Data structure manual

SUBJECT: DATA STRUCTURESUBJECT: DATA STRUCTURESUBJECT: DATA STRUCTURESUBJECT: DATA STRUCTURE 1111////50505050

Prepared By: CJ SofTech [Charanjiv Singh 98156-18658] Coaching Of C,C++,C#, Java, Blue J, VB, VB.NET, Oracle, Data Structure And Project Work

Section – A 2 Marks Questions [QUESTIONS 1 TO 18] [PAGE 1 TO 4]

Q1. What is data structure? Ans. The logical or mathematical model of a particular organization of data is called a data

structure. Q2. What are two main types of data structure? Ans. 1.Linear Data Structure:

A data structure is said be linear if its elements are stored sequentially in the form of a linear list e.g. arrays, stacks, linked lists. 2. Non-linear Data structure:

A data structure is said to be non-linear if its elements are not stored sequentially in the form of linear list e.g. trees & graphs.

Q3. Write various operations performed on data stru cture. Ans. The various operations are: -

1. Traversing 2. Inserting 3. Deleting 4. Merging 5. Searching 6. Sorting 7. Updating 8. Creating

Q4. What is an array? How array is stored in memor y. Ans . Array is collection of homogeneous data elements. They are stored in continuous

memory locations. They are accessed by using index value. int a[5];

12 4 45 67 68 1000 1002 1004 1006 1008

1000 is the location of the first element of the array. As the int data type takes two bytes of the memory so the next element is stored at 1002 and so on.

Q5. What are pointer Arrays? Ans. A pointer array is memory variable that use to store address of a variable. Pointer

arrays are use to store address of more then one variable. e.g. main()

{ int *a[3]; int x,y,z; x=10; y=20; z=30; a[0]=&x; a[1]=&y; a[2]=&z; printf(“address of x=%u”,a[0]); }

Q6. What is a linked list? Ans. A linked list or one-way list is a linear collection of data elements, called nodes,

where the linear order is given by means of pointers. Each node is divided into 2 parts. The first part contains the information of the

element & the second part called the link field, contains the address of the next node in the list.



Q7. Write syntax to declare a node of linked list. Ans. Singly linked list struct node

{ int info; node *link; }; Doubly linked list

Struct node { int info; node *next,*prev; };

Q8. What are different types of linked list? Ans. The various types of linked list are:-

1. Singly 2. Doubly 3. Circular 4. Generalized

Q9. What are Reversible linked list? Ans. A reversible linked list enable you to visit a node, Which is previously visited by the

pointer, we can visit any node, which is previously visited, By providing address of the node.

Q10. What are operations performed on linked list? Ans. 1. Insertion 2. Deletion 3. Searching 4. Traversing Q11. Write an algorithm to delete a node from linke d list from beginning. Ans . DELFIRST (LINK, START).

1. [Underflow?] If START = NULL then: Write underflow and Exit

2. Set START=LINK [START] 3. Exit.

Q12. Write an algorithm to Delete a node from linke d list from END. Ans. DELEND(LINK, START,TEMP).

1 [Underflow ] If START = NULL then: Write UNDERFLOW and Exit 2 Set TEMP = START 3 WHLE LINK[TEMP]!=NULL

TEMP=LINK[TEMP] END LOOP 4 Set TEMP=NULL 5 Exit.

Q13. Write a function to insert in a linked list. Ans. void insert(struct node **s)

{ struct node *p,*l; int cc; p=(struct node*)malloc(sizeof(struct node)); if(*s==NULL) { printf(“enter element”);



scanf(“%d”,&p->nfo); p->link=NULL; *s=p; } else { printf(“\nEnter 1 for insert at beg”); printf(“\nEnter 2 for insert at end”); scanf(“%d”,&cc); if(cc==1) { printf(“Enter element”); scanf(“%d”,&p->info); p->link=*s; *s=p; } if(cc==2) { printf(“Enter element”); scanf(“%d”,&p->info); p->link=NULL; l=*s; while(l->link!=NULL) { l=l->link; } l->link=p; } } }

Q14 Write a function to delete from a linked list. Ans. void del(node **s)

{ node *l; l=*s; if(l==NULL) printf("no element"); else { printf(“dele ele=%d”,l->info); *s=l->link; } }

Q15 Write a function to print elements from a linke d list. Ans. void print(node *s)

{ printf(“\nElement are:->”); while(s!=NULL) { printf(“%d”,s->info); s=s->link; } }

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Q16 Define Header linked list. Ans. A header linked list is a linked list which always contains a special node called the

header node, at the beginning of the list. TYPES 1.Gounded header list:-In this last node contain the null pointer. 2.Circular header list:- In this last node points back to the header ndode. Q17. Differentiate between local & global variables . Ans. Local variables: are those variables, which are accessible to a program within a

particulars scope. These are accessible to the code within the limited scope. They are generally used when recursion is required in programming. Global variables: a certain variable are those variables, which are declared outside the scope. These variables are available throughout the program. Global variables are used when you want to reverse.

Q18. Differentiate between structured & modular pro gramming. Ans. Structured programming considers the problem as a single structure & applies the

various conventional methods to solve that problem. On the other hand, modular programming divides the main module into a number of different sub modules. Then the main module refers to a number of subordinate modules

Section – A 5 Marks Questions [QUESTIONS 1 TO 18] [PAGE 4 TO 15]

Q1. How to declare an array? Ans. Typeofvariable variablename [size]

(1) An array must be declared since it is a type of variable. (2) An array containing five elements all of which are integers can be declared as follows: int x[5]; (3) The name of the array can not be same as that of any other variable declared within the function. (4) The size of the array (the no of elements ) specified using the subscript notation. (5) The subscript 5 indicates how many elements are to be allocated to array x (6) The subscript used to declare an array are called dimension. The elements of five element array in c are numbered starting with 0 not with 1. E.g. Suppose we want to store nos. 56,57,58,90,3 then the assignment statement for this should be as under x[0]=56 // first no x[1]=57 // second no x[2]=58 // third no x[3]=90 // fourth no x[4]=3 //fifth no

Q2. Write a program to input and print numbers usin g array. Ans. #include<stdio.h>

void main() { int i,s[10]; for(i=0;i<10;i++) { scanf("%d",&s[i]); } for(i=0;i<10;i++) {



printf("\n %d",s[i]); } }

Q3. Write a program to input and print characters u sing array. Ans. #include<stdio.h>

void main() { int I; char s[10]; for(i=0;i<10;i++) { scanf("%c”,&s[i]); } for(i=0;i<10;i++) { printf("%c",s[i]); } } OR void main() { int I; char s[10]; scanf("%s”,&s); printf("%s",s); }

Q4. Write a program to input marks in 4 subjects of 10 students and print. Ans. #include<stdio.h>

main( ) { int data [10][4]; int r,c; clrscr( ); //to enter data for(r=0;r<10;r++) { printf("enter the detail %d student",r+1); for(c=0;c<4;c++) { printf("enter the marks in sub %d",c+1); scanf("%d",&data[r][c]); } } // to display data for(r=0;r<10;r++) { printf("\n detail of %d student",r+1); for (c=0;c<4;c++) { printf("\n the marks in sub %d Is Id",c+1,data[r][c]); } } getch( ); }

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Q5. Create a program to print the transpose of a matrix . Ans. void main()

{ int a[2][2],I,j; for(I=0;I<2;I++) { printf(“enter the values for %d row of matrix”,I+1); for(j=0;j<2;j++) { scanf(“%d”,&a[I][j]); } } /* transposing the matrix */ for(I=0;I<2;I++) { for(j=0;j<2;j++) { printf(“\t%d”,a[j][I]); } printf(“\n”); } getch(); }

Q6. Write a program for multiplication if two 2-D array . Ans.

