Data Structure Notes

For More Notes and questions log on to www.technicalsymposium.com INTRODUCTION TO C C has emerged as the most widely used programming language for software development. Its features allow the development of well-structured programs. Most computers directly support its data types and control structures, resulting in the construction of efficient programs. It is independent of any particular machine architecture or operating system, which makes it easy to write portable programs. It is this contribution of rich control structure and data types, portability and conciseness that has contributed to the popularity of C. History of C C programming language is basically developed for UNIX Operating System. UNIX was developed in 1969 at bell telephone laboratories. It was entirely written on PDP 7 assembly language. After UNIX has been implemented Ken Thompson implemented a compiler for a new language called B used for transporting UNIX onto other machines. B was heavily influenced by BCPL (Basic Cambridge Programming Language) written for writing system software. B was latter modified by Dennis Ritchie who was also working at bell Labs. He named the successor C. Unix was later rewritten in C by Dennis Ritchie, Thompson and others by 1973. C Program Structure A basic fact about computer programming is that all programs can be written using a combination of only three control structures: Sequential, Selective and repetitive. The sequential structure consists of a sequence of program statements that are executed one after another in order, the selective structure consists of a test for a condition followed by alternative paths that the program can follow, and the repetitive structure consists of program statements that are repeatedly executed while some condition holds. The sequential structure can be pictorially represented as follows Entry Statement 1 Statement 2 Statement 3 Exit All C programs are made up of one or more functions, each performing a particular task. Every program has a special function named main. It is special because the execution of any program starts at the beginning of its main function.

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For More Notes and questions log on to www.technicalsymposium.com A typical C program has following sections 1. Preprocessor Directives 2. Global Variable Declarations 3. Functions In a C program, preprocessor directive, if present, should come first followed by global variable definition if any. Variable Declaration in C 1. 2. 3. 4. 5.

The variable can be 31 characters long. The variable can be any of a-z, A-Z, 0-9 and the underscore. Should not be a keyword. First character must be an alphabet The variable is case sensitive

Data Types Every programming language has its own data type. The basic data types in C are Int - an integer Float – a single precision floating point number Char - a character in C character set Double – a double precision floating point number Variables Variables are data objects that are manipulated in a program. Information can be stored in a variable and recalled later. Variables must be declared before they can be used in a program. Constants A constant is an entity whose value does not change during program execution. Constants are of five different types 1. 2. 3. 4.

Integer Constants Floating point Constants Character Constants String Constants

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For More Notes and questions log on to www.technicalsymposium.com C Operators The operators in C include 1. 2. 3. 4. 5. 6. 7.

Arithmetic Assignment Relational Increment and Decrement Bit Logical or Boolean Conditional expression

INPUT / OUTPUT The important aspects of C programming language are its ability to handle input and output (I/O). A program using input / output functions must include the standard header file (stdio.h) in it using the directive. Printf functions (CONIO.H, STDIO.H) printf – sends formatted output to stdout fprintf – sends formatted output to a stream cprintf – sends formatted output to the text window on the screen Scanf Function Scanf - reads data from stdin Fscanf – reads data from stream The GETCHAR and PUTCHAR Function Getchar, putchar (STDIO.h) -

getchar is a macro that gets a character from stdin putchar is a macro outputs a character on stdout

The GETCH and GETCHE Function -

getch gets a character from console but does not echo to the screen getche gets a character from console and echoes to the screen

gets, puts gets() - gets a string from stdin puts() – outputs a string to stdout

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CONDITIONAL STATEMENTS If (condition) Statement When an if statement is encountered in a program, condition is evaluated, if its value is true, then the following statements are executed. The if statement allows conditional execution of a group of statements. If-else Statement SYNTAX If condition Statement 1; Else Statement 2; If the condition is true then statement 1 is executed else statement 2 is executed (if it exists). Else part is optional. LOOPS IN C WHILE LOOP While loop provides the mechanism for looping as long as a specified condition is met. The while loop should be used in applications that do not require the modification of any variables at each iteration. SYNTAX While (condition) Statements The statement may be a single statement or a block of statements that is to be repeated. The condition may be any expression, with true being any non-zero value. The statements are executed while the condition is true. When the condition becomes false, program control passes to the line after the loop code. FOR LOOP This is used when the statements are to be executed more than once. This is the most widely used iteration construct. The for loop supported by C is much more powerful than its counterpart in any other programming language.

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SYNTAX For (exp1;exp2;exp3) { statements; ……………. } Generally exp1 is an initialization, exp2 is condition checking; exp3 is either an increment or decrement statement. The initialization is usually an assignment statement that is used to set the loop control variable. The condition is a relational expression that determines when the loop will terminate. The increment determines how the loop control variable change each time the loop is repeated.

1. Write a C program to determine the sum of odd and even numbers. # include # include main() { int n, i, seven=0, sodd=0; int a[25]; clrscr(); printf(:\n Enter the total number to be entered:”); scanf(“%d”,&n); printf(“\n Enter the values”); for(i=0;i
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2. Write a C program to count the number of positive, negative and zero number in the given list of numbers. # include # include main() { int n, i, npos=0, nneg=0, nzero=0; int a[25]; clrscr(); printf(:\n Enter the total number to be entered:”); scanf(“%d”,&n); printf(“\n Enter the values”); for(i=0;i0) npos=npos+1; if(a[I]<0) nneg=nneg+1; else nzero=nzero+1; } printf(“\n The number of positive value is %d”,npos); printf(“\n The number of negative value is %d”,nneg); printf(“\n The number of zeros is %d”,nzero); getch(); } 3. Write a C program for temperature conversion. #include #include main() { int faren,cen; clrscr(); printf(“\n Enter the farenheit value :”); scanf(“%d”,&faren); cen=(faren-32)+5/9; printf(“\n The equivalent Centigrade value is %d”,cen); getch(); }

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For More Notes and questions log on to www.technicalsymposium.com 4. Write a C program to check whether the number is prime or not. #include #include main() { int n, i; clrscr(); printf(:\n Enter the total number to be entered:”); scanf(“%d”,&n);

for(i=2;i<=n/2;i++) { if(n%i= =0) printf(“\n the given number is not prime”); break; } if(n%i) printf(“\n the given number is prime”); getch(); } 5. Write a C program to find whether the given number is palindrome or not. #include #include main() { int n, i; int p,s,e; clrscr(); printf(:\n Enter the number :”); scanf(“%d”,&n); e=0; p=n; while(p!=0) { s=p%10; e=(e*10)+s; p=p/10; }

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For More Notes and questions log on to www.technicalsymposium.com if(e= = n) printf(“\n the given number is palindrome”); else printf(“\n the given number is not a palindrome”); getch(); } 6. Write a C program to find the sum of digits. #include #include main() { int n,q,r,s=0; clrscr(); printf(“\n Enter the no"); scanf(“%d”,&n); while(n!=0) { q=n/10; r=n-q*10; s=s+r; n=q; } printf(“\n the sum of digits :%d”,s); getch(); } 7. Write a program to find whether the given number is perfect or not. #include #include main() { int a = 0; int m; printf(“Enter a number to check whether it is a perfect number or not \n”); printf(“ Enter a number \n”); scanf(“%ld”,&n); for (m=0;m
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For More Notes and questions log on to www.technicalsymposium.com { if (n % m = = 0 ) a = a + m; } if (a = = n) printf(“the given number is perfect number \n”); else printf(“the given number is not a perfect number \n”); getch(); 8. Write a program to find whether the given number is Armstrong or not. #include #include main() { int s = 0; int c= 0; int m,n,b; printf(“Enter a number to check whether it is a perfect number or not \n”); printf(“ Enter a number \n”); scanf(“%ld”,&b); n = b; while (b>0) { c = b % 10; s = s + (c*c*c); b = b / 10; } if (s = = n) printf(“the given number is armstrong number \n”); else printf(“the given number is not a armstrong number \n”); getch(); } 9. Write a C program to find the given number using linear search method. #include #include main() { int n,a[30],sea,flag; clrscr();

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For More Notes and questions log on to www.technicalsymposium.com printf(“\n Enter the number of terms :”); scanf(“%d”,&n); printf(“\n Enter the values:”); for(i=0;i #include main() { int n,a[30],sea,flag,x,y,t; int low,high,mid; clrscr(); printf(“\n Enter the number of terms :”); scanf(“%d”,&n); printf(“\n Enter the values:”); for(i=0;ia[y]) {

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For More Notes and questions log on to www.technicalsymposium.com t=a[x]; a[x]=a[y]; a[y]=t; } } printf(“\n The sorted numbers are :”); for(x=0;xa[mid]) low=mid+1; if(t= = a[mid]) { printf(“\n the number %d is present in the position %d”,t,mid); flag=0; break; } if(mid = =1 | | mid= = n) break; } if(flag) printf(“\n The given number is not present”); getch(); } 11. Write a program to print fibonacci series using functions #include #include void main() { int n; void fibo(int);

