Page 1 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , UNIT - II: FUNCTIONS AND ARRAYS, Arrays – Concept of array in C, one dimensional arrays, Accessing and manipulating elements, of arrays, array applications-Linear search, Binary search, Bubble sort, Selection sort, Insertion, sort, two – dimensional arrays, multidimensional arrays, C program examples., Functions-Designing Structured Programs, user defined functions- categories, parameter passing, mechanisms, inter function communication, Standard functions, Storage classes-auto, register,, static, extern, scope rules, type qualifiers, C program examples., Recursion- recursive functions, Limitations of recursion, C programs examples., , *****, , VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 1

Page 2 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , ARRAYS, INTRODUCTION, There are six derived types in C: arrays, functions, pointer, structure, union and enumerated types. The, function type is derived from its return type., , Figure: 3.0 Derived Types, , Array is a collection of similar data elements in which each element is unique one and located in, separate memory locations., Array is collection of homogeneous data elements which are stored in contiguous memory, locations., Arrays are broadly classified into three categories,, 1. One dimensional arrays, 2. Two dimensional arrays, 3. Multi dimensional arrays, Declaration of Array, Data-type array-variable[size];, Data type: It is the data type of array elements., The size represents no. of elements in the array., An array will stay this size throughout the execution of the program., In other words, we can change the size of an array at compile time, but cannot change it at, run-time., , To declare regular variables we just specify a data type and a unique name:, int number;, To declare an array, we just add an array size., For example:, int a[5];, , , , Creates an array,  of 5 integer elements., For example:, double stockprice[31];, creates an array of 31 doubles., , VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 2

Page 3 : PROGRAMMING FOR PROBLEM SOLVING, , Ex :, , UNIT -II, , int a[5];, , The example tells to the compiler that ‘a’ is an integer type of array and can store 5, integers. The compiler reserves 2 bytes of memory for each integer array element. Total space of, 10 bytes are allocated to variable ‘a’, Memory allocation for array a, , The elements are represented as a[0],a[1]…..a[4]., Array Initialization, The array initialization is done is given below, int a[5] = {12, 14, 16, 17, 18};, Here 5 elements are stored in an array ‘a’. The array elements are stored sequentially in separate, locations. Reading of array elements begins from ‘0’. Array elements are called by array names, followed by the element numbers. The 5 elements are referred as, Subscripted variable a[0] refers to the first element of array a, 12 i.e. a[0]=12, Subscripted variable a[1] refers to the first element of array a, 14 i.e. a[1]=14, Subscripted variable a[2] refers to the first element of array a, 16 i.e. a[2]=16, Subscripted variable a[3] refers to the first element of array a, 17 i.e. a[3]=17, Subscripted variable a[4] refers to the first element of array a ,18 i.e. a[4]=18, If the array size is declared as 5. The elements are stored from index 0 to 4. i.e. If a[5] has been, declared, then values are stored from a[0] to a[4]., The integer enclosed in brackets is the array subscript, and its value must be in the range, from zero to one less than the number of memory cells in the array., INITIALIZING ONE DIMENSIONAL ARRAYS, Option 1 Initializing all memory locations, If you know all the data at compile time, you can specify all your data within brackets:, int a[5] = {12, 14, 16, 17, 18};, during compilation, 5 contiguous memory locations are reserved by the compiler for the variable, a and all these locations are initialized as shown in Fig., If the size of integer is 2 bytes, 10 bytes will be allocated for the variable a., , VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 3

Page 4 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , a[0], , a[1], , a[2], , a[3], , a[4], , 22, , 12, , 34, , 15, , 30, , 5000, , 5002, , 5004, , 5006, , 5008, , Address, , Figure: Storage Representation of array, Option 2 initialization without size, If we omit the size of your array, but specify an initial set of data, the compiler will, automatically determine the size of your array. This way is referred as initialization without size., int a [] = {75, 79, 82, 70, 68};, In this declaration, even though we have not specified exact number of elements to be used in, array a, the array size will be set of the total number of initial values specified. Here, the, compiler creates an array of 5 elements., Option 3 Partial Array Initialization, If the number of values to be initialized is less than the size of the array, then the elements are, initialized in the order from 0th location. The remaining locations will be initialized to zero, automatically., , a[0], , a[1], , a[2], , a[3], , a[4], , 75, , 79, , 82, , 0, , 0, , int a[5] = {75, 79, 82};, , Even though compiler allocates 5 memory, locations, using this declaration statement, the, compiler initializes first three locations with 75,70, and 82,the next set of memory locations are automatically initialized to 0‟s by the compiler, , 5000, , 5002, , 5004, , 5006, , 5008, , Option 4, If you do not know any data ahead of time, but you want to initialize everything to 0, just use 0, within { }., For example:, int a [5] = {0};, VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 4

Page 5 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , This will initialize every element within the array to 0, , a[0], , a[1], , a[2], , a[3], , a[4], , 0, , 0, , 0, , 0, , 0, , 5000, , 5002, , 5004, , 5006, , 5008, , Reading one dimensional array elements from input, for(i=0; i<5; i++), {, scanf("%d",&a[i]);, }, The above loop is used to read 5 elements into array from input, , a[0], , a[1], , a[2], , a[3], , a[4], , 22, , 12, , 34, , 15, , 30, , 5000, , 5002, , 5004, , 5006, , 5008, , Writing the elements of one dimensional array, elements to output, for(i=0; i<5; i++), {, printf("%d",a[i]);, }, , The above loop is used to print 5 elements to output as shown below, 22 12 34 15 30, Sample Programs, 1. /*Program to read an array of 10 numbers and print them */, void main(), {, int a[10],i;, clrscr();, printf("Enter 10 values :");, for(i=0; i<10; i++), scanf("%d",&a[i]);, printf("Given Values :");, for(i=0; i<10; i++), printf("%3d",a[i]);, }, Output, Enter 10 values ; 21 22 23 24 25 26 27 28 29 30, Given Values : 21 22 23 24 25 26 27 28 29 30, VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 5

Page 6 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , 2./* Program to calculate the sum and average of six subject marks using arrays */, void main(), {, int a[10],i,sum=0;, float avg;, clrscr();, printf("Enter 6 subject marks :");, for(i=0; i<6; i++), {, scanf("%d",&a[i]);, sum = sum + a[i];, }, printf("Sum = %d",sum);, avg= sum/6;, printf("\nAvg = %f",avg);, }, Output, Enter 6 subject marks : 50 55 60 65 70 75, Sum = 375, Avg = 62.000000, 3./* Program to calculate maximum and minimum of given numbers */, void main(), {, int a[100],n,max=0,min,i;, clrscr();, printf("Enter total numbers :");, scanf("%d",&n);, printf("Enter %d numbers :",n);, for(i=0; i<n; i++), {, scanf("%d",&a[i]);, }, min = max = a[0];, for(i=1; i<n; i++), {, if(max<a[i]), max = a[i];, }, printf("Maximum Number = %d",max);, min=a[0];, for(i=1; i<n; i++), {, if(min>a[i]), min = a[i];, }, printf("\nMinimum Number = %d",min);, }, Output, VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 6

Page 7 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , Enter total numbers : 5, Enter 5 numbers : 16 32 03 15 12, Maximum Number = 32, Minimum Number = 36, 4./*Program to search an element in an array*/, #include<stdio.h>, int main(), {, int a[20],i,n,KEY,flag =0;, printf("Enter n:");, scanf("%d",&n);, printf("Enter %d elements:",n);, for(i=0;i<n;i++), {, scanf("%d",&a[i]);, }, printf("Element to be searched:");, scanf("%d",&KEY);, for(i=1;i<n;i++), {, if(a[i]==KEY), {, printf("Elelement is found at %d",i);, flag = 1;, break;, }, }, if(flag == 0), printf("Element was not found");, return 0;, }, Output, Enter n:5, Enter 5 elements:23 45 34 67 78, Element to be searched:67, Elelement is found at 3, Two dimensional Arrays, Two dimensional array is used to represent the elements of the matrix, Two- dimensional array can be thought as a rectangular display of elements with rows, and columns. The two dimensional array is a collection of number of one- dimensional arrays,, which are placed one after another., Syntax:, Datatype var[rowsize][colsize];, VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 7

