empty or not. -- We can implement the stack ADT either with array or linked list. • Stack ADT • struct stackNode { • int data; struct stackNode *next; • }; • init_stack( ) • push ( ) • pop ( ) • isEmpty ( ) • display ( ) • peek ( ) • Applications of stack • Reversing Data series • Conversion decimal to binary • Parsing into tokens • Backtracking the operations • Undo operations in Text Editor • Page visited History in web browser • Tracking of Function calls • Maintaining scope and lifetime of local variables in functions • Infix to postfix conversion • Evaluating postfix expression

  18. Push(a) Push(b) Pop( ) Push(d) Push(e) Pop( ) Push(c) Pop( ) Pop( ) Pop( ) e c d d d Operation b b b b b b b a a a a a a a a a Operations on Stack Output TOP value Stack’s contents 1. Init_stack( ) <empty> -1 2. Push( ‘a’ ) 0 a a b 3. Push( ‘b’ ) 1 a b c 4. Push( ‘c’ ) 2 a b c 5. Pop( ) 1 a b d c 6. Push( ‘d’ ) 2 a b d e 7. Push( ‘e’ ) c 3 a b d c e 8. Pop( ) 2 a b c e d 9. Pop( ) 1 c e d b a 10. Pop( ) 0 c e d b a -1 <empty> 11. Pop( )

  19. Implementing Stack ADT using Array #define SIZE 50 int stack[SIZE]; int top; void init_stack() { top=-1; } void push( int n ) { if( top==SIZE-1) printf("\nStack is full"); else stack[++top]= n; } int pop( ) { if(top== -1) { printf("\nStack is empty"); return -1; } else return stack[top--]; } void display( ) { int i; if(top== -1) printf("\nStack is empty."); else { printf("\nElements are : \n"); for(i=0;i<=top;i++) printf("%5d ",stack[i]); } } int isEmpty( ) { if ( top== -1 ) return 1; else return 0; } int peek( ){ return stack[top]; } int main() { int choice,item; init_stack(); do { printf("\n\t\t\tMenu\n\t1.Push.\n\t2.Pop."); printf("\n\t3.Peek.\n\t4.Display.\n\t5.Exit.\n"); printf("\nYour Choice: "); scanf("%d",&choice); switch(choice) { case 1:printf("\nEnter the element to push : "); scanf("%d",&item); push(item); break; case 2:item = pop(); printf("\nElement poped : %d",item); printf("\nPress a key to continue..."); getche(); break; case 3:item = peek(); printf("\nElement at top : %d",item); printf("\nPress a key to continue..."); getche(); break; case 4:display(); printf("\nPress a key to continue..."); getche(); break; case 5:exit(0); } }while(1); }

  20. Implementing Stack ADT using Linked List struct s_node { int data; struct s_node *link; } *stack; void push(int j) { struct s_node *m; m=(struct s_node*)malloc(sizeof(struct s_node)); m->data= j ; m->link=stack; stack=m; return; } int pop( ) { struct s_node *temp=NULL; if(stack==NULL) { printf("\nSTACK is Empty."); getch(); } else { int i=stack->data; temp = stack ; stack=stack->link; free(temp); return (i); } } int peek( ) { if(stack==NULL) { printf("\nSTACK is Empty."); getch(); } else return (stack->data); } void display() { struct s_node *temp=stack; while(temp!=NULL) { printf("%d\t",temp->data); temp=temp->link; } } void main() { int choice,num,i; while(1) { printf("\n\t\t MENU\n1. Push\n2. Pop\n3. Peek"); printf("\n4. Elements in Stack\n5. Exit\n"); printf("\n\tEnter your choice: "); scanf("%d",&choice); switch(choice) { case 1: printf("\nElement to be pushed:"); scanf("%d",&num); push(num); break; case 2: num=pop(); printf("\nElement popped: %d ",num); getch(); break; case 3: num=peek(); printf("\nElement peeked : %d ",num); getch(); break; case 4: printf("\nElements present in stack : “ ): display();getch(); break; case 5: exit(1); default: printf("\nInvalid Choice\n"); break; } } }