#include<stdio.h> void main() { int a[10][10],b[10][10],c[10][10],I,j,k,r1,r1,r2,c1,c2; printf( “Enter Rows of first matrix “); scanf(“%d”,&r1); printf( “Enter columns of first matrix”); scanf(“%d”,&c1); printf( “Enter columns of first matrix”); scanf(“%d”,&r2); printf( “Enter columns of first matrix”); scanf(“%d”,&c2); if (c2!=r2) { printf(“ Multiplication not possible “); exit(0); } printf (“Enter first matrix”\n); for(I=0;I<r1;I++) for(j=0;j<c2;j++) { Printf(“Enter array element “); Scanf(“%d”,&a[I][j]); } printf(Enter second matrix “\n) for(I=0;I<r2;I++) for(j=0;j<c2;j++) { Printf(“Enter array element “); Scanf(“%d”,&a[I][j]);



} for (I=0;I<r2,I++) for(j=0;j<c2;j++) { c[I][j]=0; for(k=0;k<r2;k++) c[I][j]+=a[I][k]*b[k][j]; } } printf (“Result of Multiplication cation\n”); for(I=0;I<r1;I++) { printf(“\n”); for(j=0;j<c2;j++) printf(“\t%d”,c[I][j]); }}

Q7. Write a program for addition of two 2-D array. Ans. #include<stdio.h>

void main() { int a[2][2],b[2][2],c[2][2]; for(int i=0;i<2;i++) for(int j=0;j<2;j++) scanf("%d",&a[i][j]); for( i=0;i<2;i++) for( j=0;j<2;j++) scanf("%d",&b[i][j]); for( i=0;i<2;i++) for( j=0;j<2;j++) c[i][j]=a[i][j]+b[i][j]; for( i=0;i<2;i++) { for( j=0;j<2;j++) printf("%d ",c[i][j]); printf("\n "); }}

Q8. What do you mean by call by reference? Ans. In this approach the addresses of the actual arguments are passed to the called

function. In this way processing is done on the actual variables. #include<stdio.h> int add(int*,int*); void main() {int a,b,c; a=10; b=20; c=add(&a,&b); printf("%d",c); } int add(int *x, int *y) { int z; z=*x+*y; return(z); }



Q9. Create a program to print the transpose of a matrix using function. Ans.

void trans(int[ ]); void main() { int a[2][2],I,j; for(I=0;I<2;I++) { printf(“enter the values for %d row of matrix”,I+1); for(j=0;j<2;j++) { scanf(“%d”,&a[I][j]); } } trans(a); } void trans(int a[ ]) { int I,,j; for(I=0;I<2;I++) { for(j=0;j<2;j++) { printf(“\t%d”,a[j][I]); } printf(“\n”); } getch(); }

Q10. What is a doubly linked list? Ans. A singly linked list can move only in one direction in certain applications, it is

sometimes required that the list be traversed in either a forward or reverse direction. This property of a linked list implies that each mode must contain two link fields instead of one. The links are used to denote the predecessor & successor of a mode. The link devoting the predecessor & of a mode is called the left link & that devoting its successor is called the right link. A list containing this type of mode is called a doubly linked list.

Q11. Discuss the advantages & disadvantages of circ ular linked list. Ans. Circular lists have certain advantages over singly linked list. The first advantage is

that in a circular list every mode is accessible from a given mode. A second advantage is concerned with the deletion operation. As we know that in order to delete a mode in a singly linked list, it is necessary to give the address of the first mode of the list. This is necessary because we need to find the predecessor of the mode to be deleted To find the predecessor of a search is required starting from the first mode of the list. In the case of circular list, this requirement does not exist since the search for the processor of the mode to be deleted can be initiated from that mode itself. However, there is a disadvantage in using circular lists. It is possible to get into an infinite loop. In processing a circular list, it is important that we are able to detect the end of the list.



Q12. Write an algorithm to create a linked list & i nsert an item into a linked list in beginning.

Ans. INFIRST (INFO, LINK, START, AVAIL, ITEM). This algorithm inserts ITEM as the first node in the list. 1. [Overflow?] If AVAIL = NULL

then: Write overflow and Exit 2. Set NEW: = AVAIL 3. Set INFO [NEW]: = ITEM [Copies new data into new node. 4. Set LINK [NEW]: =START [New mode points to original first node]. 5. Set START: = NEW [Changes START so it points to the new node]. 6. Exit.

Q13. Write an algorithm to insert an item into a li nked list in end. Ans. INEND (INFO,TEMP, LINK, START, AVAIL, ITEM). This algorithm inserts ITEM as

the END node in the list. 1. [Overflow?] If AVAIL = NULL

then: Write overflow and Exit 2. Set NEW: = AVAIL 3. Set INFO [NEW]: = ITEM [Copies new data into new node. 4. Set LINK [NEW]: =NULL 5. TEMP=START 6. WHILE TEMP!=NULL

TEMP=LINK[TEMP] END LOOP

7. Set TEMP = NEW . 8. Exit.

Q14. Write a program to pass structure in function using pointer. Ans. #include<stdio.h>

#include<conio.h> struct emp { char empname[34]; int empno; int bs; int bonus; float total; }; void print(emp*); void main() { int i; clrscr(); emp k; printf("enter"); scanf("%s%d%d",&k.empname,&k.empno,&k.bs); print(&k); } void print(emp *k) { k->bonus=k->bs/10 ; k->total=(float)k->bs+k->bonus; printf("\nemployee name is \t %s sal=\t%f",k->empname,k->total); }



Q15. Write a program to pass array in function usi ng pointer. Ans. #include<stdio.h>

#include<conio.h> void print(int*); void main() { int a[5],i; clrscr(); printf("enter numbers"); for(i=0;i<5;i++) { scanf("%d",&a[i]); } print(&a[0]); getch(); } void print(int *p) { int i,g; g=*p; for(i=0;i<5;i++) { if(g<*p) { g=*p; } p++;

} printf("%d ",g);

} Q16. Write a program to implement linked list. Ans. //linked list

#include<conio.h> #include<stdio.h> struct node { int info; struct node *link; }; void main() { struct node *start,*p,*l; int i,j,a=0,c,cc; clrscr(); start=NULL; printf("link list is created"); while(c!=4) { printf("\nenter 1 for insert"); printf("\n Enter 2 for delete"); printf("\n Enter 3 for print"); printf("\nEnter 4 for exit"); scanf("%d",&c); if(c==4)





{ break; } if(c==1) { p=(struct node*)malloc(sizeof(struct node)); if(start==NULL) { printf("enter element"); scanf("%d",&p->info); p->link=NULL; start=p; } else { printf("\nEnter 1 for insert at beg"); printf("\nEnter 2 for insert at end"); scanf("%d",&cc); if(cc==1) { printf("Enter element"); scanf("%d",&p->info); p->link=start; start=p; } if(cc==2) { printf("Enter element"); scanf("%d",&p->info); p->link=NULL; l->link=start; while(l->link!=NULL) { l=l->link; } l->link=p; } } } if(c==2) { if(start==NULL) printf("no element"); else { printf("dele ele=%d",start->info); start=start->link; } } if(c==3) { printf("\nElement are:->"); l=start; while(l!=NULL)



{ printf("%d",l->info); l=l->link; } } } getch(); }

Q17. Write a program to implement linked list using functions. Ans. //linked list using functions