Page 8 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , Datatype is the type of elements of a matrix, Rowsize represents number of rows in the matrix., colsize represents number of cols in the matrix., Declaration:, int a[3][2];, Here 3 indicates the no. of rows and 2 indicates columns, Initialization:, int a[3][2] = { 21, 22, 23, 24, 25, 26};, The values are stored in the following pattern, Col0, Col1, Row0, 21, 22, Row1, 23, 24, Row2, 25, 26, The values are represented as, a[0][0] = 21; a[0][1] = 22;, a[1][0] = 23; a[1][0] = 24;, a[2][0] = 25; a[2][1] = 26;, a[0][0], , a[0][1], , a[0][2], , 21, , 22, , 23, , a[1][0], , a[1][1], , a[1][1], , 24, , 25, , 26, , The total number of elements in two dimensional array is product of no. of rows and no. of, columns., Example : int a [3][2] ; stores 3x2=6 values conceptually stored in matrix form., , /* Program to read elements of two-dimensional array and print them in matrix format*/, void main(), {, int a[3][2],i,j;, clrscr();, printf("Enter elements of 3x2 matrix :");, for(i=0; i<3; i++), {, for(j=0; j<2; j++), {, scanf("%d",&a[i][j]);, }, }, VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 8

Page 10 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , for(j=0;j<c1;j++), {, s[i][j] = a[i][j]+b[i][j];, }, }, printf("\nThe resultant matrix \n");, for(i=0;i<r1;i++), {, for(j=0;j<c1;j++), {, printf("%4d",s[i][j]);, }, printf("\n");, }, retrun 0;, }, , Output, Enter the size of matrx A:2 2, Enter the size of matrx B:2 2, Elements of matrix A, 12, 45, Elements of matrix B, 56, 38, The resultant matrix, 6 8, 7 13, /* Program to perform multiplication of two matrices*/, #include<stdio.h>, int main(), {, int a[5][5],b[5][5],c[5][5],i,j,r1,c1,r2,c2,k;, printf("Enter the size of matrix A:");, scanf("%d%d",&r1,&c1);, printf("Enter the size of matrix B:");, scanf("%d%d",&r2,&c2);, if(c1!=r2), {, printf("Multiplication is not possible");, return 0;, }, printf("Enter elements of matrix A\n");, for(i=0;i<r1;i++), {, for(j=0;j<c1;j++), {, VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 10

Page 11 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , scanf("%d",&a[i][j]);, }, }, printf("Enter elements of matrix B\n");, for(i=0;i<r2;i++), {, for(j=0;j<c2;j++), {, scanf("%d",&b[i][j]);, }, }, for(i=0;i<r1;i++), {, for(j=0;j<c2;j++), {, c[i][j]=0;, for(k=0;k<c1;k++), {, c[i][j] = c[i][j]+a[i][k]*b[k][j];, }, }, }, printf("\nThe resultant matrix\n");, for(i=0;i<r1;i++), {, for(j=0;j<c2;j++), {, printf("%4d",c[i][j]);, }, printf("\n");, }, return 0;, }, Output, Enter the size of matrix A:2 2, Enter the size of matrix B:2 2, Enter elements of matrix A, 12, 23, Enter elements of matrix B, 45, 36, The resultant matrix, 10 17, 17 28, , VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 11

Page 12 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , /* Program to check whether given matrix is symmetric or not*/, #include<stdio.h>, int main(), {, int a[5][5],i,j,r,c,flag = 1;, printf("Enter rows and cols:");, scanf("%d%d",&r,&c);, printf("Enter the elements:");, for(i=0;i<r;i++), {, for(j=0;j<c;j++), {, scanf("%d",&a[i][j]);, }, }, for(i=0;i<r;i++), {, for(j=0;j<c;j++), {, if(a[i][j]!=a[j][i]), {, printf("Not symmetric");, flag = 0;, return 0;, }, }, }, if(flag==1), printf("symmetric matrix");, return 0;, }, , Output, Enter rows and cols:3 3, Enter the elements:, 123, 234, 345, symmetric matrix, , VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 12

Page 13 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , FUNCTIONS, INTRODUCTION, There are six derived types in C: arrays, functions, pointer, structure, union and, enumerated types. The function type is derived from its return type., , Figure: 3.0 Derived Types, DESIGNING STRUCTURED PROGRAMS (Top Down Design), For larger programs, it is not possible to understand all aspects of such programs without, reducing them in to smaller parts. The planning for large programs is as follows, i. Understand the problems as a whole, ii. Break it into simpler, understandable parts., iii. Solve individual parts and combine them., Each part of a program is termed as module. The process of sub-dividing a problem into, manageable parts is called top-down design., In top-down design, a program is divided into a main module and its related modules. Each, module in turn is divided into sub modules until the resulting modules are intrinsic; that is until, they are implicitly understood without further division. This process is known as factoring., Top-down design is usually done using a visual representation of the modules known as a, structure chart. The structure chart shows the relation between each module and its submodules. The structure chart is read top-down, left-right. The reading starts from main module, followed by reading of sub-modules of main from left to right., The main module is called calling module because it has sub modules. The sub modules are, known as called modules. Communication between modules in a structure chart is allowed only, through a calling module. No communication takes place directly between modules that do not, have a calling-called relationship. The technique used to pas data to a function is known as, parameter passing. The parameters are contained in a list that is a definition of data passed to, the function by the caller., , VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 13

Page 14 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , Figure: 3.1 Structure Chart, Moving down and left, we then read Module 1. Module 1 ,Module 2 and Module 3 are at the, same level. The Main Module consists of three sub-modules. Module 1 is further subdivided into, three modules, Module 1a, Module 1b, and Module 1c. To write the code for Module 1, we need, to write code for its three sub-modules., The main module is called calling module because it has sub modules. The sub modules, are known as called modules. Communication between modules in a structure chart is allowed, only through a calling module. No communication takes place directly between modules that do, not have a calling-called relationship., How can Module 1a send data to Module 3b?, It first sends data to Module 1, which in turn sends it to the Main Module, which passes it, to Module 3, and then on to Module 3b., The technique used to pas data to a function is known as parameter passing. The, parameters are contained in a list that is a definition of data passed to the function by the caller., , FUNCTIONS IN C, In C, idea of top-down is done using functions. A C program is made of one or more, functions, one and only one of which be called main. The execution of the program always starts, with main, but it can call other functions to do some part of job., Definition: A function is an independent module that will be called to do a specific task., A function is a self-contained block of code that carries out some specific and well-defined task., Advantages of functions:, 1. Modular Programming It facilitates top down modular programming. In this, programming style, the high level logic of the overall problem is solved first while the, details of each lower level functions is addressed later. Problem can be factored into, understandable and manageable parts., 2. Code Reusability: It provides a way to reuse code that is required in more than one place, in a program. Functions can be reusable in other programs (Files)., 3. Protecting data: Used to protect data. Local data in function is available only to function, when it is executing. When the function is not running, the data are not accessible., VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 14