  21. Queues -- Queue is a linear data structure that permits insertion of new element at one end and deletion of an element at the other end. -- The end at which insertion of a new element can take place is called ‘ rear ‘ and the end at which deletion of an element take place is called ‘ front ‘. -- The first element that gets added into queue is the first one to get removed from the list, Hence Queue is also referred to as First-In-First-Out ( FIFO ) list. -- Queue must be created as empty. -- Whenever an element is inserted into queue, it must be checked whether the queue is full or not. -- Whenever an element is deleted form queue, it must be checked whether the queue is empty or not. -- We can implement the queue ADT either with array or linked list. • Queue ADT • struct queueNode { • int data; struct queueNode *next; • }; • init_queue( ) • addq ( ) • delq ( ) • isEmpty ( ) • printQueue ( ) 4 rear front 3 6 8 2 5 addq (4) delq ( ) 7 • Applications of Queues • Execution of Threads • Job Scheduling • Event queuing • Message Queueing • Types of Queues • circular queues • priority queues • double-ended queues

  22. Implementing Queue ADT using Array int queue[10] ,front, rear ; void init_queue() { front = rear = -1 ; } void addq ( int item ){ if ( rear == 9 ) { printf("\nQueue is full"); return ; } rear++ ; queue [ rear ] = item ; if ( front == -1 )front = 0 ; } int delq( ){ int data ; if ( front == -1 ) { printf("\nQueue is Empty"); return 0; } data = queue[front] ; queue[front] = 0 ; if ( front == rear ) front = rear = -1 ; else front++ ; return data ; } void display() { int i; if(front==-1) printf("\nQueue is empty."); else { printf("\nElements are : \n"); for (i=front;i<=rear;i++) printf("%5d",queue[i]); } } int main() { int ch,num; init_queue(); do { printf("\n\tMENU\n\n1. Add to Queue”); printf(“\n2. Delete form Queue"); printf("\n3. Display Queue\n4. Exit."); printf("\n\n\tYour Choice: "); scanf("%d",&ch); switch(ch) { case 1: printf("\nEnter an element : "); scanf("%d",&num); addq(num);break; case 2: num=delq(); printf("\nElement deleted : %d",num); break; case 3: display(); break; case 4: exit(0); default: printf("\nInvalid option.."); } }while(1); }

  23. Implementing Queue ADT using Liked List struct q_node { int data; struct q_node *next; }*rear,*front; void init_queue() { rear=NULL; front=NULL; } void addq(int item) { struct q_node *t; t=(struct q_node*)malloc(sizeof(struct q_node)); t->data=item; t->next=NULL; if(front==NULL) rear=front=t; else { rear->next=t; rear=rear->next; } } int delq() { struct q_node *temp; if(front==NULL) { printf("\nQueue is empty."); return 0; } else { int num = front->data; temp = front; front=front->next; free(temp); return num; } } void display() { struct q_node *temp=front; if(front==NULL) printf("\nQueue is empty."); else { printf("\nElements in Queue :\n"); while(temp!=NULL) { printf("%5d",temp->data); temp=temp->next; } } } int main() { int ch,num; init_queue(); do { printf("\n\tMENU\n\n1. Add\n2. Delete"); printf("\n3. Display Queue\n4. Exit."); printf("\n\n\tYour Choice: "); scanf("%d",&ch); switch(ch) { case 1: printf("\nEnter an element : "); scanf("%d",&num); addq(num);break; case 2: num=delq(); printf("\nElement deleted : %d",num); break; case 3: display(); break; case 4: exit(0); default:printf("\nInvalid option.."); } }while(1); }