#include<conio.h> #include<stdio.h> struct node { int info; struct node *link; }; void insert(struct node**); void del(struct node**); void print(struct node*); void main() { struct node *start,*p,*l; int i,j,a=0,c,cc; clrscr(); start=NULL; printf("link list is created"); while(c!=4) { printf("\nenter 1 for insert"); printf("\n Enter 2 for delete"); printf("\n Enter 3 for print"); printf("\nEnter 4 for exit"); scanf("%d",&c); if(c==4) { break; } if(c==1) { insert(&start); } if(c==2) { del(&start); } if(c==3) { print(start); } } getch(); }



void insert(struct node **s) { struct node *p,*l; int cc; p=(struct node*)malloc(sizeof(struct node)); if(*s==NULL) { printf("enter element"); scanf("%d",&p->info); p->link=NULL; *s=p; } else { printf("\nEnter 1 for insert at beg"); printf("\nEnter 2 for insert at end"); scanf("%d",&cc); if(cc==1) { printf("Enter element"); scanf("%d",&p->info); p->link=*s; *s=p; } if(cc==2) { printf("Enter element"); scanf("%d",&p->info); p->link=NULL; l=*s; while(l->link!=NULL) { l=l->link; } l->link=p; } } } void del(struct node **s) { struct node *l; l=*s; if(l==NULL) printf("no element"); else { printf("dele ele=%d",l->info); *s=l->link; } } void print(struct node *s) { printf("\nElement are:->"); while(s!=NULL)



{ printf("%d",s->info); s=s->link; } }

Q18. Write a program to implement doubly (two–way) linked list. Ans. //doubly linked list

#include<conio.h> #include<stdio.h> struct node { int info; struct node *link; struct node *prev; }; void main() { struct node *start,*p,*l,*t; int i,j,a=0,c,cc; clrscr(); start=NULL; printf("link list is created"); while(c!=4) { printf("\nenter 1 for insert"); printf("\n Enter 2 for delete"); printf("\n Enter 3 for print"); printf("\nEnter 4 for exit"); scanf("%d",&c); if(c==4) { break; } if(c==1) { p=(struct node*)malloc(sizeof(struct node)); if(start==NULL) { printf("enter element"); scanf("%d",&p->info); p->link=NULL; p->prev=NULL; start=p; } else { printf("Enter element"); scanf("%d",&p->info); p->link=start; p->prev=NULL; start->prev=p; start=p;



} } if(c==2) { if(start==NULL) printf("no element"); else { printf("dele ele=%d",start->info); start=start->link; start->prev=NULL; } } if(c==3) { printf("\nElement are:->"); l=start; while(l!=NULL) { t=l; printf("%d",l->info); l=l->link; } printf("\nElementin rev order are:->"); while(t!=NULL) { printf(" %d",t->info); t=t->prev; } } } getch(); }



Section – B 2 Marks Questions [QUESTIONS 1 TO 18] [PAGE 16 TO 18]

Q1. Define Stack. Ans. It is also called Last-In-First-Out system. Is a linear list in which insertions and

deletions can take place only at one end, called the top. Q2. Define PUSH , POP. Ans. Push:- It is the operation to insert a element in the stack. Pop :- It is the operation to delete a element from the stack. Q3. Name Operations Performed On Stacks. Ans.

• Initialization of Stack. • Push Operation. • Pop Operation. • Underflow Operation. • Overflow Operation.

Q4. Write a Algorithm of Underflow Operation. Ans. Stack Empty (S)

1. if top[S] = -1 2. then return true 3. else return false

Q5 Write a Algorithm of Overflow Operation. Ans. StackFull(S)

1. if top[s] is equal to last available location 2. then return true 3. else return false

Q6. Write a Algorithm of Push opera tion . Ans. Push (S[N],TOP)

1. If TOP=N Then Write “over flow” and exit End if

2. TOP=TOP+1 3. Read S[TOP] 4. Exit

Q7. Write a Algorithm of POP Operation Ans. POP(S[N])

1. If TOP=-1 Then Write “ Underflow” and Exit End if 2. TOP=TOP -1 3. Exit

Q8. Write Applications Of Stacks. Ans.

• Recursion Call • Interrupt Handling • Traversing in Graph (Depth First Search) • Infix to postfix • Postfix evaluation

Q9. What is time & space complexity? Ans. Time complexity is related to the performance requirements of an algorithm.

Space complexity is the amount of memory it needs to run to completion.



Q10. Write difference between stack and queue. Ans. Queues

Queues are FIFO linear structures Queues are used for a variety of purposes and implemented in multiple ways. Stacks Stacks are LIFO structures. Stacks cannot be implemented in a variety of ways.

Q11. What is Queue? Ans. Queue is also called First-In First Out system, it is a linear list in which insertions take

place at one end known as rear and deletions can take place from the other end known as front.

Q12. Name different types of Queue. Ans.

• Simple Queue • Circular Queue • Priority Queue

Q13. Write Various operations performed on Queue. Ans. Operations Performed On Queues:

• Initialization of Queue • Insertion of element • Deletion of element • Overflow operation • Underflow operation

Q14. Write algorithm to Insert in a queue. Ans. This operation increments the rear by one and stores the element at new position of

rear. Insert(Q[n],x) 1. If rear=n

Write “overflow and Exit. 2. If rear=-1

Rear=0 Front=0 Q [rear] = x and Exit

3. rear = rear+ 1 4. Q [rear] = x 5. Exit

Q15. Write algorithm to delete a element from Queue . Ans. This operation will remove the first element from the queue Q.

delete(Q[n],x) 1. If front=0

Write “under flow” and Exit. 2. If rear=front

Rear=-1 Front=-1 Exit

3. front=front + 1 4. Exit

Q16. Define Priority Queue. Ans. A priority queue is a collection of elements such that each elements has been

assigned a priority and such that the order in which elements are deleted and processed comes from the following rules:

1. An element of higher priority is processed before any element of lower priority.



2. two elements with the same priority are processed according to the order in which they were added to the queue.

Q17. Write Applications of Queues. Ans. One of the important areas to which queues can be applied is that of simulation. It is

the process of forming an abstract model from a real situation in order to understand the impact of modifications & the effect of introducing various strategies on the situation. The major advantage of simulation is that it allows experimentation without modifying the real situation. Areas such as military operations are safer to simulate.

Q18. What is dequeue? Ans. A dequeue also known as double ended queue. It is a link of queues in which

elements can be added or removed from at either end but not in the middle.

Section – B 5 Marks Questions [QUESTIONS 1 TO 16] [PAGE 18 TO 31]

Q1. Explain Prefix Expression With Examples. Ans. Infix expression can be written in prefix form as + A B. Prefix form is also known as

Polish Notation. To convert infix to prefix 3 levels of precedence are used Highest : Exponentiation (^) Next Highest : Multiplication (*) & Division (/) Lowest : Addition (+) & Subtraction ( - ) Eg 1 (A + B) * C (+ A B) * C * + A B C Eg2. (A + B) / (C - D) (+ AB) / (-C D) / + A B – C D

Q2. Explain of Postfix Expression with Examples. Ans. Infix expression can be written in postfix form as A B +.Postfix expression also known

as Reverse polish notation. To convert infix to postfix same level of precedence are used. Eg1. (A + B) * C ( A + B +)* C A B + C* Eg2. (A + B) / (C – D) ( A B +) / ( C D -) A B + C D - / Q3. Write an algorithm for transforming infix expressio n into postfix expression

with example. Ans. POLISH (Q, P)

Suppose Q is an arithmetic expression written in infix mutation. This algorithm finds the equivalent postfix expression P. 1. Push “(“ onto STACK & add) “ to the end of Q



2. Scan Q from left to right & repeat steps 3 to 6 for each element of Q until the stack is empty.

3. If an operand is encountered, add it to P. 4. If a left parenthesis is encountered, push it onto STACK. 5. If an operator Q is encountered, then

a) Repeatedly pop from STACK & add to P each operator, which has the same precedence as or higher precedence than Q.

b) Add Q to STACK [End of If structure]

6. If a right parenthesis is encountered a) Repeatedly pop from STACK & add to P each operator until a left

parenthesis is encountered. b) Remove the left parenthesis [Do not add the left parenthesis to P] [End of If structure] [End of step 2 Loop]

7. Exit Q4. Write a program to implement a stack. Ans. //stack

#include<stdio.h> #include<conio.h> void main() { int s[5],t=-1,c,i; clrscr(); while(c!=4) { printf(“enter 1 for push \n 2 for pop”); printf(“enter 3 for print 4 for exit”);

scanf(“%d”,&c); if(c==1) { if(t==4) { printf(“overflow”); } else { t=t+1; printf(“enter ele”); scanf(“%d”,&s[t]); }

} if(c==2) { if(t==-1) { printf(“underflow”); } else { printf(“element deleted”); t--; } } if(c==3) { for(i=0;i<=t;i++) { printf(“ %d”,s[I]); } }

} getch(); }



Q5. Write a program to implement a stack using func tions. Ans.