Page 15 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , 4. Reduction of source code The length of the source program can be reduced by using, functions at appropriate places. This factor is critical with microcomputers where, memory space is limited., 5. Easier Debugging It is easy to locate and isolate a faulty function for further, investigation., C FUNCTIONS ARE CLASSIFIED INTO TWO TYPES, 1. Library Functions (Standard functions or Predefined functions), 2. User Defined Functions, Library Functions, These are the built in functions available in standard library of C.The standard C library is, collection various types of functions which perform some standard and predefined tasks., Example: abs (a) function gives the absolute value of a, available in <math.h> header file, pow (x, y) function computes x power y. available in <math.h> header file, printf ()/scanf () performs I/O functions. Etc..,, User Defined Functions, These functions are written by the programmer to perform a specific task., Example: main(), sum(), fac () etc., The Major distinction between these two categories is that library functions are not required to, be written by us whereas a user defined function has to be developed by the user at the time of, writing a program., The functions defined by the user are termed as user defined functions., A function is a complete and independent program which is used (or invoked) by the, main program or other subprograms. A subprogram receives values called arguments from a, calling program, performs calculations and returns the results to the calling program., THE GENERAL FORM OF A C FUNCTION, return_type function_name (argument declaration), {, //local declarations, ……, ……, //statements, ……, return (expression);, Figure: 3.2 General Form of A C Function, }, , VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 15

Page 16 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , return_type, Specifies the type of value that a function returns using the return statement. It can be, any valid data type. If no data type is specified the function is assumed to return an integer, result., function_name, Must follow same rules of variable names in C. No two functions have the same name in, a C program., argument declaration, Is a comma-separated list of variables that receive the values of the argument when function is, called. If there is no argument declaration the bracket consists of keyword void., There are three steps involved in creating and using a user defined functions. They are,  Function Declaration(Prototyping),  Function Definition,  Function Call, FUNCTION DECLARATION (PROTOTYPING), A function prototype (Declaration) tells the compiler about., 1. The return type of the function so that the compiler can generate the correct code for, the return data., 2. The type and number of arguments used by the function., The general form of the prototype is, , P arameter names can be omitted, 3., F unc tion P rototype:, from the function prototype, 4., 5., 6., 7., return_type function_name (type1 name1, type2 name2,..., typen namen), 8. Figure: 3.3 Function Prototype, R eturn type and parameter types, mus t be provided in the prototype, , ;, , S emi-colon indicates that this is only, the function prototype, and that its, definition will be found els ewhere, , Example 1: int sum(int a, int b); (or) int sum(int, int);, Here sum is function name and the function returns integer value. The, functions take two arguments of integer data types., , VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 16

Page 17 : PROGRAMMING FOR PROBLEM SOLVING, , Example 2:, , UNIT -II, , void sum(void);, Here sum is function name and the function doesn’t return any value., The functions have no parameters. So void is coded in parentheses., , Note: The prototype normally goes near the top of the program and must appear before any call, is made to the function., The function Declaration is terminated with a semi-colon., The return type and parameter list are required entries. If the program has no return, type, we write void as function return type. Function name is user defined name just like any, other C variable name. If there are no parameters to a function, we can code void in parenthesis., If a function have multiple parameters, we separate each type-identifier with commas. The C, standard does not require identifier names in a function declaration’s formal parameters., FUNCTION DEFINITION, The function definition contains the code for a function. It is made up of two parts: The function, header and the function body., ,  Function header consists of three parts: the return type, the function name, and the, formal parameter list. A semi colon is not used at the end of the function header.,  Function body contains local declarations and function statements.,  Function can not be defined inside another function., In function definition, we write the actual lines of code required to accomplish the task assigned, to the function. It is made up of two parts: the function header and the function body., The function header consists of return type, function name and formal parameter list., The return type specifies the data type of the value being returned by the function. If the, program has no return type, we write void as function return type., VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 17

Page 18 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , Function name is user defined name just like any other C variable name. All rules of, variables are applicable for function name. The function name in function declaration statement, and function definition header need not to be same but the return type must be same., The formal parameter list defines and declares the variables that will contain the data, received by the function. The parameter list is always required. If the function has no, parameters – that is, if it does not receive any data from the calling function, then void is coded, in parentheses., The function body is a compound statement i.e. it must have opening and closing braces., It contains the local declarations and function statements. After function statements, a return, statement can be coded. If a function return type is void, it can be written without return, statement., Example:, , int sum(int x, int y), {, , int z;, z = x+y;, return z;, , }, In the above example, sum is the function accepting two parameters int x, int y named, as x, y of integer data type. The function sum performs addition of two number and return the, result value with help of statement return z. As the function returns an integer value the datatype of function is given as int., FUNCTION CALL, Function call is a statement we use in your programs to invoke the services of the, function. A function call is a postfix expression. The operand in a function call is the function, name; the operator is the parentheses, which contain actual parameters. The actual parameters, identify the values that are to be sent to the called function. They match the functions formal, parameters in type and order in the parameter list. If there are multiple actual arguments, they, are separated by commas., Syntax :, , function-name(actual-parameters-list);, , Example, , sum(10,20);, Here we are calling the function named sum by passing two values 10 &, , 20, Note : There are many different ways to call a function., , VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 18

Page 19 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , Return Statement, A function may or may not send back any value to the calling function. If it does, it is, done through the return statement. While it is possible to pass any number of values to the, called function, the called function can return only a single value per call, at the most. A return, statement terminates a function. When there is no return statement at the end of function, the, system inserts one with a void return value., Syntax : return expression., Example :, , return 1;, , // 1 is a value, , return z;, , // z is a variable, , return (a+b); // (a+b) is an expression, , Generally execution of program will starts from main(). Prototyping tells the compiler about, name, return type, number& type of parameters of the function to be implemented.When the, function call(sum(x,y) ) appears immediately control is transferred to called function definition., When the called function completes it task, it returns control o the calling function(main() )., Calling Function: A function which makes call to another function is termed as calling function., In the above example, main() is defined as calling function. i.e. it makes a call to function named, sum()., Called Function: A called function receives control from a calling function. When the called, function completes it task, it returns control o the calling function. It may or may not return a, value to the caller. In the above example, sum() is defined as called function. This function is, being called from main() function., VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 19

Page 20 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , Actual Parameters: The actual parameters are the expressions(variables) in the calling, statement. In the example num1,num2 are actual parameters., Formal Parameters: The variables that are declared in the header of the function definition are, called formal parameters. In the example x, y are called formal parameters., Note : Formal and actual parameters must match exactly in type, order and he number. Their, names however do not need to match., Local Variables: The local variables are defined inside a function and used without having any, role in the communication between functions. The variable defined is local to that function or, block only. Other functions cannot access these variables. In the above example num1, num2, are local variables to the function main(), x,y are local variables to the function sum()., Global Variables: The global variables are defined outside the main() function and used for, communication between functions. The global variables can be used by multiple functions in the, program. In the above example a,b are global variables., , CATEGORY OF USER -DEFINEDFUNCTIONS, Based on the signature functions are classified as 4 categories, Signature represents,  Name of the function,  Its return type,  No of arguments,  Type of arguments, Category 1: Functions with no arguments and no return values, Category 2: Functions with arguments and no return values, Category 3: Functions with no arguments and return values, Category 4: Functions with arguments and return values, CATEGORY- 1 : Functions With No Arguments And No Return Value, This type of function has no arguments, meaning that it does not receive any data from, the calling function. Similarly this type of function will not return any value to the calling, function. Here the calling function does not receive any data from the called function. In effect,, there is no data transfer between the calling function and the called function., , VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 20

Page 21 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , EXAMPLE PROGRAM-1, , /*Program to add sum of two numbers using functions */, #include<stdio.h>, , VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 21