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For More Notes and questions log on to www.technicalsymposium.com clrscr(); printf(“\t\t PROGRAM TO PRINT THE FIBONACCI SERIES \n”); printf(“\n Enter the number of terms to be in the series \n “); scanf(“%d”,&n); fibo(n); getch(); } void fibo(int num) { int I=1,ct,ft,st; ft = 0; st = 1; printf(“\t %d \t %d”,ft,st); while(I<=num-2) { ct = ft + st; ft = st; st = ct; printf(“\t%d”,ct); I++; } } 12. Program to perform the matrix additions #include #include void main() { int a[10][10],b[10][10],c[10][10],row,col,r,co,I,j,k; clrscr(); printf(“\t\t Matrix Addition\n”); printf(“Enter Row order of Matrix A : “); scanf(“%d”,&row); printf(“Enter Column order of Matrix A : “); scanf(“%d”,&col); printf(“Enter Row order of Matrix B : “); scanf(“%d”,&r); printf(“Enter Column order of Matrix B : “); scanf(“%d”,&co); if ((row!=r) || (col != co) ) { printf(“Matrix Multiplication is impossible\n”); getch(); }

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For More Notes and questions log on to www.technicalsymposium.com else { printf(“Enter First Matrix Elements : “); for (I=0;I #include void main() { int n; clrscr(); printf(“program to print the factorial\n”); printf(“\n\n Enter the number : “); scanf(“%d”,&n); factorial(n); getch(); } void factorial(double x) { double fact = 1; for(I=1;I<=n;I++) { fact = fact * I; printf(“The factorial of a given number is %d\n”,fact); }

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14. Program to implement the Tower of Hanoi #include #include void main() { void transfer(int,char,char,char); int n; clrscr(); printf(“\t\t TOWERS OF HANOI \n”); printf(“How many disks ? “); scanf(“%d”,&n); transfer(n,’1’,’r’,’c’); getch(); } void transfer(int n, char from, char to, char temp) { if(n>0) { transfer(n-1,from,temp,to); printf(“Move disk %d from %c to %c \n”,n,from,to); transfer(n-1,temp,to,from); } return; } 15. Program to count the number of vowels, consonants, digits, white space characters and in a line of text using pointers #include main() { char line[80]; int vowels = 0; int cons = 0; int digits = 0; int ws = 0; int other = 0; void scan_line(char line[], int *pv, int *pc, int pd, int *pw, int *po); printf(“Enter a line of text \n”); scanf(“%[^\n],line); scan_line(line, &vowels, &cons, &digits, &ws, &other);

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For More Notes and questions log on to www.technicalsymposium.com printf(“%d %d %d %d %d”,vowels,cons,digits,ws,other); return(0); } void scan_line(char line[], int *pv, int *pc, int *pd, int *pw,int *po) { char c; int count = 0; while((c = toupper(line[count])) != ‘\0’) { if (c = = ‘A’ | | c = = ‘E’ | | c = =’I’ || c = = ‘O’ || c = = ‘U’) ++ *pv; else if (c > = ‘A’ && c < = ‘Z’) ++ *pc; else if ( c > = ‘0’ && c < = ‘9’) ++ *pd ; else if (c = = ‘ ‘ | | c = = ‘\0’) ++ *pw; else ++ *po; ++ count; } return; } 16. Program to implement to Floyds Triangle #include void main() { int n,i,j,x=1; clrscr(); printf("\t\t\tFloyds Triangle\n"); printf("\t\t\t===============\n"); printf("Enter the no of Lines:"); scanf("%d",&n); for(i=0;i
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17. Program to implement to Pascal Triangle #include void main() { int i=1,j,k,m,n; clrscr(); printf("\t\t\tPascal Triangle\n"); printf("\t\t\t===============\n"); printf("Enter the no of Lines:"); scanf("%d",&n); for(j=0;j0;k--) printf(" "); for(m=0;m<=j;++m) { if((m==0)||(j==0)) i=1; else i=(i*(j-m+1))/m; printf("%4d",i); } printf("\n"); } getch(); } 18. Program to implement sine series #include #include void main() { float d,x,sum=0,fact(int); int terms,sign=1,i; clrscr(); printf("\t\t\t Sine Series \n"); printf("\t\t\t =========== \n"); printf("\nEnter the X value:"); scanf("%f",&d); printf("\nEnter the number of terms:"); scanf("%d",&terms); x=3.14/180*d;

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For More Notes and questions log on to www.technicalsymposium.com for(i=1;i<=terms;i+=2) { sum=sum+sign*pow(x,i)/fact(i); sign=-sign; } printf("\nThe value of sine(%4.2f)is %8.4f",d,sum); getch(); } float fact(int n) { float f=1; int i; for(i=1;i<=n;++i) f*=i; return(f); } 19. Programs on Manipulations on strings #include void main() { int ch,i,j,l,m,sign,c,l1,k; char name[80],name1[80],name2[80],namer[80],nameff[80],ans='y'; clrscr(); printf("\t\t\tManipulations on Strings\n"); printf("\t\t\t========================\n"); printf("1.Concatenation\n"); printf("2.Reverse\n"); printf("3.Find\n"); printf("4.Replace\n"); printf("5.Length\n"); printf("Choice:"); scanf("%d",&ch); switch(ch) { case 1: { printf("\t\tConcatenation\n"); printf("\t\t=============\n"); printf("Enter the first string \n"); scanf("%s",name); printf("Enter the second string \n"); scanf("%s",name1); i=j=0; while(name[i]!='\0')

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For More Notes and questions log on to www.technicalsymposium.com { name2[i]=name[i]; i++; } while(name1[j]!='\0') { name2[i]=name1[j]; i++; j++; } name2[i]='\0'; printf("Resultant String in name2 is%s",name2); break; } case 2: { printf("\t\tReverse\n"); printf("\t\t=======\n"); printf("Enter the string \n"); scanf("%s",name); i=j=0; while(name[i]!='\0') i++; while(--i>=0) name1[j++]=name[i]; name1[j]='\0'; printf("\nThe reversed String is%s",name1); break; } case 3: { printf("\n\t\tFind\n"); printf("\t\t====\n"); printf("\nEnter first string:"); scanf(" %[^\n]",name); printf("Enter search string:"); scanf(" %[^\n]",name1); l=strlen(name); l1=strlen(name1); for(i=0;i
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For More Notes and questions log on to www.technicalsymposium.com while(name1[c]!='\0'&&sign!=1) { if(name[m]==name1[c]) { m++; c++; } else sign=1; } if(sign==0) { printf("The given string is present"); printf("\nIts starting position is%d",i+1); exit(1); k=-1; } } if(k<0)break; } if(sign!=0) printf("The given string is not present"); break; } case 4: { i=0; j=0; strcpy(nameff," "); puts("Enter the string:"); scanf(" %[^\n]",name); fflush(stdin); puts("Enter find string"); scanf(" %[^\n]",name1); fflush(stdin); puts("Enter replace string:"); scanf(" %[^\n]",namer); fflush(stdin); l=strlen(name); strcat(namer," "); while(i
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For More Notes and questions log on to www.technicalsymposium.com while(name[i]!=' '&&name[i]!='\0') { name2[j]=name[i]; ++i; ++j; } name2[j]='\0'; ++i; if((strcmp(name2,name1))==0) { strcat(nameff," "); strcat(nameff,namer); } else { strcat(nameff," "); strcat(nameff,name2); } } puts("string after replacement"); puts(nameff); break; } case 5: { i=0; printf("Enter String:"); scanf(" %[^\n]",name); while(name[i]!='\0') i++; printf("\nThe length of the given string is%d",i); break; } } getch(); }

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Data Structures An introduction to C: Dennis Ritchie at AT & T Bell laboratory, Murray Hill, New Jersey, developed the programming language C in 1972. The languages BCPL and B mainly influenced it. It was named as C to present it as the successor of B language which was Designed earlier by Ken Thompson in 1970 for the first UNIX system on the DECPDP-7 Computer. How to run C program: 1. From the Ms Dos prompt start C by typing ‘tc’. 2. Open a file by selecting File | Open | File name from the IDE menu. Or press F3 Key 3. Run the program by selecting Run | Run, Or press Ctrl+F9 Key 4. To see the program’s output select Window | User screen or press Alt+F5 Key. We may compile and run the programs from the Dos command Line like tcc Filename . After the program is compiled, we may run it and view the output by typing Filename Problem solving using computer: To solve a problem using a computer, the following steps are required :  A program is developed using a high level programming language (program development)  The developed program is entered into a commuter (Program editing).  The edited program is translated and is produced as an executable machine code.  The Executable machine code is run in the computer to carry out the actual task (execution). To implement the above steps, the programmer develops a program and the developed program is entered and edited with the help of an editor. Normally the editor is provided along with the compiler. After editing the program, the compilation commands us used for the translation process. Then the execution command is used to run the program to get the desired output.

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Compilation: High-level languages allow some English –like words and mathematical expressions that facilitate the better understanding of the logic involved in a program. High-level languages are machine independent. Since a computer system cannot follow programs written in a high language, high language programs are translated into lowlevel language programs and then executed. Translation of a high-level language program to allow level language program is done by software known as Compiler. Object code is an intermediate code between the source code and the executable code. Linking: Linker performs the linking of libraries with the object code, to make the generated object code into an executable machine code. Thus the object code becomes an input to the linker, which produces an executable machine code. Sometimes programs are divided into modules and these modules are compiled separately and then linked by the linker and executed. When running a program, the following files will be created automatically.    