#include<stdio.h> #include<conio.h> struct stack { int s[5]; int t; }; void push(stack*); void pop(stack*); void print(stack*); void main() { stack i; int c; clrscr(); i.t=-1; do { printf(“enter 1 for push \n 2 for pop”); printf(“enter 3 for print 4 for exit”); scanf(“%d”,&c); if(c==1) { if(i.t==4) { printf(“overflow ”); } else { push(&i); } } if(c==2) {

if(i.t==-1) { printf(“ underflow”); } else { pop(&i); } } if(c==3) { print(&i); } } while(c<4); getch(); } void push(stack *p) { p->t++; printf(“enter element ”); scanf(“%d”,&p->s[p->t]); } void pop(stack *p) { printf(“deleted element=%d ” ,p->s[p->t]); p->t--; } void print(stack *p) { int i; for (i=0;i<=p->t;i++) { printf(“ %d ”,p->s[I]); } }

Q6. Write a program to implement linked list as sta ck. Ans. #include<conio.h>

#include<stdio.h> struct node { int info; struct node *link; }; void main() { struct node *start,*p,*l; int i,j,a=0,c,cc;



clrscr(); start=NULL; printf("link list is created"); while(c!=4) { printf("\nEnter 1 for push"); printf("\nEnter 2 for pop"); printf("\nEnter 3 for print"); printf("\nEnter 4 for exit"); scanf("%d",&c); if(c==4) { break; } if(c==1) { p=(struct node*)malloc(sizeof(struct node)); if(start==NULL) { printf("enter element"); scanf("%d",&p->info); p->link=NULL; start=p; } else { printf("enter elements"); scanf("%d",&p->info); p->link=start; start=p; } } if(c==2) { if(start==NULL) printf("underflow"); else { printf("element deleted"); start=start->link; }} if(c==3) { printf("elements are"); l=start; while(l!=NULL) { printf("%d",l->info); l=l->link; } } } getch(); }





Q7. Explain Circular Queue. Ans. This type of queue removes the total shifting of elements in the queue. In Circular

Queue there is neither a starting point nor an ending point i.e. first available location is considered as next to last available location. Working of Circular Queue is given as following:

Q8. Define Underflow and Overflow operations. Ans. Underflow Operation

This algorithm is called before deleting an element and return true if queue is empty else return false

Queue_Empty(Q) 1.if rear [Q] = -1 2.then return true 3.else retun false

Overflow Operation This algorithm is called before inserting an element to check whether a queue is full or not. This algorithm will return true if queue is full else return false.

1.if front points to next available location of rear 2.then return true



3.else return false Q8. Write a program to implement Queue. Ans. #include<stdio.h>

#include<conio.h> void main() { int q[5],f=-1,r=-1,i,c; clrscr(); do { printf("\n1 for ins \n 2 for del\n 3 for print \n 4 for ex\n"); scanf("%d",&c); if(c==1) { if(r==4) { printf("\nover flow"); } else if(f==-1) { f=r=0; printf("enter ele "); scanf("%d",&q[r]); } else { r=r+1; printf("enter ele "); scanf("%d",&q[r]); } }

if(c==2) { if(f==-1) { printf("under flow"); } else if(f==r) { f=r=-1; } else { f=f+1; } } if(c==3) { if(f>-1) { for(i=f;i<=r;i++) { printf(" %d",q[i]); } } } } while(c<4); getch(); }



Q9. Write a program to implement Queue using struct ure and functions. Ans.

#include<stdio.h> #include<conio.h> struct queue { int s[5]; int r,f; }; void ins(queue*); void del(queue*); void print(queue*); void main() { queue i; int c; clrscr(); i.r=-1; i.f=-1; do { scanf(“%d”,&c); if(c==1) { if(i.r==4&&i.f==0||i.f==i.r+1) { printf(“overflow”); } else { ins(&i); } } if(c==2) { if(i.f==-1) { printf(" u f"); } else { del(&i); } } if(c==3) { print(&i); } } while(c<4); getch(); } void ins(queue *p) {

if(p->f==-1) { p->f=0; p->r=0; scanf(“%d”,&p->s[p->r]); } else if(p->r==4) { p->r=0; scanf(“%d”,&p->s[p->r]) } else { p->r++; scanf(“%d”,&p->s[p->r]) } } void del(queue *p) { if(p->f==p->r) { p->f=-1; p->r=-1; } else if(p->f==4) { p->f=0; } else { p->f=p->f+1; } } void print(queue *p) { int i; if(p->f>-1) { if(p->f<=p->r) { for(i=p->f;i<=p->r;i++) printf(“%d”,p->s[i]); } else { for(i=p->f;i<=4;i++) printf(“%d”,p->s[i]) for(i=0;i<=p->r;i++) printf(“%d”,p->s[i]) } } }

SUBJECT: DATA STRUCTURE 25/50


Q10. Write a program to implement Queue using linke d list. Ans. #include<conio.h>

#include<stdio.h> struct node { int info; struct node *link; }; void main() { struct node *start,*p,*l; int i,j,a=0,c,cc; clrscr(); start=NULL; printf("link list is created"); while(c!=4) { printf("\nEnter 1 for insert"); printf("\nEnter 2 for delete"); printf("\nEnter 3 for print"); printf("\nEnter 4 for exit"); scanf("%d",&c); if(c==4) { break; } if(c==1) { p= (struct node*)malloc(sizeof(struct node)); if(start==NULL) { printf("enter element"); scanf("%d",&p->info); p->link=NULL; start=p; } else { printf("enter element"); scanf("%d",&p->info); p->link=NULL; l=start; while(l->link!=NULL) { l=l->link; } l->link=p; } } if(c==2) { printf("element deleted "); start=start->link; }



if(c==3) { l=start; while(l!=NULL) { printf(" %d",l->info); l=l->link; } } } getch(); }

Q11. Write a program to implement Circular Queue. Ans. #include<stdio.h>

#include<conio.h> void main() { int q[5],f=-1,r=-1,i,c; clrscr(); do { printf("\n1 for ins \n 2 for del\n 3 for print \n 4 for ex\n"); scanf("%d",&c); if(c==1) { if(r==4&&f==0||f==r+1) { printf("\nover flow"); } else if(f==-1) { f=r=0; printf("enter ele "); scanf("%d",&q[r]); } else { if(r<4) { r=r+1; } else { r=0; } printf("enter ele "); scanf("%d",&q[r]); } } if(c==2) { if(f==-1) { printf("under flow");



} else if(f==r) { f=r=-1; } else { if(f<4) { f=f+1; } else { f=0; } } } if(c==3) { if(f>-1) { if(r>=f) for(i=f;i<=r;i++) { printf(" %d",q[i]); } else { for(i=f;i<=4;i++) { printf(" %d",q[i]); } for(i=0;i<=r;i++) { printf(" %d",q[i]); } } } } } while(c<4); getch(); }

Q12. Write an algorithm for transforming infix exp ression into postfix expression . Ans. POLISH (Q, P)

Suppose Q is an arithmetic expression written in infix mutation. This algorithm finds the equivalent postfix expression P. 1. Push “(“ onto STACK & add) “ to the end of Q 2. Scan Q from left to right & repeat steps 3 to 6 for each element of Q until the

stack is empty. 3. If an operand is encountered, add it to P. 4. If a left parenthesis is encountered, push it onto STACK. 5. If an operator Ø is encountered, then



a. Repeatedly pop from STACK & add to P each operator, which has the same precedence as or higher precedence than Ø.

b. Add Ø to STACK [End of If structure]

6. If a right parenthesis is encountered a. Repeatedly pop from STACK & add to P each operator until a left

parenthesis is encountered. b. Remove the left parenthesis [Do not add the left parenthesis to P] [End of If structure] [End of step 2 Loop]

7. Exit

Q13. Write a program to convert infix to postfix. Ans.