Page 22 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , EXAMPLE PROGRAM-2, /*Program to find factorial of given integer */, int main(), {, void fact();, , fact();, , /*Prototyping or function declaration */, , /*Function calling */, , return 0;, }, /*Function definition starts */, void fact(), {, int n,i,f=1;, printf("Enter the value of n:");, scanf("%d",&n);, for(i=n;i>=1;i--), {, f=f*i;, }, printf("\nFactorial=%d",f);, }, OUTPUT, Enter n:5, Factorial=120, , VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 22

Page 23 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , From the above program the function fact () do not receive any values from the function main (), and it does not return any value to the function main (). Observe the transfer of control between, the functions indicated with arrows., EXAMPLE PROGRAM-3, //Program to find GCD using functions, int main(), {, void gcd();/*Prototyping or function declaration */, gcd();, , /*Function calling */, , return 0;, }, /*Function definition starts */, void gcd(), {, int r,a,b;, printf("Enter any two integer values :");, scanf("%d%d",&a,&b);, while(b!=0), {, r=a%b;, a=b;, b=r;, }, printf("\n The GCD of given two values is %d:",a);, }, OUTPUT, Enter any two integer values :52 91, The GCD of given two values is 13:, , VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 23

Page 24 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , CATEGORY 2: Functions with arguments and no return value, In this category there is data is transfer from the calling function to the called function using, parameters. But, there is no data transfer from called function to the calling function. The result, obtained is utilized by the called function and there is no gain to main()., Local Variables, Variables that are defined within a function are called local variables. A local variable comes into, existence when the function is entered and is destroyed upon exit., Function arguments, The arguments that are supplied in to two categories, 1. Actual arguments/parameters, 2. Formal arguments/parameters, Actual arguments/parameters, Actual parameters are the expressions in the calling functions. These are the parameters present, in the calling statement (function call)., Formal arguments/parameters, Formal parameters are the variables that are declared in the header of the function definition., This list defines and declares that will contain the data received by the function. These are the, value parameters, copies of the values being passed are stored in the called functions memory, area., Note: Actual and Formal parameters must match exactly in type, order, and number. Their, names however, do not need to match., , VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 24

Page 25 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , Note: Here type means any valid Data type like int, float, char etc;, , EXAMPLE PROGRAM-1, /* Program to calculate sum to two numbers */, #include<stdio.h>, int main(), {, void sum(int,int);, int a,b,result;, , printf("Enter two numbers :");, scanf("%d%d",&a,&b);, sum(a,b);, return 0;, }, VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 25

Page 26 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , void sum(int x, int y), {, int z;, z=x+y;, printf("Sum = %d",z);, }, OUTPUT, , Enter two numbers : 12 13, Sum = 25, , EXAMPLE PROGRAM-2, /*Program to find factorial of given integer */, #include<stdio.h>, #include<conio.h>, int main(), {, void fact(int);, , /*Prototyping or function declaration */, , int n;, printf("Enter a vlue for n:");, scanf("%d",&n);, fact(n);, , /*Function calling */, , return 0;, }, , /*Function definition starts */, VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 26

Page 27 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , void fact(int m), {, int i,f=1;, for(i=m;i>=1;i--), {, f=f*i;, }, printf("\nFactorial=%d",f);, }, OUTPUT, Enter a value for n:6, Factorial of given value is =720, , EXAMPLE PROGRAM-3, //Program to find GCD using functions, int main(), {, void gcd(int,int); /*Prototyping or function declaration */, int a,b;, printf("Enter any two integer values :");, scanf("%d%d",&a,&b);, gcd(a,b);, , /*Function calling */, , return 0;, }, /*Function definition starts */, void gcd(int x,int y), VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 27

Page 28 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , {, int r;, while(y!=0), {, r=x%y;, x=y;, y=r;, }, printf("\n The GCD of given two values is %d:",x);, }, OUTPUT, , Enter any two integer values :56 98, The GCD of given two values is 14:, Explanation: In above program calling function (main() ) is passing the values of actual, paramaters(a,b) to the formal parameters of called function ( gcd() ) . But The called function is, not returning any value back to the calling function., Note :, , void gcd(int,int);, , From above statement void Means the function gcd() is not returning any value to, the calling function. (int,int) means there two parameters to pass as arguments., CATEGORY 3: Functions With No Arguments And Return Value, In this category, there is no data transfer from the calling function to the called function. But,, there is data transfer from called function to the calling function. In other words calling function, is not passing any argument to the called function but called function is returning a value back to, the calling function., , VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 28

Page 29 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , There are two ways that a function terminates execution and returns to the caller., 1. When the last statement in the function has executed and conceptually the function’s, ending ‘}’ is, encountered., 2. Whenever it faces return statement., THE return STATEMENT,  The return statement is the mechanism for returning a value from the called function to, its caller.,  The general form of the return statement is, return expression;,  The calling function is free to ignore the returned value. Further more, there need not be, expression after the return.,  The return statement has two important uses, 1. It causes an immediate exit of the control from the function.That is ,it causes, program execution to return to the calling function., VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 29

Page 30 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , 2. It returns the value present in the expression., example: return(x+y);, return (6*8);, return (3);, return;, EXAMPLE PROGRAM-1, /* Program to calculate sum of two numbers */, #include<stdio.h>, int main(), {, int sum();, int result;, result = sum();, printf("Sum = %d",result);, return 0;, }, int sum(void), {, , int a,b,c;, printf("Enter two numbers :");, scanf("%d%d",&a,&b);, c=a+b;, return c;, , }, OUTPUT, Enter two numbers : 20 32, EXAMPLE PROGRAM-2, Sum = 52, VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 30

Page 31 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , /*Program to find factorial of given integer */, #include<stdio.h>, #include<conio.h>, int main(), {, int fact();, , /*Prototyping or function declaration */, , int res;, , res=fact();, , /*Function calling */, , printf("\nFactorial of given value is =%d",res);, return 0;, }, /*Function definition starts */, int fact(), { int n,i,f=1;, printf("Enter a vlue for n:");, scanf("%d",&n);, for(i=n;i>=1;i--), {, f=f*i;, }, return f;, , }, , OUTPUT, Enter a value for n:7, , Explanation: In above program calling function (main() ) is not passing any value to the called, Factorial of given value is =5040, function, VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 31

Page 32 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , ( fact () ) . But The called function is returning a value back to the calling function., Note :, , int fact();, means fact() is function which is returning an int value to the calling function., , EXAMPLE PROGRAM-3, //Program to find GCD using functions, int main(), {, int gcd(); /*Prototyping or function declaration */, int a,b,res;, res=gcd();, , /*Function calling */, , printf("\n The GCD of given two values is %d:",res);, return 0;, }, /*Function definition starts */, int gcd(), {, int x,y,r;, printf("Enter any two integer values :");, scanf("%d%d",&x,&y);, while(y!=0), {, r=x%y;, x=y;, y=r;, }, return x;, , VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 32

Page 33 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , }, , OUTPUT, , Enter any two integer values :52 91, CATEGORY 4: Functions with arguments and return value, The GCD of given two values is 13:, In this category there is data transfer between the calling function and called function., In this category, there is data transfer from the calling function to the called function. And, also there is data transfer from called function to the calling function. In other words calling, function is passing arguments to the called function and also called function is returning a value, back to the calling function., , EXAMPLE PROGRAM-1, /*Program to calculate sum of two numbers */, #include<stdio.h>, int main(), VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 33

Page 34 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , {, int sum(int,int);, , int a,b,result;, , printf("Enter two numbers :");, scanf("%d%d",&a,&b);, result = sum(a,b);, printf("Sum = %d",result);, return 0;, }, int sum(int x, int y), {, int z;, z=x+y;, return z;, }, OUTPUT, , Enter two numbers : 12 13, Sum = 25, EXAMPLE PROGRAM-2, /*Program to find factorial of given integer */, #include<stdio.h>, #include<conio.h>, int main(), VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 34