OBJ (Object file) EXE (Executable file) Bak (Backup file) SWP (Swap file)

Data Structures Definition Data Structure is a specialized format for storing data so that the data’s can be organized in an efficient way. Classification

Primitive Example: • Integer • Real • Character • Pointer • Logical

Non – Primitive

• •

Linear Example: •Linear List Stack Queue

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Non – Linear Example: • Graph •Tree



Array An array is a finite collection of similar elements stored in contiguous location. The operations done on an array are: • Insertion • Deletion • Changing a particular element Linked List There are three types of linked lists. They are:    

Single Linked List Doubly Linked List Singly Circular Linked List Doubly Circular Linked List

Single Linked List Node structure Data Field

Pointer Field

The data field contains the data elements that have to be stored in the list. The pointer will point the next node in the list. The operations done on a list are:  Insertion  Deletion Insertion  Insertion in the head node To insert a node in the head node, just change the pointer field of the new node to point to the head node. Let the new node be ‘Temp’ and the head node be ‘Head’, then the insertion is Temp → data = X; Head → next = head

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

Insertion in the middle node To insert in the middle node we need to change two pointers. Let the new node be ‘Temp’ and the present node is ‘Present’ and, the next node to the present node is ‘future’. The pointers used are ‘data’ for the data field, ‘next’ to the pointer field, the data to be inserted is ‘X ’then the insertion is Temp → data = X Present → next = temp Temp → next = future



Insertion in the last node To insert an element in the last position just change the pointer field of the present last node to point to the new node, then set the pointer field of the new node to NULL. Let the new node be ‘Temp’ and the present node is ‘Present’. The pointers used are ‘data’ for the data field, ‘next’ to the pointer field, the data to be inserted is ‘X ’then the insertion is Present → next =Temp Temp → next =null Temp → data = X Deletion Deletion in the head node

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To delete a node in the head node, just point the head node as the second node. Let the head node be ‘Head’, and then the deletion is Head → next = head 

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Deletion in the middle node To delete a node in the middle we need to change two pointers. Let the node to be deleted is ‘Temp’ and the node previous to the node to be deleted is ‘Present’ and, the next node to the present node is ‘future’. The pointers used are ‘data’ for the data field, ‘next’ to the pointer field, the data to be inserted is ‘X ’then the insertion is Present → next = future Deletion in the last node To delete an element in the last position just change the pointer field of the previous node to the last to null. Let the last node be ‘Temp’ and the previous node is ‘Present’. The pointers used are ‘data’ for the data field, ‘next’ to the pointer field, the data to be inserted is ‘X ’then the insertion is

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Previous → next =NULL Singly Circular Linked List The advantage of using Circular Linked List is the last null pointer is replaced and the pointer field of the last node points to the first node, due to this circular arrangement the traversing become quite easier. The insertion and deletion in the first and middle are same as singly linked list except the last node. Insertion •

Insertion in the last node To insert a node in the last position, insert the new node after the current last node, and then change the pointer field of the new node to point to the first node. Let the last node be last, the new node to be inserted to be new, the first node in the list to be first. The pointers used are ‘data’ for the data field, ‘next’ to the pointer field, the data to be inserted is ‘X ’then the insertion is Last → next = new New → next =first Deletion • Deletion in the last node To delete a node in the last position, change the pointer field of the previous node to the current last to point the first node. Let the last node be last, the previous node to the current last node to be pre, the first node in the list to be first. The pointers used are ‘data’ for the data field, ‘next’ to the pointer field, the data to be inserted is ‘X ’then the deletion is Prev → next = first Stack An important subclass of lists permits the insertion and deletion of an element to occur only at one end. A linear list of this type is known as ‘stack’. The insertion is referred to as ‘push’. The deletion is referred to as ‘pop’. The two pointers used for accessing is top & bottom pointer. Pointer PUSH – Storing the element intoBottom the stack. Check top<= allowed size if yes increment the top position and store the value in the top position. POP - Deleting the element from the stack. If top<= we can not delete. Otherwise decrement the top by one and return the top+1 element. Queue The information in this list is processed in the same order as it was received, that is first in first out order (FIFO) or a first – come first – served (FCFS) basis. This type of

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For More Notes and questions log on to www.technicalsymposium.com frequently used list is known as queue. We have two pointers to access the queue. They are 1. Front (used for deletion) 2. Rear (Used for insertion) Insertion : if rear>n queue overflow else increment the rear pointer and insert the value in the rear position. Deletion : If front =0 then queue underflow Else Increment the front pointer and return the front-1 value Tree An important class of digraph, which involves for the description of hierarchy. A directed tree is an acyclic digraph which has one node called root with in degree 0, while other nodes have in degree 1. Every directed tree must have at least one node. An isolated node is also called as directed tree. The node with out degree as 0 is called as leaf. The length of the path from root to particular node level of the node. If the ordering of the node at each level is prescribed then the tree is called as ordered tree. Binary Tree If a tree has at most of two children, then such tree is called as Binary tree. If the elements in the binary tree are arranged in the following order Left element is lesser than the root Right element is greater then the root No duplication of elements Then such binary tree is called as Binary Search Tree Operations performed in a binary tree are: o Inserting a node o Deleting a node o Traversing the tree Traversing Methods 1. 2. 3. 4. 5. 6.

Pre – order method In – order method Post – order method Converse Pre – order method Converse In – order method Converse post – order method

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Pre – order method This method gives the tree key value in the following manner: 1. Process the root 2. Traverse the left sub tree 3. Traverse the right Sub tree In – order method This method gives the tree key value in the following manner: 1. Traverse the left sub tree 2. Process the root 3. Traverse the right Sub tree Post – order method This method gives the tree key value in the following manner: 1. Traverse the left sub tree 2. Traverse the right Sub tree 3. Process the root Sorting Sorting is, without doubt, the most fundamental algorithmic problem 1. Supposedly, 25% of all CPU cycles are spent sorting 2. Sorting is fundamental to most other algorithmic problems, for example binary search. 3. Many different approaches lead to useful sorting algorithms, and these ideas can be used to solve many other problems. What is sorting? It is the problem of taking an arbitrary permutation of n items and rearranging them into the total order,

Issues in Sorting Increasing or Decreasing Order? - The same algorithm can be used by both all we need do is change

to

in the comparison function as we desire.

What about equal keys? – May be we need to sort on secondary keys, or leave in the same order as the original permutations. 27


For More Notes and questions log on to www.technicalsymposium.com What about non-numerical data? - Alphabetizing is sorting text strings, and libraries have very complicated rules concerning punctuation, etc. Is Brown-Williams before or after Brown America before or after Brown, John? We can ignore all three of these issues by assuming a comparison function which depends on the application. Compare (a,b) should return ``<'', ``>'', or ''=''. Applications of Sorting One reason why sorting is so important is that once a set of items is sorted, many other problems become easy. Heaps A heap is a complete binary tree with values stored in its nodes such that no child has a value bigger than the value of the parent. Below is a heap. 9 /\ 8 2 /\ 6 4 A heap provides a representation for a priority queue. Example: messages processed by priority at a server • • •

messages given priority weighting, higher numbers give better service highly dynamic, messages coming and going frequently need efficient insert new message and remove highest priority message

Removal causes heap to be reheapified. For example if we remove 9 9 /\ 8 2 /\ 6 4 then we reheapify by copying rightmost leaf to root (4 becomes the root) 4 /\ 8 2 / 6

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For More Notes and questions log on to www.technicalsymposium.com and then we recursively reestablish the heap property as follows: if the parent is greater than a child, swap the parent with the highest priority child. Keep swapping until no more swaps are possible. So in the above tree, first we would swamp 4 with 8. 8 /\ 4 2 / 6 Then we would swap 4 with 6. 8 /\ 6 2 / 4 The final swap yields a heap! The cost of removing an item (reheapifiying after removing the item) is O(log n). The algorithm just traverses one path in the tree, which is O(log n) in length. For each node on that path it performs at most two comparisons and one swap (3 operations -> constant time). So overall the algorithm has a worst case time complexity of O(log n). Space complexity is O(n) since a sequential array representation can be used. Quick sort is a very efficient sorting algorithm invented by C.A.R. Hoarer. It has two phases: • •

The partition phase and The sort phase.

As we will see, most of the work is done in the partition phase - it works out where to divide the work. The sort phase simply sorts the two smaller problems that are generated in the partition phase. This makes Quick sort a good example of the divide and conquers strategy for solving problems. (You've already seen an example of this approach in the binary search procedure.) In quick sort, we divide the array of items to be sorted into two partitions and then call the quick sort procedure recursively to sort the two partitions, i.e. we divide the problem into two smaller ones and conquer by solving the smaller ones. Thus the conquer part of the quick sort routine looks like this:

29



quicksort( void *a, int low, int high ) { int pivot; /* Termination condition! */ if ( high > low ) { pivot = partition( a, low, high ); quicksort( a, low, pivot-1 ); quicksort( a, pivot+1, high ); } }

Initial Step - First Partition

Sort Left Partition in the same way For the strategy to be effective, the partition phase must ensure that all the items in one part (the lower part) and less than all those in the other (upper) part. To do this, we choose a pivot element and arrange that all the items in the lower part are less than the pivot and all those in the upper part greater than it. In the most general case, we don't know anything about the items to be sorted, so that any choice of the pivot element will do - the first element is a convenient one. Dijkstra's Algorithm Djikstra's algorithm (named after its discover, E.W. Dijkstra) solves the problem of finding the shortest path from a point in a graph (the source) to a destination. It turns out that one can find the shortest paths from a given source to all points in a graph in the same time, hence this problem is sometimes called the single-source shortest paths problem. Graph Traversal Systematic traversals of graph are similar to preorder and post order traversal for trees. There are two graph traversals, depth-first and breadth-first search. Frequently the graph searches start at an arbitrary vertex. The searches are efficient if they are done in O(n + m), where n is the number of vertices and m the number of edges. Graph traversal can be used to determine the general characteristic of the graph, or to solve a specific problem on a particular graph, for example: • • •

Routing phone calls, or packets Planning a car trip Locate particular vertices, for example a win position in a game.