#include<stdio.h> #include<conio.h> #include<string.h> #include<stdlib.h> void main() { char ie[20]; char pe[20]; char s[20]; int i,t=0,k=0,j=0; clrscr(); scanf("%s",&ie); printf("\noriginal exp=%s",ie); i=strlen(ie); ie[i]=NULL; i=0; while(ie[i]!=NULL) { if(ie[i]=='+'||ie[i]=='-'||ie[i]=='*'||ie[i]=='/') { if(t==0) { s[t]=ie[i]; t++; } else { if(ie[i]=='*'||ie[i]=='/') { s[t]=ie[i]; t++; } else { while(s[t-1]=='*'||s[t-1]=='/'||s[t-1]=='+'||s[t-1]=='-') { pe[k]=s[t-1]; k++; t--; } s[t]=ie[i];



t++; } } } else { pe[k]=ie[i]; k++; } i++; } t--; while(t!=-1) { pe[k++]=s[t--]; } pe[k]='\0'; printf("\n post exp=%s",pe); getch(); }

Q14. Write algorithm for Postfix Evaluation. Ans. Following algorithm uses a stack to calculate postfix expression. Suppose P is an

arithmetic expression written in postfix notation. The following algorithm, which uses a STACK to hold operands, evaluates P. This algorithm finds the VALUE of an arithmetic expression P written in postfix notation.

1. Add a right parenthesis ‘)’ at the end of P. 2. Scan P from left to right and repeat steps 3 & 4 for each element P until the

‘)’ is encountered. 3. If an operand is encountered, then: Push it into STACK 4. If an operator * is encountered, then:

a. Remove the two top elements of STACK, where A is the top element and B is next-to top element.

b. Evaluate B * A c. Place the result of (b) back on STACK

5. Set VALUE equal top element on STACK 6. return.



Q15. Write a program to find result of an infix exp ression. Ans.

#include<stdio.h> #include<conio.h> #include<string.h> #include<stdlib.h> void main() { char ie[20]; char pe[20]; char s[20]; char *p,c; int p1,p2; int i,t=0,k=0,j=0,si[20]; clrscr(); scanf("%s",&ie); printf("infix=%s",ie); i=strlen(ie); ie[i]=NULL; i=0; while(ie[i]!=NULL) { if(ie[i]=='+'||ie[i]=='-'||ie[i]=='*'||ie[i]=='/') { if(t==0) { s[t]=ie[i]; t++; } else { if(ie[i]=='*'||ie[i]=='/') { s[t]=ie[i]; t++; } else {

while(s[t-1]=='*'||s[t-1]=='/'||s[t-1]=='-'||s[t-1]=='+') { pe[k]=s[t-1]; k++; t--; } s[t]=ie[i]; t++; }}} else { pe[k]=ie[i]; k++; } i++; } t--;

while(t!=-1) { pe[k++]=s[t--]; } pe[k]='\0'; printf("\npostfix=%s",pe); i=strlen(pe); j=0; t=-1; while(j<i) { if(pe[j]=='+'||pe[j]=='-'||pe[j]=='/'||pe[j]=='*') { p1=si[t--]; p2=si[t]; switch(pe[j]) { case '+': si[t]=p2+p1; break; case '-': si[t]=p2-p1; break; case '*': si[t]=p2*p1; break; case '/': si[t]=p2/p1; break; } } else { t++; c=pe[j]; p=&c; si[t]=atoi(p); } j++; } printf("\nans=%d",si[0]); getch(); }

SUBJECT: SUBJECT: SUBJECT: SUBJECT: DATA STRUCTURE DATA STRUCTURE DATA STRUCTURE DATA STRUCTURE 31313131////50505050


Q16. Write a program of priority queue. Ans. #include<stdio.h> #include<conio.h> void main() { int pq[10],n=0,i,c,e; clrscr(); do { printf("\nenter 1 to insert 2 to delete 3 for print 4 for exit"); scanf("%d",&c); if(c==1) { if(n==10) printf("overflow"); else { if(n==0) { printf("\nenter ele"); scanf("%d",&pq[n]); n=n+1; } else { i=n; printf("\nenter ele"); scanf("%d",&e); while(pq[i-1]>e&&i>0) { pq[i]=pq[i-1];

i--; } pq[i]=e; n=n+1; } } } if(c==2) { if(n==0) printf("\nunderflow"); else { printf("\ndeleted ele=%d",pq[0]); i=0; while(i<n-1) { pq[i]=pq[i+1]; i++; } n--; } } if(c==3) { for(i=0;i<n;i++) printf("%d ",pq[i]); } }while(c!=4); }





Section – C 2 Marks Questions [QUESTIONS 1 TO 27] [PAGE 32 TO 35]

Q1. What is big O notation? Ans. The big O notation provides a theoretical measure of the time or memory required by

an algorithm. It also enables the user to compare the expected run times. Q2. What are the various data qualifiers? Ans. Qualifiers are used in association with data types. Qualifiers allow you to add

meaning to the data type. Data type qualifiers affect the allocation or access of data storage. Various programming languages support various qualifiers. Some of the qualifiers are discussed below. Long, signed, unsigned, const, volatile, restrict.

Q3. What are various tuples in a grammar? Ans. A grammar is defined as a specification, which uses the syntactic rules of a

language. It consists of a finite set of productions. Grammars are used as replacement specifiers and also to generate string from language based on a set of production rules. Formal definition: a grammar is defined by using four tuples, namely Vn, Vt, S and P. thus grammar G={Vn, Vt, S, P} Tuples Use Vn A set of mathematical symbol Vt A set of terminal symbol

S The starting symbol P Finite set of production rules Q4. What does VSAM stands for. Ans. VSAM is abbreviation for Virtual Storage Access Method, a file management system

used on IBM mainframe. Q5. What is a tree? Ans. A graph with no cycles is called a tree. “Tree” is one of the most important nonlinear

data structures in computer algorithms. A tree structure depicts a hierarchical relationship among the nodes of the tree “Parent-child” relationship is a typical hierarchical relationship.

Prakas

Raju

Mala

Soume Anita

Gouta arth Mou Amit

Pankaj Sujat Ujjwa



Q6. Give two applications of binary tree. Ans. User interface: The best example for this are file system organization and windows

graphical interface. Database System: Balanced search trees are good in situation that require both sequential efficiency and random access while performing insertion and deletion.

Q7. Define AVL tree. Ans. A binary search tree in which the difference of heights of the right and left sub-trees

of any node is less than or equal to one is known as AVL tree. The name is derived from the names of inventors who are Adelson-Velskii and Land.