Page 35 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , {, int fact(int);, , /*Prototyping or function declaration */, , int n,res;, printf("Enter a vlue for n:");, scanf("%d",&n);, res=fact(n);, , /*Function calling */, , printf("\nFactorial of given value is =%d",res);, }, /*Function definition starts */, int fact(int x), {, int i,f=1;, , for(i=x;i>=1;i--), {, f=f*i;, }, return f; }, OUTPUT, , EXAMPLE PROGRAM-3, VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 35

Page 36 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , //Program to find GCD using functions, int main(), {, int gcd(int,int);/*Prototyping or function declaration */, int x,y,res;, , printf("Enter any two integer values :");, scanf("%d%d",&x,&y);, res=gcd(x,y);, , /*Function calling */, , printf("\n The GCD of given two values is %d:",res);, return 0;, }, /*Function definition starts */, int gcd(int a,int b), {, int r;, while(b!=0), {, r=a%b;, a=b;, b=r;, }, return a;, }, , VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 36

Page 37 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , OUTPUT, , Explanation:, function, , In above program parameters are passed from calling function( main() ) to called, , (gcd() ). And also called function returns the value of a back to calling function., INTER FUNCTION COMMUNICATION, Although calling and called functions are two different entities, they need to, communicate to exchange data. The data flow is classified into three strategies. They are, , , , , Downward Flow (Call by value ), Upward Flow, Bi-directional Flow(Call by reference), , DOWNWARD FLOW (Call by value), In downward communication, the calling function sends data to the called function. No, data flows in the opposite direction. In this strategy, copies of the data items are passed from, the calling function to the called function. The called function may change the values passed, but, the original values in the calling function remain unchanged., C language uses pass-by-value mechanism to implement this communication. A variable, is declared and defined in the called function for each value to be received from the calling, function. The calling function sends a copy of each value to the called function; no data flows, upward., When a function is called with actual parameters, the values of actual parameters are, copied into the formal parameters. If the values of the formal parameters changes in the, function, the values of the actual parameters are not changed. This way of passing parameters is, called call by value (pass by value)., VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 37

Page 38 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , In the below example, the values of the arguments to swap () 10 and 20 are copied into, the parameters x and y.Note that the values of x and y are swaped in the function. But, the, values of actual parameters remain same before swap and after swap., Example program 1, /* Program to swap two numbers using functions(Call by vaue)*/, int main(), {, , void swap(int ,int );, int a,b;, a=20;b=30;, printf("\nValues Before Function call : a = %d, b= %d",a,b);, swap(a,b);, printf("\nValues After Function call: a = %d, b = %d",a,b);, return 0;, , }, void swap(int x, int y), {, int temp;, printf("\nValues in function before operation: x = %d, y = %d",x,y);, temp = x;, x = y;, y = temp;, printf("\nValues in function after operation: x = %d, y = %d ",x,y);, }, OUTPUT, Values Before Function call : a = 20, b= 30, Values in function before operation: x = 20, y = 30, Values in function after operation: x = 30, y = 20, Values After Function call: a = 20, b = 30, , VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 38

Page 39 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , Note: In call by value any changes done on the formal parameter will not affect the actual, parameters., Example program 2, /* Program to demonstrate pass by value mechanism (or) downward communication */, int main(), {, void down(int,int);, int a=10,b=20;, printf("Before Function : a = %d, b = %d",a,b);, down(a,b);, printf("\nAfter Function : a = %d, b = %d",a,b);, }, void down(int x, int y), {, printf("\nIn function before operation: x = %d, y = %d",x,y);, x = x * 10;, y = y * 10;, printf("\nIn function after operation: x = %d, y = %d ",x,y);, }, OUTPUT:, Before Function : a= 10, b = 20, In function before operation : x = 10, y = 20, In function after operation : x = 100, y = 200, After Function : a = 10 , b = 20, , VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 39

Page 40 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , RULES,  Use values in the function call to pass data.,  Use appropriate data types in the function parameter list to receive the data values.,  Use the parameter identifiers in the called function to access the local copies of the data., UPWARD FLOW, Upward communication occurs when the called function sends data back to the called, function with our receiving any data from it. A good example is when the called function reads, data from keyboard that needs to be passed back to the called function., C provides only one upward direction flow, i.e. return statement. While it works well,, only one data item can be returned. The only way that a called function can pass multiple data, items up to the calling function is to access variables in the calling function and deposit there., This is done by calling function by passing address of variable to the called function., Given the variables address, the called function can then put the data in the calling, function. The calling function needs to declare a data variable to receive the data. The called, function needs to declare a variable to store the address that it receives from the calling, function., In C, a variable can store data of different type. But here the called function needs a, special variable which stores the address of variable. It is called as pointer variable. To pass, address of a variable, we use address operator(&). To receive the address of variable we use, asterisk(*) after the type. Asterick(*) is known as indirection operator. The mechanism used for, this communication is pass-by-reference mechanism., /* Program to demonstrate the usage of upward communication*/, int main(), {, void upward(int*,int*);, int a,b;, upward(&a,&b);, printf("\nAfter Function : a = %d, b = %d",a,b);, }, void upward(int *x, int *y), {, *x = 28;, VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 40

Page 41 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , *y = 38;, printf("\nIn function after operation: *x = %d, *y = %d ",*x,*y);, }, OUTPUT:, , In function after operation : *x = 28, *y = 38, After Function : a = 28 , b = 38, RULES, , , , , Use &variableName in the function call to pass a reference to the variable., Use type* in the function parameter list to receive the variables address., Use *parameterName in the function to reference the original variable., , BI-DIRECTIONAL FLOW(call by reference), Bi-directional communication occurs when the calling function sends data down to the, called function. During or at the end of its processing, the called function then sends data up to, the calling function. For example, the calling function may send data to the called function,, which it manipulates and sends up the calling function., The strategy used for upward direction can be augmented to allow the communications, in both directions. The only difference is that the indirect reference must be used in both sides, of the assignment statement. The variable in the called function first is accessed for retrieving, using address variable in the right hand side. The same parameter is accessed again to sore a, vale in the left-hand side. The mechanism used for this communication is pass-by-reference., Instead of passing the values of the variables to the called function, we pass their, addresses, so that the called function can change the values stored in the calling routine. This is, known as "call by reference", since we are referencing the variables., Here the addresses of actual arguments in the calling function are copied into formal, arguments of the called function. Here The formal parameters should be declared as pointer, variables to store the address., The following shows the swap() function modified from a "call by value" to a "call by, reference". Note that the values are now swapped when the control is returned to main, function., Example program 1, /* Program to swap two numbers using functions(call by reference)*/, int main(), VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 41

Page 42 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , {, void swap(int * ,int *);, int a,b;, a=20;b=30;, printf("\nThe values Before Function call: a = %d, b= %d",a,b);, swap(&a,&b);, printf("\nThe values After Function call : a = %d, b = %d",a,b);, return 0;, }, void swap(int *x, int *y), {, int temp;, printf("\nThe values in function before operation: *x = %d, *y = %d",*x,*y);, temp = *x;, *x = *y;, *y = temp;, printf("\nThe vakues in function after operation: *x = %d, *y = %d ",*x,*y);, }, OUTPUT:, , The values Before Function call: a = 20, b= 30, The values in function before operation: *x = 20, *y = 30, The vakues in function after operation: *x = 30, *y = 20, The values After Function call : a = 30, b = 20, , VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 42