30


For More Notes and questions log on to www.technicalsymposium.com Depth-first Search We start the graph traversal at arbitrary vertices, and go down a particular branch until we reach a dead end. Then we back up and go as deep possible. In this way we visit all vertices, and all edges. Breath-First Search Breadth-first search visit all adjacent vertices before going deeper. Then we go deeper in one of the adjacent vertices. Sparse Matrix : A matrix consists of more number of zeros is called sparse matrix. Once the matrix is stored as it is then there is wastage of memory. For an efficient memory utilization the sparse matrix can be stored in a linear form. The linear form can be of array type or linked list type. DATA STRUCTURES Definition: Data structure is collection of data elements organized in a specified manner and accessing functions are defined to store and retrieve individual data elements. Data structures are sometimes called Data types. Classification of Data Structure: A data type may be defined as a set and the elements of the set are called the values of the type. There are four basic or atomic or primitive data types in C. They are int, float, char and double. The Simple data types built from primitives are arrays , pointers, strings and records with which we can build new types called structured or composite types such as stacks, queues, and trees etc. The structured data types can be categorized as linear and non-linear. The linear data structures are stacks, queues and linked lists. The non-linear data structures are trees and graphs. Stacks Definition: A stack is an ordered collection of items into which new items may be inserted and from which items may be deleted at one end, called the top of the stack. The first example of stack, which permits the selection of only its end element , is a pile of coins. Second example could be a pile of trays or a books lying one above the other. Let us draw a stack containing integers as in the following figure. 5 9 1 3 7

top

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For More Notes and questions log on to www.technicalsymposium.com Here, 5 is the current of the stack. If we add any element in the stack, it will be placed on top of 5 , and if we delete an element , it will be 5, which is on top of the stack. Operations on Stacks: Associated with the stack , there are several primitives operations. We can define the following necessary operations on stack. a)

create(s) - To create s as an empty stack.

b)

push(s,i) - To insert the element I on top of the stack s.

c)

pop(s)

- To remove the top element of the stack and to return the removed element as a function value.

d)

top(s)

- To return the top element of stack(s).

e) empty(s) - To check whether the stack is empty or not. It returns true if stack is empty and returns false otherwise. If a stack is empty and it contains no element, it is not possible to pop the stack. Therefore, before popping an element, we must ensure that the stack is not empty. PUSH & POP OPERATIONS: When we add an element to a stack, we stay that we push it on the stack and if we delete an element from a stack, we say that we pop it from the stack. Let us see how stack shrinks or grows when we pop or push an element in the following figures. Push (8) on the stack 8 5 9 1 3 7

top Push (4) on to stack 4 8 5 9 1 3 7

top

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Pop an element from the stack Top

8 5 9 1 3 7

Popped element = 4

Pop an element from the stack

Top

5 9 1 3 7

Popped element = 8

We may notice that the last item pushed onto a stack is always the first that will be popped from the stack. That is why stack is called last in, first out or LIFO in short. Implementation of Stacks There are two ways to implement stacks, one using arrays and other is using linked list. Array: Since the elements of the stack are ordered , an obvious choice would be an array as a structure t contains a stack. We can fix one end of the array as bottom of the stack. The other end of the array may be used as a top of the stack, which keeps shifting constantly as items are popped and pushed. We must store the index of the array containing the top element. 33



We can , therefore, declare a stack as a structure containing two fields- an array to hold the elements of the stack, and an integer top to indicate the position of the current top of the stack within the array. # define MAX 50 struct stack{ int top; int elements [5]; }; struct stack s; Here s is defined to be a stack containing elements of type integer . The maximum number of elements in the stack is defined to be 50. Elements [0] contain the first element so that the value of top is 0. If there are five elements in the stack, the value of top will be four and the top element is in elements[4]. A stack is empty when it contains no elements we can indicate this by making top as –1. We can write our function clearstack as clearstack(ts) struct stack *ts; { ts->top = -1; } Another operation is to check whether the stack is empty. To do this we must check whether s.top = = -1. Let us now consider the PUSH operation . To push or add an element we must perform the two steps: i. increment top indicator ii. put the new element at the new top.

We might code the PUSH & POP operations as follows: push(ts,x) Struct stack *ts; Int x; { if (fullstack(ts)){ printf( “ %s”, “ Stack overflow”); exit(1);

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For More Notes and questions log on to www.technicalsymposium.com } else ts->elements[++(ts->top)] = x; return; } This routine increments the top by 1 and puts x into array s.elements at the new top position. In this routine we use another routine Full Stack which checks whether the stack is full, before we push an element onto stack. A stack is full when ts->top = = MAX-1. Full Stack routine as follows: fullstack (ts) struct stack *ts; { if ( ts->top = = MAX-1) return(1); else return(0); } To remove an element or pop an element from the stack, we must first check the possibility of underflow as it is quite possible that somebody tries to pop an element from an empty stack. Therefore, we can write function POP as, Pop(ts) struct stack *ts; { if (empty(ts)) printf( “ % s” , “ stack underflow”); return(0); else return(ts->elements[ts->top--]); } We can write function empty (s) that returns 1 if the stack is empty and 0 if it is not empty as follows: empty(ts) struct stack *ts; { if ( ts -> top = = -1) return (1); else return(0); }

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Stack as a Linked List ( Using Pointers): Using this representation we are using the pool of available nodes and we will never have to test whether a particular stack is full. We can declare such as a stack as follows. Node structure:

Each node has two fields. i.e. Data and Next field

Data field

Next field

Stack- Node representation: A

B

C

D

Stack

End

node

Top element Declaration : ( Using C++) # include # include < process.h> class sta{ struct node { int data; node * next; } *stack ; public : void push(); void pop(); void disp(); }

PUSH OPERATION: Void sta :: push() { int n; node temp; temp = new node; cout << “ Push the element “ << endl;

3 ( First node of

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For More Notes and questions log on to www.technicalsymposium.com temp cin >> temp->data; temp->next=NULL; if(stack= = NULL) stack=temp; else { temp->next=stack; stack=temp; }

the stack). stack

3 stack 4 4 temp

} 4

3

stack

POP Operation: stack

2

4

3

Void sta :: pop() { temp node *temp; if (stack= = NULL) cout << “ Stack is empty “ << endl; else { stack temp= stack; stack= stack->next; temp cout << “Popped element “ << endl; cout << temp->data; delete temp; } }

TREE TRAVERSAL: When traversing a binary tree, we want to treat each node and its sub trees in the same fashion. If we let L, V, and R stand for moving left, visiting the node, and moving right when at a node, then there are six possible combinations of tree traversal: LVR, LRV, VLR, VRL, RVL, and RLV. If we adopt the convention that we traverse left before right, then only three traversals remain : LVR, LRV and VLR. To these we assign the names inorder, postorder, and preorder, respectively, because of the position of the V with respect to the L and the R.

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Procedure for Preorder: 1. 2. 3.

Visit the root node. Traverse the Left sub tree in preorder. Traverse the Right sub tree in preorder.

Example: Fig.1

The result is : + A B Algorithm: void preorder(node *nodeptr) { if ( nodeptr != NULL) { printf(“%d\n”, nodeptr->data); /* visit the root node */ preorder(nodeptr->left); /* Traverse the left sub tree */ perorder(nodeptr->right); /* Traverse the right sub tree */ } } Procedure for Inorder: 1. 2. 3.

Traverse the Left sub tree in inorder. Visit the root node Traverse the Right sub tree in inorder.

Fig.2

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The result is : A + B void inorder( node *nodeptr) { if ( nodeptr != NULL) { inorder(nodeptr->left); printf(“%d\n”, nodeptr->data); inorder(nodeptr->right); } }

/* Traverse the left sub tree */ /* Visit the root node */ /* Traverse the right sub tree */

Procedure for Postorder: 1. 2. 3.

Traverse the Left sub tree in postorder. Traverse the Right sub tree in postorder. Visit the root node.

Fig.3

The result is : A B +

void postorder( node * nodeptr) { if (nodeptr != NULL) { postorder(nodeptr->left); postorder(nodeptr->right); printf(“%d\n”, nodeptr->data); }

/* Traverse the left sub tree */ /* Traverse the right sub tree */ /* Visit the root node */

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For More Notes and questions log on to www.technicalsymposium.com } Fig.4

PRE ORDER

: A,B,D,C,E,AND F

IN ORDER

: B,D,A,E,F,C

POSTORDER

: D,B,F,E,C,AND A

Fig.5.

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PREORDER

: * +AB/CD

INORDER

: A+B*C/D

POSTORDER

: AB+CD/*

BINARY SEARCH TREES Definition: A binary search tree is a binary tree. It may be empty. If it is not empty then it satisfies the following properties: 1. 2. 3. 4.