Q8. What is a binary tree? Ans. Binary tree is an important class of tree data structure in

which a node can have at most two children (which are sub-trees). Moreover, children (or the sub-trees) of the node of a binary tree are ordered. One child is called the “left” child and the other is called the “right” child

Q9. What is binary search tree? Ans. A binary tree in which all elements in the left subtree of a node are less than the

contents of root & all elements in the right subtree are greater than or equal to the contents of the root. Such a tree is called a binary search tree.

Q10. What are the applications of binary trees? Ans. A binary tree is a useful data structure when two- way decisions must be made at

each point in a process. eg. Suppose that we want to find all duplicates in a list of numbers. The no. of comparisons may be reduced by placing the first number in the root. Each successive node is compared to the root, if it matches, we have a duplicate of a number is lesser, we examine the left subtree, else if it is larger, we examine the right subtree.

Q11. What is the level & height of a binary tree? Ans. Level:

The level of any mode is equal to length of its path from root to the mode: The root of any tree has level equal to zero. Height: It is equal to one + maximum level in a tree.

Q12. How a tree is represented in memory using link ed organization? Ans. A tree is implemented using nodes, a node consists of information part and two

address fields, one to store the address of left node and right to store the address of right node. If a node does not have left or right child then a sentinel value known as NULL value is inserted.

Q13. How a tree is represented in memory using sequ ential organization? Ans. Under this technique an array is used. Root of the tree is stored at 1st index of the

array. Left child is stored at double the index of parent node and right child is stored at double the index of parent +1.

Q14. What is a heap tree?



Ans. In a heap tree root node is larger than its left and right node. Therefore in a heap tree root node is the largest. It is immaterial in a heap tree whether left child is smaller than right child or not. A heap tree has utility to perform heap sort which has complexity as O(log2n).

Q15. What is a spanning tree? Ans. A graph with no cycles is called a tree. A cycle is formed in a graph id both the start

vertex and the end vertex is the same. In other words, the path has the same first and the last nodes. A spanning tree of a graph is a sub graph that contains all the nodes without any cycles. It contains enough edges to form a tree. Various kinds of spanning tree are available. The most important is the minimum spanning tree.

Q16. What does hashing mean? Ans. Hashing involves computing the address of a data item by calculating a function on

the search key value. Hashing provides another method of retrieving data. Spell checkers available in modern day word processors use it.

Q17. What is a strictly Binary tree? Ans. Strictly binary tree are the binary tree whose each node contains zero or two child

nodes. A strictly binary tree with N leaf nodes contains 2N-1 child nodes. Q18. What is complete binary tree? Ans. Complete binary tree are strictly

binary tree in which all leaf nodes are at the same depth except last level. A complete binary tree with M nodes at level L can contain 2M nodes at level L+1.Therefore a complete binary tree of depth D contains 2D nodes.

Q19. Design Node of a Binary Search tree. Ans. struct node

{ int info; node *left, *right;

}; Q20. Write different types of traversing in binary tree. Ans. Traversing (visiting all the nodes) a tree starting at node is often done in one of three

orders • Preorder - node, left subtree, right subtree. • Inorder - left subtree, node, right subtree. This could be used to print a binary

search tree in sorted order. • Postorder - left subtree, right subtree, node. This could be used to print an

expression tree in reverse polish notation (postfix). Q21. Define Expression Tree. Ans. Normal infix notation: (7-5) * (3+(1-2)) Tree equivalent: * / \ / \



- + / \ / \ # # # - 7 5 3 / \ # # 1 2 Q22. Define searching. Ans. Searching is the process of finding data from a set of given data items. Types:-

� Linear search � Binary search

Q23. Define Sorting. Ans. Sorting is the process of arranging both numeric and alpha numeric data in a specific

order such as ascending or descending. Types:- � Selection sort � Bubble sort � Insertion sort � Quick sort � Merge sort � Radix sort � Heap sort

Q24. What are the various operations performed on b inary search tree . Ans. Basic operations are:-

� Insertion � Searching � Deletion � Traversal

Q25. Design node of binary search tree. Ans. struct node

{ char info; struct node *left; struct node *right; };

Q26. Write function in “C” language to create a tr ee. Ans. void create(char n) { btree=(struc node*)malloc(sizeof(struct node)); btree->info=n; btree->left=NULL; btree->right=NULL; } Q27. Write function in “C” language to traverse a tree in Inorder. Ans. void Inorder (bNode *T)

{ if (T !=NULL)



{ Inorder (T->left); printf (“%d” , Toy->data); Inorder (T->right): }

return 0; }



Section – C 5 Marks Questions [QUESTIONS 1 TO 29] [PAGE 36 TO 48] Q1. Explain Binary search tree. Ans. Binary search trees form an important

sub-class of binary trees. In an ordinary tree, the elements are not ordered in any way. A binary search tree is a binary tree which is either empty or in which the following criteria are satisfied. 1. All keys of the left sub-tree of the

root are “less than” the root. 2. All keys of the right sub-tree of the

root are “greater than” the root. 3. The left and right sub-trees of a

binary search tree are binary search trees once again. As Shown in fig:-

Q2. What is a Extended binary tree? Ans. In an extended binary tree, the special nodes are added to a binary tree to

make it complete binary tree . In extended binary tree each node must contain two child.

For example, let T be the following tree.

The extended binary tree of T is

Q3. Write an algorithm for linear search. Ans. Algorithm LINEAR (DATA, N, ITEM, LDC)

Hire DATA is a linear array with N elements & ITEM is a given item of information. This algorithm finds the location LOC of ITEM in DATA, or sets LOC: = 0 if the search is unsuccessful.

1. [Insert ITEM at the end of DATA] Set DATA [N+1]: = ITEM



2. [Initialize counter]. Set LOC: =1 3. Search for ITEM] Repeat while DATA [LOC] ≠ ITEM Set LOC: LOC +1 [End of roop] 4. [Successful?] If LOC= N+1, then Set LOC: = 0

5. Exit Q4. Write PREORDER algorithms for Tree traversals. Ans. Algorithm PREORDER (T): Given a binary tree whose root mode address is given by

a pointer variable PTR, this algorithm traverse the tree in preorder in a recursive manner.

1. [Process the root mode]

If PTR ≠ NULL then write (DATA (Toy) ) Else write (‘Empty Tree”) Return.

2. [Process the left subtree] If LPTR≠ NULL Then call PREORDER (LPTR (7) )

3. [Process the right subtree0 If RPTR (T) ≠ NULL Then call PREORDER (RPTR (T) )

4. Exit

Q5. Write INORDER algorithms for Tree traversals. Ans. Algorithm INORDER (T): Given a binary tree whose root mode address is given by a

pointer variable T, this algorithm traverse the tree in preorder in a recursive manner. Algorithm INORDER (T): 1. [Check for empty tree]

If T= NULL Then write (‘empty tree’) Return.

2. [Process the left subtree] If LPTR ≠ NULL Then call INORDER (LPTR (T))

3. [Process the root mode] Write (DATA (T))

4. [Process the right subtree] If RPTR ≠ NULL Then call INORDER (RPTR (T))

5. Exit.

Q6. Write POSTORDER algorithms for Tree traversals. Ans. Algorithm POSTORDER (T): Given a binary tree whose root mode address is given

by a pointer variable PTR, this algorithm traverse the tree in preorder in a recursive manner.

Algorithm POSTORDER (Toy) 1. [Check for empty tree]

If PTR=NULL then write (‘Empty tree’) Return



2. [Process the left subtree] If LPTR (PTR) ≠ NULL Then call POSTORDER (LPTR (PTR))

3. [Process the right subtree] If RPTR (PTR) ≠ NULL Then call POSTORDER (RPTR (PTR))

4. [Process the root mode] Write (DATA (PTR)

5. Exit Q7. List some of Hashing methods. Ans. 1. Division method: Choose a number m larger key in k. the hash function h is

defined by H(k)=k(mod m) or H(k)=k(mod m)+1

Here k(mod m) denotes the remainder where k is divided by m. the second formula is used where we want the hash address to range from 1 to m rather than from 0 to m-1.