Page 43 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , Example program 2, /* Program to demonstrate the usage of birectional communication(call by reference)*/, int main(), {, void bidirection(int*,int*);, int a=10,b=20;, , printf("Before Function : a = %d, b = %d",a,b);, bidirection (&a,&b);, printf("\nAfter Function : a = %d, b = %d",a,b);, }, void bidirection (int *x, int *y), {, printf("\nIn function before operation: *x = %d, *y = %d",*x,*y);, *x = *x * 5;, *y = *y * 5;, printf("\nIn function after operation: *x = %d, *y = %d ",*x,*y);, }, OUTPUT:, , Before Function : a= 10, b = 20, In function before operation : *x = 50, *y = 100, In function after operation : *x = 50, *y = 100, After Function : a = 50 , b = 100, , VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 43

Page 44 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , Observe the following points when the program is executed,,  The address of actual parameters a and b are copied into formal parameters x and y.,  In the function header of swap (), the variables x and y are declared as pointer variables.,  The values of a and b accessed and changed using pointer variables x and y., DIFFERENCE BETWEEN CALL BY VALUE AND CALL BY REFERENCE, CALL BY VALUE, , CALL BY REFERENCE, , In call by value, a copy of actual arguments is, In call by reference, the location (address), passed to formal arguments of the called function. of actual arguments is passed to, formal arguments of the called function., Any change made to the formal arguments in, the called function has no effect on the values, of actual arguments in the calling function., , By accessing the addresses of actual, arguments we can alter them within, from the called function., , In call by reference, alteration to actual, In call by value, actual arguments will remain safe,, arguments is possible within from called, they cannot be modified accidentally., function; therefore the code must handle, arguments carefully else you get unexpected, results., , NESTING OF FUNCTIONS, C permits nesting of functions, main can call function1, which calls function2, which calls, function3 .., There is no limit as how deeply functions can be nested ., Example:, #include<stdio.h>, void main (), {, int read ();, int sum (int, in t);, int a, b;, printf (“%d”, sum ());, }, VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 44

Page 45 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , int sum (int x, int y), {, x=read ();, y=read ();, return x+y;, }, int read (), {, int p;, printf (“\n Enter any value: “);, scanf (“%d”, &p);, return p;, }, In the above example ,when the main() function executes it finds the function call, sum(), then the control is transferred from main() to the function sum(),here we are calling the, function read(), then the control transferred to read() function, then the body of the function, read() executes, the control transferred from read to sum() and once again the same is done for, reading some other value. Then the addition is performed this value is carried from sum() to, main().Observe the chain of control transfers between the nested functions., , Standard Library Functions, C provides a rich collection of standard functions whose definition have been written and, are ready to be used in our programs. To include functions, we must include their function, declarations. The function declarations for these functions are grouped together and collected in, several header files. Instead of adding individual function declarations of each function, we, simply include the headers at the top of our file., Math Functions, Many important library functions are available for mathematical calculations. Most of the, function declarations for these functions are in either math header file (math.h) or standard, library (stdlib.h). In general, the integer functions are found in stdlib.h., , VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 45

Page 46 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , 1) Absolute Value functions, An absolute value is the positive rendering of the value regardless of its sign. There are, three integer functions and three real functions. The integer functions are abs, labs, llabs. The, real functions are fabs, fabsf, fabsl. Examples are, abs(6) returns 6, fabs(-3.4) returns 3.4, Function Prototype, , Library, , int abs(int number);, , stdlib.h, , long labs (long number);, , stdlib.h, , long long llabs(long long number);, , stdlib.h, , double fabs(double number);, , math.h, , float fabsf(float number);, , math.h, , long double fabsl(long double number);, , math.h, , 2) Ceiling Function, A ceiling is the smallest integral value greater than or equal to a number. Although the, ceiling functions determine an integral value, the return type is defined as a real value that, corresponds to the argument., Examples, ceil(-1.9), , returns 1.0, , ceil(1.1), , returns 2.0, , Function Prototype, , Library, , float ceilf(float number);, , math.h, , double ceil(double number);, , math.h, , long double ceill(long double number);, , math.h, , VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 46

Page 47 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , 3) Floor Functions, A floor is the largest integral value that is equal to or less than a number., Examples, floor(-1.1), , returns -2.0, , floor(1.9), , returns 1.0, , Function Prototype, , Library, , float floorf(float number);, , math.h, , double floor(double number);, , math.h, , long double floorl(long double number);, , math.h, , 4) Truncate Functions, The truncate functions returns the integral in the direction of 0. They are the same as, floor function for positive numbers and the same as ceiling function for negative numbers., Examples, trunc (-1.1)returns -1.0, trunc (1.9), , returns 1.0, , Function Prototype, , Library, , float truncf(float number);, , math.h, , double trunc(double number);, , math.h, , long double truncl(long double number);, , math.h, , 5) Round Functions, The round functions return the nearest integral value., Examples, round (-1.1)returns -1.0, round (1.9), , returns 2.0, , round(-1.5), , returns -2.0, , VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 47

Page 48 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , Function Prototype, , Library, , float roundf(float number);, , math.h, , double round(double number);, , math.h, , long double roundl(long double number);, , math.h, , long int lround(double number);, , stdlib.h, , long int lroundf(float number);, , stdlib.h, , long int lroundl(long double number);, , stdlib.h, , long long int llround(double number);, , stdlib.h, , long long int llroundf( float number);, , stdlib.h, , long long int llroundl(long double number);, , stdlib.h, , 6) Power Function, The power function returns the value of the x raised to the power y i.e. x y. An error, occurs if he base is negative and the exponent is not an integer, or if the base is zero and the, exponent in not positive., Examples, pow(3.0, 4.0), , returns 81.0, , pow(3.4, 2.3) returns 16.68893, , Function Prototype, , Library, , float powf(float n1, float n2);, , math.h, , double pow(double n1, double n2);, , math.h, , long double powl(long double n1, long double n2);, , math.h, , VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 48

Page 49 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , 7) Square Root Function, The square root functions return the non-negative square root of a number. An error, occurs if the number is negative., Examples, sqrt(25), , returns 5.0, , Function Prototype, , Library, , float sqrtf(float number);, , math.h, , double sqrt(double number);, , math.h, , long double sqrtl(long double number);, , math.h, , Random Numbers, A random number is a number selected from a set in which all members have the same, probability of being selected. Random numbers are useful in many areas of Computer Science., Two examples are application testing and gaming., C provides tow functions to build random number series. They are seed random (srand), and random (rand) functions. These functions are found in stdlib.h, 1)Seed Random Number Function, The seed random function creates the starting seed for a number series. The function, declaration is, void srand(unsigned int seed);, Examples, 1) srand(997), Generates the same number series in each run, we can either omit srand or we, can provide a constant seed random, preferably a prime number such as 997., 2) srand(time(NULL)), Generates the different series in each run, we use the time of day as seed. C call, of the time which requires the time.h library., 2) Random Number Function, The random number function returns a pseudorandom integer between 0 and, RAND_MAX, which is defined in the standard library as the largest number that rand can, VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 49

Page 50 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , generate. Each call generates the next number in a random number series. The function, declaration is, int rand(void);, Example, , rand();, , /* Program to generate random numbers in range 10-20 */, #include<stdio.h>, #include<stdlib.h>, #include<time.h>, int main(), {, int range;, srand(time(NULL));, range = (20 – 10) + 1;, printf(“Random Numbers :%d\t”, rand() % range + 10);, printf(“%d\t”, rand() % range + 10);, printf(“%d”, rand() % range + 10);, }, Output, Random Numbers : 10 11 16, , VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 50