Every element has a key and no two elements have the same key. The keys in the left sub tree are smaller than the key in the root. The keys in the right sub tree are larger than the key in the root. The left and right sub trees are also binary search trees.

It has two operations. They are, 1. Insertion 2. Deletion

Example Fig.

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To construct (Insertion) the Binary search tree for the following elements: 25, 15, 27, 13, 17, 26, 29, 28

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For More Notes and questions log on to www.technicalsymposium.com To delete a particular node from the Binary search tree: 1. Leaf node Deletion of a leaf node is quite easy. To delete 28 from the below tree the left child field of its parent is set to 0 and the node disposed. To delete the 17 from this tree, the right-child field of 15 is set to 0 , and the node containing 17 is disposed. To delete a leaf node 28

To delete a leaf node 17

2. Non-leaf node: 44



The deletion of a non-leaf element or node that has only one child is also easy. The node containing the element to be deleted is disposed, and the single-child takes the place of the disposed node. So, to delete the element 15 from the above tree, we simply change the pointer from the parent node (25) to the single-child node(13).

3. Root node: When the element to be deleted is in a non-leaf node that has two children, the element is replaced by either the largest element in its left sub tree or the smallest one in its right sub tree. Then we proceed to delete this replacing element from the sub tree from which it was taken.

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If we wish to delete the element with key 25 from the above tree, then we replace it by either the largest element, 17 , in its left sub tree or the smallest element , 26 , in its right sub tree. Suppose we opt for the largest element in the left sub tree. The 17 is moved in to the root and the following tree is obtained.

HEAPS Priority Queue:

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For More Notes and questions log on to www.technicalsymposium.com The priority queue is a data structure in which the intrinsic ordering of the elements does determine the results of its basic operations. There are two types of priority queues: An ascending priority queue and a descending priority queue. An ascending priority queue is a collection of items into which items can be inserted arbitrarily and from which only the smallest item can be removed. A descending priority queue is similar but allows deletion of only the largest item. Heaps Definition: A max (min) heap is a tree in which the key value in each node is no smaller (larger) than the key values in its children (if any). A max heap is a complete binary tree that is also a max tree. A min heap is a complete binary tree that is also a min tree.

Max. Heap

Min. Heap

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QUEUE Definition: A queue is an ordered collection of items from which items may be deleted at one end ( called the front of the queue) and into which items may be inserted at the other end ( called rear of the queue). This data structure is commonly known as FIFO or first-infirst-out. Fig.1 3

6

3

6

Fig.2 8

OPERATION S ON QUEUES: It has two operations. They are

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For More Notes and questions log on to www.technicalsymposium.com  Insertion  Deletion Insertion an element is popularly known as ENQ and deleting an element is known as DEQ. A minimum set of useful operations on queue includes the following. i. ii. iii. iv. v. vi.

CREATEQ(Q) – which creates Q as an empty Queue. ENQ(i) – which adds the element I to the rear of a queue and returns the new queue. DEQ(Q)- which removes the element at the front end of the queue and returns the resulting queue as well as the removed element. EMPTY(Q)- It checks the queue whether it is empty or not and returns true if it is empty and returns false otherwise. FRONT(Q)- which returns the front element of the queue without changing the queue. QUEUESIZE(Q)-which returns the number of entries in the queue.

We can obtain the queue by the following sequence of operations. We assume that the queue in initially empty. ENQ(q,8) 5

7

8

5

7

8

ENQ(q,9) 9

ENQ(q,4)

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For More Notes and questions log on to www.technicalsymposium.com 5

7

8

9

4

x =DEQ(q) Element 5 is deleted 7

8

9

4

x =DEQ(q) Element 7 is deleted 8

9

4

IMPLEMENTING THE QUEUE There are two ways to implement queue, one using arrays, and another is using Linked list. i.

Array : Let us implement the queue within an array so that the array holds the elements of the queue. There are two variables front and rear to indicate the positions of the first and last element of the queue within the array. Let the size of the array be 4. Initially let us assume that the queue is empty which means front = 0 and rear = -1.

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For More Notes and questions log on to www.technicalsymposium.com Empty Queue:

q[0]

q[1]

q[2]

front = 0(array position)

q[3] rear = -1 ( NULL)

Insertion: There are two variables front and rear to indicate the positions of the first and last element of the queue within the array. Let the size of the array be 4. Initially let us assume that the queue is empty which means front = 0 and rear = -1.After we have added three elements to the queue rear becomes 2 and front becomes 0. Now if we add one more elements to the queue from the rear, the value of rear changes to 3. Now the queue becomes full. ENQ(q,3) 3 q[0]

q[1]

q[2]

q[3]

q[2]

q[3]

front = 0 rear =0 ENQ(q,5) 3

5

q[0]

q[1]

front = 0 rear = 1 ENQ(q,7) 3

5

7

q[0]

q[1]

q[2]

q[3]

front = 0 rear = 2

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For More Notes and questions log on to www.technicalsymposium.com ENQ(q,9) [ Q is full ] 3

5

7

9

q[0]

q[1]

q[2]

q[3]

front = 0 rear = 3 Deletion: At this point, we delete one element. The element which is deleted is 3. This leaves a hole in the first position. To delete this element we must increment front, to indicate the true first element of the queue and assign the value of that slot to x. To check whether queue is empty or not, we must check whether front = rear. To add an element we must increment rear so that it points to the location next to the rear and place an element in that slot of the array. If we wish to add another element, and we increment rear by 1, rear becomes equal to front, which indicates that the queue is full. X= DEQ(q)

q[0]

5

7

9

q[1]

q[2]

q[3]

front = 1 rear = 3 x=DEQ(q) 7 q[0]

q[1]

9

q[2]

q[3]

front = 2 rear = 3

x=DEQ(q) 9 q[0]

q[1]

q[2]

q[3]

front = 3 rear = 3

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For More Notes and questions log on to www.technicalsymposium.com x=DEQ(q) [ Queue is empty]

q[0]

q[1]

q[2]

q[3]

front = rear = -1(NULL) Therefore, the condition for full queue is that the next slot of rear is equal to front and the condition for empty queue is that front = rear. Before we DEQ an element from queue we must make sure that queue is not empty and before we ENQ an element we must ensure that the queue is not full. Queue implementations in ARRAY using C++ class qu{ Public : Int front, rear, n , q[10]; void get(){ cout<< “ Enter the Queue size “ << endl; cin>> n; front = rear =-1; } void enq(); void deq(); }; int I, a[10]; void qu :: enq(){ int item; if ( rear >= n) { cout << “ Queue is full \n”; return; } else { cout << “ Enter the item to be inserted” <>item; rear = rear+1;

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For More Notes and questions log on to www.technicalsymposium.com q[rear] = item; i++; } } void qu :: deq() { int t; if ( front >= rear) { cout << “ Queue is Empty” << endl; return; } else { front = fornt +1; t = q[front]; cout << “ The deleted element : “ << t << endl; } } Implementation of Queue as Linked list Another way of implementing queues is as a linked list. Let us have two pointers, front to the first element of the list and rear to the last element of the list. 4 6 8

front rear . class que { struct node { int data; node *next; } * front, *rear;

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public: void insq(); void delq(); que(){ front = rear = NULL; } }; void que :: insq() { int n; node *temp; temp = new node; cout << “ Insert the element “ << endl; cin >> n; temp-data = n; temp->next = NULL; if ( front = = NULL) front = rear=temp; else 4 { rear->next = temp; front rear= rear->next; } } void que :: delq() { node *temp; temp = front;

temp 4 front

5 rear

4 temp

6

if ( front = = NULL) cout << “ Queue is empty “ << endl; else { front = front->next; cout << temp->data; delete temp; }

front

8

rear

} DEQUE:

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For More Notes and questions log on to www.technicalsymposium.com A single queue behaves in a FIFO manner in the sense that each deletion removes the oldest remaining item in the structure. A double ended queue or deque, in short is a linear list in which insertions and deletions are made to or from either end of the structure. Deletion

Insertion

Insertion

Deletion Front

Rear

We can have two variations of a deque, namely, the input-restricted deque and the output –restricted deque. The output-restricted deque allows deletion from only one end and input-restricted deque allows insertions at only one end. Queue Applications: The most useful application of queues is the simulation of a real world situation so that it is possible to understand what happens in a real world in a particular situation without actually observing its occurrence. Queues are also very useful in a time-sharing computer system where many users share the system simultaneously. Whenever a user requests the system to run a particular program, the operating system adds the request at the end of the queue of jobs waiting to be executed. Whenever the CPU is free, it executes the job, which is at the front of the job queue. Similarly there are queues for sharing I/O devices. Each device maintains its own queue of request. Another useful application of queues is in the solution of problems involving searching a nonlinear collection of states. Queue is used for finding a path using breadth-first-search of graphs. LINKED LIST Definition: A collection of node is called list. Each node or item in a linked list must contain at least two fields, an information field or data field and the next address field. The first, field contains the actual element on the list which may be a simple integer, a character, a string or even a large record. The second field, which is a pointer, contains the address of the next node in the list used to access the next node. A node of a linked list may be represented by the following figure.