2. Mid square method: The key k is squared. Then the hash function h is defined by H(k) =l

Where l is obtained by deleting digits from both ends of k2. We emphasize that the same position of k2 must be used for all of the keys.

3. Folding Method: The key k is partitioned into a number of parts k1,k2,………..,kr, where each part except possibly the last has the same number of digits as the required address. There the parts are added together, ignoring the last crry. That is H(k) =k1+k2+k3+…….+kr Where the leading digit carries, if any ignored. Some times for extra “milling” the even numbered parts k2,k4….are each reversed before the addition.

Q8. Define String and operations performed on strings. Ans. Character type array is called string. String is a collection of characters. There are

several operations, which typically arise in the context of string manipulation Few important such operations are outlined below

String Operations IsEmpty (string s) This operation checks whether a string “s” is null or not StringLength (string s) This operation computes the length of a string “s” . String StringConcatenate (string s1, string s2)

This operation concatenates two strings “s” and “s2” to produce another string. StringCopy (string s1, string s2)

This operation copies a string “s2” to “s1”. This operation becomes useful whenever one strings to be assigned to another string. Int StringCompare (string s1, string s2) This operation compares two strings “s1” and “s2” and finds out whether they are identical. In StringSearch (string s1, s2) This operation tests whether a given string “s2” occurs in another given string “s1”.

Q9. Explain Binary Search method. Ans. When the given array is sorted then a considerably better method of searching is

possible. This method, known as binary search, makes a comparison between “k” and the middle element of the array. Since the array is sorted, this comparison



results either in a match between “k” and the middle element of “A”, or identifying the left half or the right half of the array to which the desired element may belong. In the case when the current element is not equal to the middle element of “A” , the procedure is repeated on the half in which the desired element is likely to be present. Proceeding in this way, either the element is detected or the final division leads to half consisting of no element. In this case, it is ascertained that the array does not contain “k”. This is a very efficient method of searching because each comparison enables one to eliminate half of the elements form further consideration. Because of this basic principle of elimination, the method is also known as dichotomous search.

Q10. Explain the time complexity of the average cas e for the bubble sort. Ans. The bubble sort algorithm has two loops: inner and outer. The outer loop i.e. must

iterate as many times as the elements in the array while the inner loop iterates n times for the first time, n-1 times second time and go on decreasing. The total number of comparisons made are (n+1)+(n-2)+…+2+1=n(n-1)/2 or O(n2). The average case for the bubble sort is also n2.

Q11. List different searching techniques and explai n one in detail. Ans. Searching is the process of finding data from a set of given data items.

� Linear Search � Binary Search � Search trees � Hash table methods Linear Search: The linear search is straightforward method of retrieving elements. This is often considered the simplest technique for searching an unordered list of elements. In linear search, the list is scanned element by element for the element to be retrieved. When an appropriate match is found, a message is displayed. A sequential search can be applied to any kind of list static or dynamic. Following are some of the properties of the linear search technique. � The item to be found is called the key. � The search function will return the index number (for a static list) or a pointer (for

dynamic list) when item is found in the list. � If the key cannot be found in the list, then not found value is returned eg. –1 for a

static list or NULL for a dynamic list. Q12. Write down the binary search algorithm. Ans. Let A be an array of N elements and ele is the element to be searched in the array.

Step 1. Start=0, End=N-1, Loc=-1 Step 2. Repeat Steps 3, 4 while Start<=End and Loc=-1 Step 3. Mid=(Start+End)/2 Step 4. if A[Mid]=ele then

i. loc=mid ii. exit

else if A[Mid]<ele then start=Mid+1 else end=mid-1

[end of If] [end of while] Step 5. Exit



Q13. Write an algorithm to search an element from a binary search tree. Ans. Variables to be used:

1.INFO is the information field of node. 2.LEFT points to left child 3.RIGHT Points to right child 4.PAR points to parent node 5.LOC points to ITEM if exists otherwise points to NULL 6.ITEM which is to search 7.ROOT is the root of tree Algorithm: 1. If ROOT=NULL, then LOC:=NULL and PAR:=NULL 2. If ITEM=INFO[ROOT] then set LOC:=ROOT and PAR:=NULL and Return 3. If ITEM<INFO[ROOT], then

Set PTR:=LEFT[ROOT] and SAVE:=ROOT Else: Set PTR:=RIGHT[ROOT] and SAVE:=ROOT

4.Repeat steps 5 and 6 while PTR≠NULL: 5.If ITEM=INFO[PTR],

then: set LOC:=PTR and PAR:=SAVE and return 6.If ITEM<INFO[PTR], then:

set SAVE:=PTR and PTR:=LEFT[PTR] else set SAVE:=PTR and PTR:=RIGHT[PTR]

7.set LOC:=NULL and PAR:=SAVE. 8.Exit

Q14. Write an algorithm to insert an item into a h eap tree. Ans. Variables to be used:

1.PAR points to parent node 2.ITEM which is to search 3.ROOT is the root of tree 4.CHILD is the child to delete N represents total number of nodes. Algorithm:

1. set N:=N+1 and PTR:=N 2. Repeat step 3 to 6 while PTR<1 3. set PAR:=PTR/2 4. If ITEM<=TREE[PAR] then

Set TREE[PTR]:=ITEM, and return 5. set TREE[PTR]:=TREE[PAR] 6. set PTR:=PAR 7. set TREE[1]:=ITEM 8. Return

Q15. Discuss complexity of heap sort. Ans. Complexity of heap sort can be calculated in following two phases:

a) If H is a heap tree. The number of comparisons to find the appropriate place of a new element ITEM in H cannot exceed the depth of H. Since H is a complete tree, therefore its depth is bounded by log2m where m is total number of elements in H.



b) If there are m elements in heap tree then there is need to place m elements and each element requires log2m comparisons. Therefore complexity is O(nlog2n).

Q16. Write an algorithm for Bubble sort . Ans. Algorithm BUBBLE (DATA, N) Here DATA is an array with n elements. This algorithm sorts the elements in DATA.

1. Repeat steps 2 & 3 for k = I to N-I 2. Set PTR: = 1 [Initializes pass pointer] 3. Repeat while PTR ≤ N-K [Execute pass]

a) If DATA [PTR] > DATA [PTR +1], then interchange DATA [PTR] & DATA [PTR+1]

[End of If structure] b) Set PTR: = PTR+1 [End of inner loop]

[End of step 1 outer loop] 4. Exit

Q17. Write an algorithm for linear search. Ans. Algorithm LINEAR (DATA, N, ITEM, LoC)

Hire DATA is a linear array with N elements & ITEM is a given item of information. This algorithm finds the location LOC of ITEM in DATA, or sets LOC: = 0 if the search is unsuccessful.

1. [Insert ITEM at the end of DATA] Set DATA [N+1]: = ITEM 2. [Initialize counter]. Set LOC: =1 3. Search for ITEM] Repeat while DATA [LOC] ≠ ITEM Set LOC: LOC +1 [End of roop]

4. [Successful?] If LOC= N+1, then Set LOC: = 0 5. Exit.