Page 51 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , STORAGE CLASSES, The characteristics of objects(variables or functions) are given below., 1), Scope., 2), Lifetime (Extent)., 3), Default initial value., 4), Storage area of variable., The storage class specifies the characteristics of an object which are shown above., Scope, Scope determines the region of the program in which a defined object is visible – that is,, the part of the program in which we can use the objects name. Scope pertains to any object that, can be declared, such as variable or a function declaration. Scope is a source program concept. It, has no direct bearing on run-time program., Statements enclosed in the set of braces are called a block. A function body is enclosed in, set of braces, thus a body is also a block. An object’s scope extends from its declaration until the, end of its block. A variable is in scope if it is visible to the statement being examined. Variables, are in scope from their point of declaration until the end of block., Scope defines the visibility of an object; it defines where an object can be referenced. In, C, an object can have four levels of scope. They are block, file, function and function-prototype., When scope of object is block, it is visible only in the block in which it is defined. When, scope of object is file, it is visible through the entire source file. When the scope of object is, function, it is visible in that function body in which it is declared., Global Scope, The scope of object defined in the global area of program is termed as global scope i.e., the object’s scope is up to end of the program. Global scope variables are visible every where in, the program., Local Scope, Variables defined within a block have local scope. They exist only from the point of their, declaration until the end of the block (usually a function) in which they are declared. Outside the, block they are invisible., Extent(Lifetime), The extent of an object defines the duration for which the computer allocates memory, for it. The extent of an object is also known as storage function. In C, an object can be automatic,, static extent or dynamic extent., , VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 51

Page 52 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , An object with an automatic scope is created each time its declaration is encountered, and is destroyed each time its block is exited., An object with a static extent is created when the program is loaded fro execution and, destroyed when execution stops., An object with dynamic extent is created by the program through the malloc and its, related library functions., Linkage, A large application broken into modules, with each module potentially written by, programmer in separate source file with its own objects. Different modules ma be related when, the program is link edited. In C, linkage can be of two types: internal and external., An object with an internal linkage is declared and visible in one module. Other modules, refer to this object. An object with an external linkage is declared in one module but is visible in, all other modules that declare it with a special keyword extern., There are four storage classes., 1., 2., 3., 4., , Automatic storage class., Static storage class., External storage class., Register storage., , AUTOMATIC STORAGE CLASS, Automatic variables are declared inside a function(or block) in which they are to be, utilized. They are created when the function (block) is called and destroyed automatically when, the function is exited., Syntax : auto data_type variable_name;, Example :, , auto int a;, , A variable with an auto specification has the following storage characteristic:, , , The default and the most commonly used storage class is auto., , , , Memory for automatic variables is allocated when a block or function is entered. They are, defined and are “local” to the block., , , , When the block is exited, the system releases the memory that was allocated to the auto, variables, and their values are lost., Auto variables are available to use (scope) within the block(function) only., It is not possible to use outside of the block., These variables pertains their values till end of the block only(lifetime)., , , , , , These are also referred with local variables, , VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 52

Page 53 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , Declaration:, auto type variable name;, By default all variables are created as automatic variables. These variables are declared and, defined inside the function body or block., Initialization, An auto variable can be initialized where it is defined or left uninitialized. When auto, variables are not initialized its value is garbage value., Note : The keyword auto is not mandatory because the default storage class in C is auto., /*Program to illustrate use of automatic storage class*/, *automatic storage class */, #include<stdio.h>, int main(), {, void test();, test();, test();, test();, return 0;, }, void test(), {, auto int x;, x++;, printf("\n%d",x);, }, Output, 1, 2, 3, VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 53

Page 54 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , In above program auto variable is used . Variable is created when the control entered in, to the function, And is vanished while exiting the function. The variable can be used any where, in the block after declarations., , Scope, , Within the block or function body.(local scope), , Life time, , Within the block, Till end of the block from declaration, , Default Initial value, , Garbage value(We can‟t predict), , Storage, , Primary memory, , Where to be declared, , Inside the block or function, , Keyword, , Auto, , STATIC STORAGE CLASS:, When a variable is declared as static, it is stored in memory. The default intitial value of the, variable will be zero. A static variable can be initialized only once, it cannot be reinitialized. To, define a variable as static storage class, the keyword static is used., Static variable is available (scope) for use in the function body only., The value of static variable persists (life time) until the end of the program., Example 2:, /*Program to illustrate use of static storage class*/, int main(), {, void show();, show();, show();, show();, return 0;, }, , VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 54

Page 55 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , void show(), {, static int i;, i++;, printf("\n%d",i);, }, Output, 1, 2, 3, A static variable may be either internal type or external type., Static internal:, The scope of static internal variables extends up to end of the function where in which, they are defined. These variables remain in existence (alive) throughout the remainder of the, program. Therefore internal static variables can be used to retain values between function, calls. A static variable is initialized only once , when the program is compiled. It is never, initialized again., Scope, , Within the function body., , Life time, , Till end of the program, , Default Initial value, , Zero, , Storage, , Primary memory, , Where to be declared, , Inside the function, , Keyword, , Static, , Static external:, Static external variable is declared outside of all functions and is available (scope) to all the, functions in that program., These variables also remain in existence (alive) throughout the program., , VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 55

Page 56 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , Example program 2:, /*Program to illustrate use of external static storage class*/, static int i;, int main(), {, void show();, show();, show();, show();, i++;, printf("\n%d",i);, return 0;, }, , void show(), {, static int i;, i++;, printf("\n%d",i);, }, output, 1, 2, 3, 1, VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 56

Page 57 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , Scope, , All functions which are after declaration of variable., , Life time, , Till end of the program(Global), , Default Initial value, , Zero, , Storage, , Primary memory, , Where to be declared, , Outside the functions, , Keyword, , Static, , REGISTER STORAGE CLASS, A variable with a register specification has the following characteristics, Scope = Block, Life time, , = until end of block/function, , By defining a variable as register storage class, it is stored in the CPU register. The time, required to access a CPU register is significantly less than the time required to access a memory, location. The default value of the variable will be garbage value. To define a variable as register, storage class, the keyword auto is used., Syntax : register data_type variable_name;, Example :, , register int a;, , By defining a variable as register storage class, it is stored in the CPU register. The time, required to access a CPU register is significantly less than the time required to access a memory, location. The default value of the variable will be garbage value. To define a variable as register, storage class, the keyword auto is used., /* Program to illustrate the usage of register variable */, int main(), {, register int i;, for(i=1; i<=5; i++), printf("%3d",i);, }, Output, 12345, VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 57

Page 58 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , Scope, , Within the block or function body., , Life time, , Within the block, Till end of the block from declaration, , Default Initial value, , Garbage value(We can‟t predict), , Storage, , CPU registers, , Where to be declared, , Inside the block or function, , Keyword, , Register, , EXTERNAL STORAGE CLASS, Variables that are both alive and active throughout the entire program are known as, external variables. They are also known as global variables. Global variables can be accessed by, any function in the program. External variables are declared outside of all functions., A variable with a extern specification has the following characteristics, Scope = File, Life time = global, When a variable is declared as extern, it is stored in the memory. The default value is initialized, to zero. An extern variable is also called as global variable. To define a variable as extern, storage class, the keyword extern is used., Syntax : extern data_type variable_name;, EXAMPLE : extern int a;, Scope, , File, , Life time, , Global, , Default Initial value, , Zero, , Storage, , Primary memory, , Where to be declared, , Outside of all functions, , Keyword, , Extern, , VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 58

Page 59 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , /*Program to show the working of external variable */, extern int v=10;, void divert();, int main(), {, , printf("In main() : %d",v);, divert();, return 0;, }, void divert(), {, v=v+3;, printf("In divert() : %d",v);, }, Output :, In main() : 10, In divert() :13, TYPE QUALIFIERS, C provides three type qualifiers const, volatile and restrict. Const, volatile can be applied, to any variables, but restrict qualifiers may only applied to pointer., CONST VARIABLE, A variable value can be made unchanged during program execution by declaring the, variable as constant. The keyword const is placed before the declaration. For a const pointer,, place the keyword between * and identifier., a). constant variable, Ex :, , const int a;, , VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 59