List ( External pointer)

Data or Info

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Next


For More Notes and questions log on to www.technicalsymposium.com The entire linked list is accessed from an external pointer List pointing to the first node in the list. We can access the first node through the external pointer, the second node through next pointer of the first node, the third node through the next pointer of the second node till the end of the list. The next address field of the last node contains a special value, known as the NULL value. This is not a valid address. This only tells us that we have reached the end of the list. We will draw linked lists as an ordered sequence of nodes with links being represented by arrows. List 4

5

6

OPERATIONS ON LINKED LIST There are five basic types of operations associated with the list data abstraction: 1. To determine if the list is empty. Returns true if the list contains no elements. 2. Add new elements any in the list 3. To check if a particular element is present in the list. 4. To delete a particular element from the list placed anywhere in the list. 5. To print all the elements of the list.

We will introduce some notations to be used in algorithms: If p is a pointer to a node, then node(p) refers to the node pointed to by p info(p) refers to the data part of that node next(p) refers to the address part of that node info(next(p)) refers to the data part of the next node which node, which follows node(p) in the list if next(p) is not null. We can initialize the list by making the external pointer null. List = null Also, we can check whether the list is empty by checking whether the external pointer is null. if list = null then return(true)

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For More Notes and questions log on to www.technicalsymposium.com else return(false) This routine will return true if the list is empty, otherwise it will return false. To traverse or to print the elements of a linked list, we need to use a temporary pointer, p known as a traversal pointer. P = list while list < > null do begin print( info(p)) p= next(p) end Inserting into a Linked list To add a new node containing data value x in the beginning of the list we need to follow the step: i. To get a new node which is not in use. ii. To set the data field of the new node to x iii. To set the next field of the new node to point to list iv. To set pointer list point to the new node. To do this we can write the following algorithm: getnode(p) info(p) = x next(p) = list list = p

We are assuming that the operation getnode(p) obtains an empty node and sets the contents of a variable named p to the address of that node. p Getnode(p) p x Info(x) = p p

List x

5

6

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For More Notes and questions log on to www.technicalsymposium.com next(p) = list List 4

5

p

6

list = p Sample programs : Ex. No. 1

Stack

Program: #include #include int top=1; int a[20]; void main() { int n,x,b,c,i,temp; clrscr(); printf("Enter the no of elements\n"); scanf("%d",&n); do { printf("1.PUSH\n"); printf("2.POP\n"); printf("3.DISPLAY\n"); printf("4.EXIT\n"); break; printf("enter your choice\n"); scanf("%d",&b); switch(b) { case 1: printf("enter the number\n"); if(top>=n+1) printf("\nstack is overflow\n"); else scanf("%d",&x); a[top]=x; top=top+1;

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For More Notes and questions log on to www.technicalsymposium.com break; case 2: if (top<=0) printf("stack is underflow\n"); else { top=top-1; temp=a[top]; } break; case 3: for(i=1;i",a[i]); printf("%d",a[top-1]); break; case 4: exit(0); } printf("\ndo you want to continue(1/0)\n"); scanf("%d",&c); } while(c==1); getch(); } Ex. No. 2

Queue

Program: #include #include int n,x,b,c,i,r=0,f=0,te; int q[20]; void main() { clrscr(); printf("Enter the no of elements\n"); scanf("%d",&n); do { printf("1.insertion\n"); printf("2.deletion\n"); printf("3.display\n"); printf("4.exit\n");

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For More Notes and questions log on to www.technicalsymposium.com printf("enter your choice\n"); scanf("%d",&b); switch(b) { case 1: insert(); display(); break; case 2: delet(); display(); break; case 3: display(); break; case 4: exit(0); } printf("\ndo you want to continue(1/0)\n"); scanf("%d",&c); } while(c==1); getch(); } insert() { if(r>=n) printf("\nqueue is overflow\n"); else { printf("enter the number\n"); scanf("%d",&x); r=r+1; q[r]=x; } if(f==0) f=1; return(0); } int delet() { int te; if (f==0)

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For More Notes and questions log on to www.technicalsymposium.com printf("queue is underflow\n"); else if (f==r) { f=0;r=0; } else { te=q[f]; f=f+1; } return(te); } display() { if(r==0) { printf(" queue is empty"); } else { for(i=f;i",q[i]); printf("%d",q[r]); } return(0); } Ex. No: 3

Singly Linked list

Program: #include #include #define null 0 int a,s; struct node { int data; struct node *link; }; struct node *head,*first,*previous,*temp; void main() { first=null; head=null;

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For More Notes and questions log on to www.technicalsymposium.com clrscr(); do { printf("1.creation\n"); printf("2.display\n"); printf("3.insert first\n"); printf("4.insert last\n"); printf("5.insert middle\n"); printf("6.delete first\n"); printf("7.delete last\n"); printf("8.delete middle\n"); printf("enter your choice"); scanf("%d",&a); switch(a) { case 1: create(); display(); break; case 2: display(); break; case 3: insfirst(); display(); break; case 4: inslast(); display(); break; case 5: insmiddle(); display(); break; case 6: delfirst(); display(); break; case 7: dellast(); display(); break; case 8: delmiddle();

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For More Notes and questions log on to www.technicalsymposium.com display(); break; case 9: exit(0); } printf("\ndo you want to continue(1/0)\n"); scanf("%d",&s); } while(s==1); } create() { int s; s=sizeof (struct node); first=(struct node*) malloc (s); printf("enter the data"); scanf("%d",&first->data); first->link=null; if(head==null) head=first; else { previous=head; while(previous->link !=null) previous=previous->link; } previous->link=first; previous=first; return(0); } display() { if(head==null) printf("null first"); else temp=head; while(temp!=null) { printf("%d->",temp->data); temp=temp->link; } printf("null\n"); return(0); }

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insfirst() { int s; if (head==null) printf("list is null"); else { s=sizeof (temp); temp=(struct node*) malloc(s); printf("enter data\n"); scanf("%d",&temp->data); temp->link=head; head=temp; } return(0); } delfirst() { int s; if(head==null) printf("list is null"); else head=head->link; return(0); } inslast() { int s; struct node *temp,*last; if (head==null) printf("list is null"); else { s=sizeof (last); last=(struct node*) malloc(s); printf("enter the data\n"); scanf("%d",&last->data); last->link=null; temp=head; while(temp->link!=null) temp=temp->link; temp->link=last; }

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For More Notes and questions log on to www.technicalsymposium.com return(0); } dellast() { int s,m; struct node *pre,*next; if(head==null) printf("list is null"); else { next=head; next=head->link; pre=head; while(next->link!=null) { next=next->link; pre=pre->link; } pre->link=next->link; } return(0); } insmiddle() { int s,f,count; struct node *next,*pre,*nex; if (head==null) printf("list is null"); else { s=sizeof (temp); temp=(struct node*) malloc(s); pre=head; next=pre->link; count=2; printf("enter the position of the element"); scanf("%d",&f); printf("enter the data\n"); scanf("%d",&nex->data); while((countlink!=null)) { next=next->link; pre=pre->link; count=count+1; }

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For More Notes and questions log on to www.technicalsymposium.com if((countlink==null)) { printf("not possible to insert. the list is contains %d elements",count); } else { pre->link=nex; nex->link=next; } } return(0); } delmiddle() { int s,f,count; struct node *next,*pre,*nex; if (head==null) printf("list is null"); else { s=sizeof (temp); temp=(struct node*) malloc(s); pre=head; next=pre->link; count=2; printf("enter the position of the element"); scanf("%d",&f); while((countlink!=null)) { next=next->link; pre=pre->link; count=count+1; } if((countlink==null)) { printf("not possible to insert. the list is contains %d elements",count); } pre->link=next->link; } return(0); }

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For More Notes and questions log on to www.technicalsymposium.com Ex. No. 4

doubly linked list

Program: 4. Write a C program to implement the Double Linked List. #include #include #include struct student { int rollno; struct student *prev; struct student *next; }; typedef struct student list; void add(list *head,int rollno) { list *new_elt,*temp=head; new_elt=(list *)malloc(sizeof(list)); new_elt->rollno=rollno; new_elt->next=NULL; while(temp->next!=NULL) temp=temp->next; new_elt->prev=temp; temp->next=new_elt; } void insert(list *head,int rollno,int position) { int i; list *new_elt,*adj_elt,*temp=head; new_elt=(list *)malloc(sizeof(list)); new_elt->rollno=rollno; for(i=1;inext; adj_elt=temp->next; adj_elt->prev=new_elt;

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For More Notes and questions log on to www.technicalsymposium.com new_elt->next=adj_elt; new_elt->prev=temp; temp->next=new_elt; } int find(list *head,int rollno) { list *temp=head->next; int found=0,i=1;; while(temp!=NULL) { if(temp->rollno==rollno) { found=i; break; } i++; temp=temp->next; } return found; } void removeElt(list *head,int rollno) { list *del_elt,*successor,*predecsor,*temp=head->next; int i,found; found=find(head,rollno); if(found!=0) { while(temp->rollno!=rollno) temp=temp->next; del_elt=temp; predecsor=del_elt->prev; successor=del_elt->next; predecsor->next=del_elt->next; successor->prev=del_elt->prev; free(del_elt); printf("\nOne Element is deleted"); } else printf("\nElement has not Found!Cann't perform Deletion!"); } void print_list(list *head) { if(head->next!=NULL)