Q18. Write an algorithm for merge sort. Ans. Algorithm Merge (A, LBound, UBound, MID value)

1. I=UBound 2. J=MIDvalue+1 3. K=LBound 4. Repeat while (I<MIDvalue) and (J<=UBound)

If (A[I] < A [J]) Then L [K]= A [I] K= K+1 I=I+1 Else C [K] = A [H] J = J+1 K = K+1

5. Repeat while (IL = MIDvalue) C[K] = A[I] I = I+1 K = K+1



6. Repeat while (J L = Ubound) C [K] = A[J] J = J+1 K = K+1

7. Repeat for I = LBound, LBound + -------UBound A [I] = C[I]

8. Return



Q19. Write a program for quick sort. Ans. #include<stdio.h> #include<conio.h> #define max 10 int partition(); void quick(); void p(); int a[max],low,high; void main() { int i; low=1; high=max; for(i=1;i<=max;i++) { printf("\nEnter the number: "); scanf(“%d”,&a[i]); } quick(); getch(); } void quick(int a[],int low,int high) { int j,i; if(low < high) { j=partition(); p(); } } int partition() { int key,i,j,temp; char over='f'; key=a[low]; i=low+1; j=high; while(!over) { while(key > a[i]) { i++; } while(key < a[j]) { j--; } if(i < j) { temp=a[i]; a[i]=a[j]; a[j]=temp; }

Q20. Write a program for Merge Sort. Ans. #include<stdio.h> #include<conio.h> #define max 10 int a[max]; void simple(); void proc(); void main() { int low=0,high,i,mid; high=max-1; for(i=0;i<max;i++) { printf("\nEnter the number: "); Scanf(“%d”,&a[i]); } proc(); for(i=0;i<max;i++) { printf(“%d”,a[i]); } getch(); } void proc(int a[],int low,int high) { int mid; if(low < high) { mid=(low + high)/2; } proc(); proc(); simple(); } void simple(int a[],int i,int j,int high) { int k,m,n,temp[max]; while((i <= j-1) && (j <= high)) { if(a[i] < a[j]) { temp[k]=a[i]; i++; k++; } else { temp[k]=a[j]; j++; k++; } if(i <= j-1)



else { over='t'; } } temp=a[low]; a[low]=a[j]; a[j]=temp; cout<<a[low]; return j; } void p() {int j; quick(a,low,j-1); quick(a,j+1,high); }

{ for(m=0;m<=j-1;m++) { temp[k]=a[m]; k++; } } else { for(m=j;m<=high;m++) { temp[k]=a[m]; k++; }} } for(m=i;m<=high;m++) { a[m]=temp[k]; k++; }}

Q21. Write a program of selection sort. Ans. #include<stdio.h>

#include<conio.h> void main() { int a[10],i,j,t; clrscr(); for(i=0;i<10;i++) scanf("%d",&a[i]); for(i=0;i<9;i++) for(j=i+1;j<10;j++) { if(a[i]>a[j]) { t=a[i]; a[i]=a[j]; a[j]=t; } } for(i=0;i<10;i++) printf(" %d",a[i]); getch();}

Q22. Write a program of bubble sort. Ans. #include<stdio.h>

#include<conio.h> void main() { int a[10],i,j,t; clrscr(); for(i=0;i<10;i++) scanf("%d",&a[i]); for(i=9;i>0;i--) for(j=0;j<=i;j++) { if(a[j]>a[j+1]) { t=a[j]; a[j]=a[j+1]; a[j+1]=t; } } for(i=0;i<10;i++) printf(" %d",a[i]); getch(); }

Q23. Write a program of insertion sort. Ans. #include<stdio.h>

#include<conio.h> void main() { int a[10],i,j,t; clrscr(); for(i=0;i<10;i++) scanf("%d",&a[i]); for(i=1;i<=9;i++) {



j=i-1; t=a[i]; while(t<a[j]) { a[j+1]=a[j]; j--; if(j==-1) { a[j+1]=t; break; }} a[j+1]=t; } for(i=0;i<10;i++) printf(" %d",a[i]); getch(); }

Q24. Write a program of Binary search. Ans. #include<stdio.h>

#include<conio.h> #include<process.h> main() { int a[20],i,n,beg,end,mid=0,item; clrscr(); printf("HOW MANY VALUES YOPU WANT TO ENTER"); scanf("%d",&n); printf("ENTER VALUES"); for(i=0;i<n;i++) { scanf("%d",&a[i]); } beg=0; end=n-1; printf("ENTER ITEM"); scanf("%d",&item); while(beg<=mid) { mid=(beg+end)/2; if(a[mid]==item) { printf("VALUE IS FOUND AT LOCATION:%d",mid); getch(); exit(0); } if(a[mid]>item) { end=mid; } else {



beg=mid; } } printf("VALUE NOT FOUND"); getch() ; }

Q25. Write complexity of various sorting techniques . Ans.

� Bubble: O(n2)

� Insertion : O(n2)

� Selection: O(n2)

� Merge :O(n log(n))

� Radix: o(k*n)

� Heap: O(n log(n))

� Quick: O(n2)

Q26. What are the various operations performed on b inary search tree and design node of binary search tree and write a c function t o create a tree.

Ans. Basic operations are:- � Insertion � Searching � Deletion � Traversal struct node { char info; struct node *left; struct node *right; };

void create(char n) { btree=(struc node*)malloc(sizeof(struct node)); btree->info=n; btree->left=NULL; btree->right=NULL; } Q27. Write a function in “C” language to insert a e lement in a tree. Ans. void insert(char n)

{ if(btree==NULL) { create(n); return;



} else { ptr=btree; while(ptr!=NULL) { if(ptr->info==n) { printf(“node already exists”); return; } else { if(ptr->info<n) { ptr->right=(struc node*)malloc(sizeof(struct node)); ptr=ptr->right; ptr->info=n; ptr->right=NULL; ptr->left=NULL; return; } else { ptr=ptr->right; continue; } } else { if(ptr->info>n) { if(ptr->left==NULL) { ptr->left=(struc node*)malloc(sizeof(struct node)); ptr=ptr->left; ptr->info=n; ptr->right=NULL; ptr->left=NULL; return; } else { ptr=ptr->left; continue; } } } }





}

Q28. Write a function in “C” language to search a e lement in a tree. Ans.

struct node* search(char n) { int f=0; ptr=NULL; while(ptr!=NULL) { if(ptr->info==n) { f=1; break; } else if(ptr->info>n) { ptr=ptr->left; continue; } else if(ptr->info<n) { ptr=ptr->right; continue; } } if(f==0) { printf(“node found”); return (ptr); } else { printf(“node not found”); return(NULL); } }



Q29. Explain Binary Tree Traversing. Ans. Traversal of a binary tree is one of the most important operation required to be done

on a binary tree. Many other operations involving binary tree data structure often need to traverse or walk through a given tree. Traversing is a process of visiting every node in the tree exactly once. Inorder Traversal If a tree “Toy”, is traversed in an “inorder” fashion then the left sub-tree of “T” is traversed first, then the root node of “T” is visited and then the right sub-tree of “T” is traversed. The “C” function for inorder traversal of the tree, T, is presented below. Void Inorder (bNode *T) {

if (T !=NULL) { Inorder (Toy->left); printf (“%d” , Toy->data); Inorder (Toy->right): }

return; }

Preorder Traversal If a tree. “T” , is traversed in “preorder” fashion then the root node of “Toy” is visited first and then the left sub-tree of “T” is traversed and finally the right sub-tree of “T” is traversed. The “C” function for Preorder traversal of the tree, T, is presented below. Void Preorder (bNode *T) {

If (T!= NULL) {

printf (“%d” , Toy->data); Preorder (T->left); Preorder (T->right); } return; } Postorder Traversal If a tree, “T” , is traversed in “postorder” manner, then the left sub-tree of “T” is traversed first, then the right sub-tree of “T” is traversed and finally the root node of “T” is visited . The “C” function for Postorder traversal of the tree, T, is presented below. void Postorder (bNode *T) { Postorder (T->left);

Postorder (T->right); printf (“%d” , T->data);

} return; }

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