Page 60 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , Here a is a constant and its value cannot be changed., int * const x;, In the above example, the pointer to x is constant. The value that x points can be changed, but, the value of x cannot be changed., b).Constant pointer, The constant pointer has address which is constant throughout program., The value stored at the address can be altered., //constant pointer, #include<stdio.h>, int main(), {, int x = 50,y = 100;, int *const p = &x; // p is constant pointer to x, printf("Initial value of x = %d",*p);, //, , p = &y; it is not allowed, , *p = 500;, printf("\nValue of x = %d",x);, return 0;, }, Output :, Initial value of x = 50, Value of x = 500, c) Pointer to constant, Pointer to constant allows us change the address stored in the pointer variable. But it is not, allowed to change the value stored at the address., //pointer to constant, #include<stdio.h>, VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 60

Page 61 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , int main(), {, int x = 50,y = 100;, int const *p = &x; // cannot change the value of x through p, printf("%d",*p);, //*p = 200; not allowed, p = &y;, printf("\n%d",*p);, //p* = 500; not allowed, return 0;, }, Output :, 50, 100, d) Constant pointer to constant, Constant pointer to constant contains both address and values as constants., //const pointer to a constant, #include<stdio.h>, int main(), {, int x = 50,y = 100;, const int *const p = &x;, printf("%d",*p);, // p = &y; not allowed, //, , *p = 300; not allowed, return 0;, , VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 61

Page 62 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , }, Output :, 50, VOLATILE VARIABLE, Variables that can be changed at any time by external programs or the same program are, called volatile variables. The keyword volatile is placed before declaration. To make a variable, value changeable by the current program and unchangeable by other programs, declare the, variable, declare it as volatile and constant., Ex :, , volatile int x;, int * volatile z;, , The variable x and pointer variable z can be changed by any program at any time., volatile const int y;, The variable y can be changed by current program but not by external program., RESTRICT VARIABLE, The restrict type qualifier may only be applied to a pointer. A pointer declaration that, uses this type qualifier establishes a special association between the pointer and the object it, accesses, making the pointer and expressions based on that pointer, the only ways to directly or, indirectly access the value of that object. The restrict type qualifier is an indication to the, compiler that, if the memory addressed by the restrict qualified pointer is modified, no other, pointer will access that same memory., Ex :, , int * restrict z;, , RECURSION, Definition: A function which is called by itself and returns to the caller at a particular condition is, called a recursive function., Recursion is a process of calling a function by itself and returns at a specific condition is called a, recursion, Two approaches are used to write repetitive algorithms. One approach uses loops, the other, uses recursion. Recursion is a repetitive process in which a function calls itself., A repetitive function is defined recursively whenever the function appears within the, definition itself. All recursive functions have two elements: each call either solves one part of, the problem or it reduces the size of the problem. The statement that solves the problem is, VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 62

Page 63 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , known as base case. Every recursive function must have a base case. The rest of function is, known as the general case., Rules for designing a Recursive Function,  First, determine the base case.,  Then, determine the general case.,  Finally combine the base case and general case into a function, Limitations of Recursive Functions, , , , Recursion solutions involve extensive overhead because they use function calls., Each time we make a call, it uses some of memory allocation. If the recursion is deep,, that is, if the program has a large number of recursive calls, then we may run out of, memory., Examples, 1. Factorial of a number, The factorial function can be defined recursively., Factorial (n) =, , 1, , if n=0, , n * factorial (n-1), , if n>0, , 1./*Program to find factorial of a number using recursion function */, int fact(int);, int main(), {, int num,res;, printf("Enter a number :");, scanf("%d",&num);, res = fact(num);, printf("Factorial = %d",res);, }, int fact(int n), {, int f=1;, if(n==0), VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 63

Page 64 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , return 1;, else, {, f = n * fact(n-1);, return f;, }, }, Output:, Enter a number : 5, Factorial = 120, In this example, the base case is return 1 statement. The general case is return f i.e. n* fact(n-1), statement. In this problem, once the base case has been reached, the solution begins. The, program has found one part of the answer and can return that part to the next more general, statement. As, the program solves each general case, the program can solve the next higher, general statements until it finally solves the most general case, the original problem., 2. Fibonacci Series, The Fibonacci series for few numbers is as follows, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, The function of Fibonacci series is, Given : Fibonacci0 = 0, Fibonacci1 = 1, Then : Fibonacci n = Fibonacci n-1 + Fibonacci n-2, /*Program to print Fibonacci series using recursion function */, int fib(int);, int main(), {, int n,i;, printf("Enter a number :");, scanf("%d",&n);, for(i=0; i<=n; i++), printf(“%d”, fib(i));, }, VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 64

Page 65 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , int fib(int num), {, if(num==0 || num==1), return num;, else, return (fib(num-1)+ fib(num-2));, }, Output:, Enter a number : 8, Fibonacci Series : 0 1 1 2 3 5 8 13 21, 3. Towers of Hanoi, According to legend, the monks in a remote monastery knew how to predict when the, world would end. They had a set of three diamond needles. Stacked on the first diamond needle, were 64 gold disks of decreasing size. The monks moved one disk to another needle each hour,, subject to the following rules, a) Only one disk could be moved at a time, b) A larger disk must never b stacked above a smaller one., c) One and only one auxiliary needle could be used for the intermediate storage of disks., Generalized solution for problem is, 1) Move n-1 disks from source to auxiliary needle., (General Case), 2) Move one disk from source to destination needle. (Base Case), 3) Move n-1 disks from auxiliary to destination needle., (General Case), Our solution requires four parameters : the number of disks to be moved, the source needle, the, destination needle, and the auxiliary needle. Using the above pseudo code, three moves are, 1) Call Towers(n-1, source, auxiliary, destination), 2) Move one disk from source to destination, 3) Call Towers(n-1, auxiliary, destination, source), /* Program to implement Towers of Hanoi using Recursion function*/, void towers(int, char, char, char);, int main(), {, int num;, VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 65

Page 66 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , printf(“Enter number of disks :”);, scanf(“%d”,&num);, towers(num, ‘A’,’C’,’B’);, }, void towers(int n, char src, char dest, char aux), {, if(n==1), printf(“Move from %c to %c\n”,src,dest);, else, {, towers(n-1, src, aux, dest);, printf(“Move from %c to %c\n”,src,dest);, towers(n-1, aux, dest, src);, }, }, Output, Enter number of disks : 3, Move from A to C, Move from A to B, Move from C to B, Move from A to C, Move from B to A, Move from B to C, Move from A to C, , VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 66

Page 67 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , 3. Greatest Common Divisor(GCD) using recursion, (a). int main(), {, int gcd(int,int); int s,a,b;, printf("Enter any two integer values:");, scanf("%d%d",&a,&b);, s=gcd(a,b);, printf("\n The GCD is %d:",s); return 0;, }, int gcd(int x,int y), {, int g,r;, if(y==0), return x;, r=x%y;, g=gcd(y,r);, return g;, }, Greatest Common Divisor(GCD) using recursion, (b)//GCD USING RECURSION, #include<stdio.h>, #include<conio.h>, int main(), {, int a,b,g;, VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 67

Page 68 : PROGRAMMING FOR PROBLEM SOLVING, , UNIT -II, , printf("Enter two values:");, scanf("%d%d",&a,&b);, g=gcd(a,b);, printf("The GCD=%d",g);, return 0;, }, int gcd(int x,int y), {, int r;, if(x==y), return x;, if(x>y), {, r=gcd(x-y,y);, }, else, {, r=gcd(x,y-x);, }, return r;, }, OUTPUT, Enter any two integer values:45 99, The GCD is 9:, , VIGNANA BHARATHI INSTITUTE OF TECHNOLOGY, , Page 68