  24. --Arithmetic Expressions are represented using three notations infix, prefix and postfix. The prefixes ‘pre’, ‘post’, and ‘in’ refer to position of operators with respect to two operands. -- In infix notation, the operator is placed between the two operands. Ex: A + B A * B + C (A * B) + (C * D) -- In Prefix notation, the operator is placed before the two operands. Ex: +AB *A+BC +*AB*CD -- In Postfix notation, the operator is placed after the two operands. Ex: AB+ ABC+* AB*CD*+ Algorithm to Infix to Postfix Conversion • In-To-Post ( infix-expression ) • Scan the Infix expression left to right • If the character x is an operand • Output the character into the Postfix Expression • If the character x is a left or right parenthesis • If the character is “( • Push it into the stack • If the character is “)” • Repeatedly pop and output all the operators/characters until “(“ is popped from the stack. • If the character x is a is a regular operator • Check the character y currently at the top of the stack. • If Stack is empty or y is ‘(‘ or y is an operator of lower precedence than x, then • Push x into stack. • If y is an operator of higher or equal precedence than x, • Pop and output y and push x into the stack. • When all characters in infix expression are processed • repeatedly pop the character(s) from the stack and output them until the stack is empty.

  25. In-Fix To Post-Fix convertion #define STACKSIZE 20 typedef struct { int top; char items[STACKSIZE]; }STACK; /*pushes ps into stack*/ void push(STACK *sptr, char ps) { if(sptr->top == STACKSIZE-1) { printf("Stack is full\n"); exit(1); } else sptr->items[++sptr->top]= ps; } char pop(STACK *sptr) { if(sptr->top == -1) { printf("Stack is empty\n"); exit(1); } else return sptr->items[sptr->top--]; } int main() { int i; STACK s; char x, y, E[20] ; s.top = -1; /* Initialize the stack is */ printf("Enter the Infix Expression:"); scanf("%s",E); for(i=0;E[i] != '\0';i++) { x= E[i]; /* Consider all lowercase letter from a to z are operands */ if(x<='z' && x>='a') printf("%c",x); else if(x == '(') push(&s ,x); else if( x == ')‘ ){ y=pop(&s) ; while(y != '(') { printf("%c",y); y=pop(&s) ; } } else { if(s.top ==-1 || s.items[s.top] == '(') push(&s ,x); else { /* y is the top operator in the stack*/ y = s.items[s.top]; /* precedence of y is higher/equal to x*/ if( y=='*' || y=='/'){ printf("%c", pop(&s)); push(&s ,x); } else if ( y=='+' || y=='-') /* precedence of y is equal to x*/ if( x=='+' || x=='-') { printf("%c", pop(&s)); push(&s ,x); } /* precedence of y is less than x*/ else push(&s ,x); } } } while(s.top != -1) printf("%c",pop(&s)); }

  26. Evaluation of Post-Fix Expression #include<stdio.h> #include<ctype.h> #include<math.h> float stack[10]; int top=-1; void push(char c) { stack[++top]=c; } float pop() { float n; n=stack[top--]; return (n); } float evaluate(char expr[], float data[]) { int j=0; float op1=0,op2=0; char ch; while(expr[j]!='\0') { ch = expr[j]; if(isalpha(expr[j])) { push(data[j]); } else { op2=pop(); op1=pop(); switch(ch) { case '+':push(op1+op2);break; case '-':push(op1-op2);break; case '*':push(op1*op2);break; case '/':push(op1/op2);break; case '^':push(pow(op1,op2)); break; } } j++; } return pop(); } int main() { int j=0; char expr[20]; float number[20],result; printf("\nEnter a post fix expression : "); gets(expr); while(expr[j]!='\0') { if(isalpha(expr[j])) { fflush(stdin); printf("\nEnter number for %c : ",expr[j]); scanf("%f",&number[j]); } j++; } result = evaluate(expr,number); printf("\nThe result of %s is %f",expr,result); }

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