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For More Notes and questions log on to www.technicalsymposium.com { list *temp=head->next; printf("\nThe List:\n"); while(temp!=NULL) { printf("%d--> ",temp->rollno); temp=temp->next; } printf("Null"); } else printf("\n The List is Empty"); } void make_emptylist(list *head) { head->prev=NULL; head->next=NULL; printf("\nThe List has been deleted!"); } void main() { list *head; int position,rollno,option; head=(list *)malloc(sizeof(list*)); head->prev=NULL; head->next=NULL; clrscr(); while(1) { printf("\n\n1.Add\n2.Insert a Item\n3.Remove a Item\n4.Find\n5.Print the List\n6.Delete the List\n7.Exit"); printf("\nEnter your Choice:"); scanf("%d",&option); switch(option) { case 1: printf("\nEnter Rollno of the New Element:"); scanf("%d",&rollno); add(head,rollno); break; case 2: printf("\nEnter Rollno of Element to be Inserted:"); scanf("%d",&rollno); printf("\nEnter Position to insert:");

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For More Notes and questions log on to www.technicalsymposium.com scanf("%d",&position); insert(head,rollno,position); break; case 3: printf("\nEnter the Rollno of the element to Removed:"); scanf("%d",&rollno); removeElt(head,rollno); break; case 4: printf("Enter rollno of Item to be found:"); scanf("%d",&rollno); position=find(head,rollno); if(position!=0) printf("\nElement has been found!Position=%d",position); else printf("\nElement has not found in the List!"); break; case 5: print_list(head); break; case 6: make_emptylist(head); break; case 7: exit(0); } } getch(); }

Ex. No: 5

Circular Singly Linked list

Program : #include #include int a,s; struct node { int data; struct node *link; }; struct node *head,*first,*previous,*last,*temp; void main() {

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For More Notes and questions log on to www.technicalsymposium.com first=NULL; head=NULL; previous=NULL; clrscr(); do { printf("1.creation\n"); printf("2.display\n"); printf("3.insert first\n"); printf("4.insert last\n"); printf("5.insert middle\n"); printf("6.delete first\n"); printf("7.delete last\n"); printf("8.delete middle\n"); printf("enter your choice"); scanf("%d",&a); switch(a) { case 1: create(); display(); break; case 2: display(); break; case 3: insfirst(); display(); break; case 4: inslast(); display(); break; case 5: insmiddle(); display(); break; case 6: delfirst(); display(); break; case 7: dellast();

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For More Notes and questions log on to www.technicalsymposium.com display(); break; case 8: delmiddle(); display(); break; case 9: exit(0); } printf("\ndo you want to continue(1/0)\n"); scanf("%d",&s); } while(s==1); } create() { int s; s=sizeof (struct node); first=(struct node*) malloc (s); printf("enter the data"); scanf("%d",&first->data); first->link=first; if(head==NULL) { head=first; previous=first; } else { previous=head; while(previous->link !=head) previous=previous->link; previous->link=first; previous=first; } last=first; return(0); } display() { if(head==NULL) printf("list is null"); else {

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For More Notes and questions log on to www.technicalsymposium.com temp=head; while(temp!=last) { printf("%d->",temp->data); temp=temp->link; } if(temp==last) { printf("%d ->",temp->data); temp=temp->link; } } return(0); } insfirst() { int s; if (head==NULL) printf("list is null"); else { s=sizeof (temp); temp=(struct node*) malloc(s); printf("enter data\n"); scanf("%d",&temp->data); temp->link=head; head=temp; first=temp; last->link=temp; } return(0); } delfirst() { int s; if(head==NULL) printf("list is null"); else head=head->link; last->link=head; if(last->link==head) head=NULL;

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For More Notes and questions log on to www.technicalsymposium.com return(0); } inslast() { int s; struct node *last1,*first1; if (head==NULL) printf("list is null"); else { s=sizeof (last1); last1=(struct node*) malloc(s); printf("enter the data\n"); scanf("%d",&last1->data); last1->link=NULL; temp=head; while(temp->link!=head) temp=temp->link; temp->link=last1; last1->link=head; last=last1; } return(0); } dellast() { int s,m; struct node *pre,*next; if(head==NULL) printf("list is null"); else { if(head==last) head=last=NULL; else { next=head; while(next->link!=last) next=next->link; next->link=head; last=next; }

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For More Notes and questions log on to www.technicalsymposium.com } return(0); } insmiddle() { int s,f,count; struct node *next,*pre,*nex; if (head==NULL) printf("list is null"); else { s=sizeof (temp); temp=(struct node*) malloc(s); pre=head; next=pre->link; count=2; printf("enter the position of the elemant"); scanf("%d",&f); printf("enter the data\n"); scanf("%d",&nex->data); while((countlink!=head)) { next=next->link; pre=pre->link; count=count+1; } if((countlink==head)) { printf("not possible to insert. the list is contains %d elements",count); } else { pre->link=nex; nex->link=next; } } return(0); } delmiddle() { int s,f,count; struct node *next,*pre,*nex; if (head==NULL) printf("list is null"); else

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For More Notes and questions log on to www.technicalsymposium.com { s=sizeof (temp); temp=(struct node*) malloc(s); pre=head; next=pre->link; count=2; printf("enter the position of the elemant"); scanf("%d",&f); while((countlink!=head)) { next=next->link; pre=pre->link; count=count+1; } if((countlink==head)) { printf("not possible to insert. the list is contains %d elements",count); } pre->link=next->link; } return(0); }

Ex. No: 6

Operations On Binary Trees

Program : #include #include struct node { int data; struct node *lchild; struct node *rchild; } void creation() { printf("\n Enter the value of the root node \n"); t=(struct node*)malloc(sizeof(struct node));

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For More Notes and questions log on to www.technicalsymposium.com scanf("%d",&t->data); t->lchild=NULL; t->rchild=NULL; } void insert(int n,struct node *a) { struct node *x; if(a->data !=0) { if(a->data>n) insert(n,a->lchild); else insert(n,a->rchild); } x=(struct node*) malloc(sizeof(struct node)); x->data=n; if(a->data>n) { if((a->lchild)==NULL) { a->lchild=x; a->lchild->lchild=NULL; a->lchild->rchild=NULL; } } else if(a->rchild==NULL) { a->rchild=x; a->rchild->lchild=NULL; a->rchild->rchild=NULL; } } void inorder(struct node* a) { if(a!=NULL) { inorder(a->lchild); printf(" %10d ",a->data); inorder(a->rchild); } }

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For More Notes and questions log on to www.technicalsymposium.com void preorder(struct node *a) { if(a!=NULL) { printf(" %10d",a->data); preorder(a->lchild); preorder(a->rchild); } } void postorder(struct node *a) { if(a!=NULL) { postorder(a->lchild); postorder(a->rchild); printf(" %10d",a->data); } } void main() { int num,c; clrscr(); creation(); do{ printf("\n 1. Insertion \n2. Inorder \n3. preorder \n4.postorder "); printf("\n for exit give choice greater than four"); printf(" \nEnter your choice "); scanf("%d",&c); switch(c) { case 1:printf(" \n Data to be inserted "); scanf("%d",&num); insert(num,t); break; case 2: inorder(t); break; case 3: preorder(t); break; case 4: postorder(t); break; } }while(c<5); }

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binary tree operation

Program: 7. Write a C program to implement the binary tree operations – insert, delete, and search. #include #include #include struct bstree { int data; struct bstree *left; struct bstree *right; }; struct bstree *root,*temp; struct bstree* insertbst(struct bstree *root,int x) { if( root == NULL) { root=malloc(sizeof(struct bstree)); root->data=x; root->left=root->right=NULL; } else if(x < root->data) root->left=insertbst(root->left,x); else if(x > root->data) root->right=insertbst(root->right,x); return root; } struct bstree* findMin(struct bstree *t) { if(t==NULL) return NULL; else if(t->left != NULL) return findMin(t->left); else return t; } struct bstree* findMax(struct bstree *t) {

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For More Notes and questions log on to www.technicalsymposium.com if(t==NULL) return NULL; else if(t->right != NULL) return findMax(t->right); else return t; } int find(struct bstree *temp,int key) { if (temp==NULL) { return NULL; } else { if(key < temp->data) return find(temp->left,key); else if (key > temp->data) return find(temp->right,key); else return temp; } } int find_min(struct bstree *temp) { if(temp->left == NULL) return temp->data; else return find_min(temp->left); } int find_max(struct bstree *temp) { if(temp->right == NULL) return temp->data; else return find_max(temp->right); } struct bstree* removeElt(struct bstree *t,int key) { struct bstree *temp;

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For More Notes and questions log on to www.technicalsymposium.com if (t==NULL) printf("\nNode is not available"); else if(key < t->data) t->left=removeElt(t->left,key); else if(key > t->data) t->right=removeElt(t->right,key); else if(t->left != NULL && t->right != NULL) { temp=findMin(t->right); t->data=temp->data; t->right=removeElt(t->right,t->data); } else { temp=t; if(t->left==NULL) t=t->right; else if(t->right==NULL) t=t->left; free(temp); } return t; } void print_list(struct bstree *root) { if(root!=NULL) { if(root->left != NULL) print_list(root->left); printf(" %d",root->data); if(root->right != NULL) print_list(root->right); } } void main() { struct bstree *new_elt; int option,rollno,info; root=NULL; clrscr();

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For More Notes and questions log on to www.technicalsymposium.com while(1) { printf("\n\n1.Insert a Item\n2.Remove a Item\n3.Find\n4.Find Minimum Value\n5.Find Maximum Value\n6.Print the List\n7.Exit"); printf("\nEnter your Choice:"); scanf("%d",&option); switch(option) { case 1: printf("\nEnter Rollno of Element to be Inserted:"); scanf("%d",&rollno); root=insertbst(root,rollno); break; case 2: printf("\nEnter the Rollno of the element to Removed:"); scanf("%d",&rollno); root=removeElt(root,rollno); break; case 3: printf("Enter rollno of Item to be found:"); scanf("%d",&rollno); info=find(root,rollno); if(info!=0) printf("\nElement has been found! at Position=%d",info); if(info == 0) printf("\nElement has not found in the List!"); break; case 4: if(root == NULL) printf("\nTree is empty"); else { info=find_min(root); printf("\n The Minimum Value is:%d",info); } break; case 5: if(root == NULL) printf("\nTree is empty"); else { info=find_max(root); printf("\n The Maximum Value is:%d",info); }

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For More Notes and questions log on to www.technicalsymposium.com break; case 6: if(root == NULL) printf("\nTree is empty"); else print_list(root); break; case 7: exit(0); } } getch(); } Ex. No. 8 Program:

Quick Sort

#include #include int n,a[30],pass=1; void quicksort(int low, int high) { if(lowv) high--;

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For More Notes and questions log on to www.technicalsymposium.com if(i
Ex. No. 9

Heap Sort

Program: #include #include int x[20],n,n1; void heapsort(); void adjust(); void heapify(); void main() { int i; clrscr(); printf("ENTER THE NO. OF ELEMENTS :"); scanf("%d",&n); n1=n;

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For More Notes and questions log on to www.technicalsymposium.com printf(“ENTER THE ELEMENTS\n”); for(i=1;i<=n;i++) scanf("%d",&x[i]); clrscr(); printf(" \n ARRAY BEFORE SORT :"); for(i=1;i<=n;i++) printf("%d\t",x[i]); heapsort(); getch(); } void heapsort() { int i,t,j; heapify(); for(i=n;i>=2;i--) { t=x[i]; x[i]=x[1]; x[1]=t; adjust(1,i-1); printf("\npass %d \n",n-(i-1)); for(j=1;j<=n1;j++) printf(" %d\t",x[j]); } } void adjust(int i,int n) { int j; int t; j=2*i; t=x[i]; while(j<=n) { if(j=x[j]) break; x[j/2]=x[j]; j=2*j; } x[j/2]=t;

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For More Notes and questions log on to www.technicalsymposium.com } void heapify() { int i,j; for(i=n/2;i>=1;i--) adjust(i,n); } Ex. No. 10

Depth first search

Program: 10. Write a C program to implement the Depth First Search. #include #include int graph[10][10]; int visited[10]; void Intilize_Graph(int no_v) { int i,j; for(i=1;i<=no_v;i++) //Intialize the Graph { visited[i]=0; for(j=1;j<=no_v;j++) graph[i][j]=0; } } void print_graph(int no_v) { int i,j; printf("\nThe Graph(Matrix Representation):\n"); for(i=1;i<=no_v;i++) printf("\tV%d",i); for(i=1;i<=no_v;i++) { printf("\nV%d",i); for(j=1;j<=no_v;j++) { printf("\t%d",graph[i][j]); } } }

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For More Notes and questions log on to www.technicalsymposium.com void DFS(int start_v,int no_v) { int i; visited[start_v]=1; printf("%d-->",start_v); for(i=1;i<=no_v;i++) { if(i!=start_v && visited[i]==0 && graph[start_v][i]==1) { DFS(i,no_v); } } } void main() { int no_v,no_e; int s_v,e_v,start_v; int i,j; clrscr(); printf("\nEnter the No of Vertices in the Graph:"); scanf("%d",&no_v); printf("Enter the no of Edges in the Graph:"); scanf("%d",&no_e); printf("\nEnter the Adjacent vertices of each edge"); for(i=1;i<=no_e;i++) { printf("\nEdge:%d-->Start_V & End_V:",i); scanf("%d %d",&s_v,&e_v); graph[s_v][e_v]=1; graph[e_v][s_v]=1; } print_graph(no_v); printf("\nDepth First Search:\nEnter the Starting Vertex for Searching:"); scanf("%d",&start_v); printf("Depth First Search Tree:\n"); DFS(start_v,no_v); getch(); }

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shortest path of the graph

Program: 11. Write a C program to find the shortest path of a graph. #include #include int start_V[20],end_V[20],weight[20]; int no_v,no_e; struct VertexInfo { int known; int distance; int prev_vertex; }vertex[20]; void Intilize_VertexInfo() { int i,j; for(i=1;i<=no_v;i++) //Intialize the Graph { vertex[i].known=0; vertex[i].distance=1000; vertex[i].prev_vertex=0; } } void print_Path(int e_v) { int temp=e_v; if(vertex[e_v].prev_vertex==0) printf("\nNo path from Source to Given Destination!"); else { printf("\nShortest Path:%d ",e_v); while(vertex[e_v].prev_vertex!=0) { printf("%d ",vertex[e_v].prev_vertex); e_v=vertex[e_v].prev_vertex; } printf("\nThe Distance is:%d",vertex[temp].distance); } }

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void main() { int s_v,e_v,start_v; int i,j; int v,w,index; int min,qw,next_v; char ch; clrscr(); printf("\nEnter the No of Vertices in the Graph:"); scanf("%d",&no_v); printf("Enter the no of Edges in the Graph:"); scanf("%d",&no_e); printf("\nEnter the Adjacent vertices of each edge"); for(i=1;i<=no_e;i++) { printf("\nEdge:%d-->Start_V & End_V & Weight:",i); scanf("%d %d %d",&start_V[i],&end_V[i],&weight[i]); } Intilize_VertexInfo(); printf("\nEnter Vertices to find the Shortest Path:"); scanf("%d %d",&s_v,&e_v); vertex[s_v].distance=0; next_v=s_v;

while(next_v) { v=next_v; vertex[v].known=1; for(i=1;i<=no_e;i++) { if(start_V[i]==v) { w=end_V[i]; if(vertex[v].distance+weight[i] < vertex[w].distance) { vertex[w].distance=vertex[v].distance+weight[i]; vertex[w].prev_vertex=v; } } }

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For More Notes and questions log on to www.technicalsymposium.com min=1000; for(j=1;j<=no_v;j++) { if(vertex[j].known==0 && min>vertex[j].distance) { min=vertex[j].distance; next_v=j; } } if(min==1000) next_v=0; } print_Path(e_v); while(1) { printf("\nDo you want shortest to one more destination:"); fflush(stdin); ch=getchar(); if(ch=='y' | ch=='Y') { printf("\nEnter the Destination Vertex:"); scanf("%d",&e_v); print_Path(e_v); } else break; } getch(); }

K.L.N COLLEGE OF ENGINEERING, POTTAPALAYAM DEPARTMENT OF COMPUTER APPLICATIONS (MCA) DATA STRUCTURES LAB(MC1606) I SEMESTER – (June 2006 – November 2006) DATA STRUCTURES LAB CYCLE PROGRAMS 1. Represent the given sparse matrix using one-dimensional array and linked list. 2. Create a Stack and do the following operations using arrays and linked lists (i)Push (ii) Pop (iii) Peep

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3. Create a Queue and do the following operations using arrays and linked lists (i)Add (ii) Remove 4. Implement the operations on singly linked list, doubly linked list and circular linked list. 5. Create a binary search tree and do the following traversals (i)In-order (ii) Pre order (iii) Post order 6. Implement the following operations on a binary search tree. (i) Insert a node (ii) Delete a node 7. Sort the given list of numbers using heap and quick sort. 8. Perform the following operations in a given graph (i) Depth first search (ii) Breadth first search 9. Find the shortest path in a given graph using Dijkstra algorithm

K.L.N COLLEGE OF ENGINEERING, POTTAPALAYAM DEPARTMENT OF COMPUTER APPLICATIONS (MCA) PROGRAMMING LAB (MC1607) I SEMESTER – (June 2006 – November 2006) C LAB CYCLE PROGRAMS 1. Display the following: (i) Floyd’s triangle (ii) Pascal Triangle 2. Generate the following series of numbers: 92


For More Notes and questions log on to www.technicalsymposium.com Armstrong numbers between 1 to 100 Prime numbers between 1 to 50 Fibonacci series up to N numbers 3. Manipulate the strings with following operations. (i) Concatenating two strings (ii) Reversing the string (iii) Finding the sub string (iv) Replacing a string (v) Finding length of the string 4. Find the summation of the following series: (i) Sine (ii) Cosine (iii) Exponential 5. Create the sales report for M sales person and N products using two-dimensional array. 6. Simulate following Banking operations using functions. (i) Deposit (ii) Withdrawal (iii) Balance Enquiry 7. Implement using recursion I, Find the solution of Towers of Hanoi problem using recursion. II, Fibonacci number generation. III, Factorial 8. Generate Student mark sheets using structures. 9. Create a collection of books using arrays of structures and do the following: (i) Search a book with title and author name (ii) Sorts the books on title.

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Data Structure Notes

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