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   Introduction
   Function Definition
   Void function
   Global Vs Local variables
   Random Number Generator
   Recursion
   Function Overloading
   Sample Code
   Experience has shown that the best way to develop and maintain large
    programs is to construct it from smaller pieces(Modules)
   This technique Called “Divide and Conquer”
    Bad Development Approach                              Wise Development Approach

                                                                main()
    main()                         •Easer To                    {
    {                                                             -----
       -----                       Design                         ----
       -----                       Build                       }
       -----                       Debug
       -----                       Extend                      function f1()
       .                           Modify                      {
       .                           Understand                     ---
       .                           Reuse                          ---
       ----                        Better Organization         }
       -----
       -----                                                    function f2()
    Return 0;                                                   {
    }                                                              ---
                                                                   ---
                                                                }
   In FORTRAN Modules Known as Subprograms
   In Pascal Modules known as Procedures &
    Functions
   In C++ Modules Known as Functions & Classes
   Programs use new and “prepackaged” modules
      New: programmer-defined functions and classes
      Prepackaged: from the standard library
      Functions invoked by a function–call-statement which consist of it’s
         name and information it needs (arguments)
        Boss To Worker Analogy
           A Boss (the calling/caller function) asks a worker (the called
         function) to perform a task and return result when it is done.

                                      Boss
                                     Main

                                                                          Worker
Worker               Worker
                                                                   Function Z
Function A           Function B

          Worker          Worker
                                             Note: usual main( ) Calls other
            Function B1       Function B2    functions, but other functions
                                                   can call each other
• Functions   called by writing
        functionName (argument);
        or
        functionName(argument1, argument2, …);
• Example
         cout << sqrt( 900.0 );
    • sqrt (square root) function
    • The preceding statement would print 30
    • All functions in math library return a double
   Function Arguments can be:
-   Constant         sqrt(9);
-   Variable         sqrt(x);
-   Expression sqrt( x*9 + y) ;
                     sqrt( sqrt(x) ) ;
• Calling/invoking a function
   – sqrt(x);
   – Parentheses an operator used to call function
       • Pass argument x
       • Function gets its own copy of arguments
   – After finished, passes back result

        Function Name           argument          Output
                                              3
       cout<< sqrt(9);


        Parentheses used to enclose argument(s)
Math Library Functions Revisited
Method              Description                      Example
ceil( x )           rounds x to the smallest integer ceil( 9.2 ) is 10.0
                    not less than x                  ceil( -9.8 ) is -9.0
cos( x )            trigonometric cosine of x        cos( 0.0 ) is 1.0
                    (x in radians)
exp( x )            exponential function ex          exp( 1.0 ) is 2.71828
                                                     exp( 2.0 ) is 7.38906
fabs( x )           absolute value of x              fabs( 5.1 ) is 5.1
                                                     fabs( 0.0 ) is 0.0
                                                     fabs( -8.76 ) is 8.76
floor( x )          rounds x to the largest integer floor( 9.2 ) is 9.0
                    not greater than x               floor( -9.8 ) is -10.0
fmod( x, y )        remainder of x/y as a floating- fmod( 13.657, 2.333 ) is 1.992
                    point number
log( x )            natural logarithm of x (base e) log( 2.718282 ) is 1.0
                                                     log( 7.389056 ) is 2.0
log10( x )          logarithm of x (base 10)         log10( 10.0 ) is 1.0
                                                     log10( 100.0 ) is 2.0
pow( x, y )         x raised to power y (xy)         pow( 2, 7 ) is 128
                                                     pow( 9, .5 ) is 3
sin( x )            trigonometric sine of x          sin( 0.0 ) is 0
                    (x in radians)
sqrt( x )           square root of x                 sqrt( 900.0 ) is 30.0
                                                     sqrt( 9.0 ) is 3.0
tan( x )            trigonometric tangent of x       tan( 0.0 ) is 0
                    (x in radians)
Fig. 3.2 Math library functions.
   Functions
       Modularize a program
       Software reusability
          Call function multiple times

   Local variables
       Known only in the function in which they are defined
       All variables declared in function definitions are local variables
   Parameters
       Local variables passed to function when called
       Provide outside information
   Function prototype
       Tells compiler argument type and return type of function
       int square( int );
            Function takes an int and returns an int
       Explained in more detail later

   Calling/invoking a function
      square(x);
      Parentheses an operator used to call function
            Pass argument x
            Function gets its own copy of arguments
       After finished, passes back result
   Syntax format for function definition
    returned-value-type function-name (parameter-list)
    {
         Declarations of local variables and Statements
    }

        Parameter list
             Comma separated list of arguments
                 Data type needed for each argument
             If no arguments, use void or leave blank
        Return-value-type
             Data type of result returned (use void if nothing
              returned)
   Example function
    int square( int y )
    {

        return y * y;
    }
   return keyword
      Returns data, and control goes to function’s
       caller
            If no data to return, use return;
       Function ends when reaches right brace
            Control goes to caller
   Functions cannot be defined inside other functions
// Creating and using a programmer-defined function.
        #include <iostream.h>
                                                          Function prototype: specifies
        int square( int );        // function prototype   data types of arguments and
                                                          return values. square
     int main()
                                                          expects an int, and returns
     {
                                                          an int.
        // loop 10 times and calculate and output
        // square of x each time
        for ( int x = 1; x <= 10; x++ )
           cout << square( x ) << " "; // function call

                                                          Parentheses () cause function to be called.
          cout << endl;
                                                          When done, it returns the result.
          return 0;    // indicates successful termination

     } // end main


     // square function definition returns square of an integer
     int square( int y ) // y is a copy of argument to function
     {
        return y * y;     // returns square of y as an int
                                                             Definition         of square. y is a
                                                                     copy of the argument passed.
     } // end function square                                        Returns y * y, or y squared.



1   4    9   16   25   36   49   64   81   100
#include<iostream.h>

int square(int); // prototype                        Output
int cube(int);   // prototype                        1 square=1
main()                                               1 cube=1
{ int i;                                             2 square=4
   for (int i=1;i<=10;i++){                          2 cube=8
                                                     .
                                                     .
        cout<< i<< “square=“ << square(i) << endl;
                                                     .
        cout<< i<< “cube=“   <<cube(i) << endl;      .
   } // end for                                      10 square=100
   return 0;                                         10 cube=1000
} // end main function
int square(int y) //function definition
{
   return y*y; // returned Result
}

int cube(int y) //function definition
{
   return y*y*y; // returned Result
}
// Finding the maximum of three floating-point (real) numbers.
    #include <iostream.h>
    double maximum( double, double, double ); // function prototype
    int main()
    {
       double number1, number2;
       double number3;                                    Function maximum takes 3
                                                        arguments (all double) and
      cout << "Enter three real numbers: ";             returns a double.
      cin >> number1 >> number2 >> number3;

      // number1, number2 and number3 are arguments to the maximum function call
      cout << "Maximum is: "
           << maximum( number1, number2, number3 ) << endl;
      return 0; // indicates successful termination

   } // end main

   // function maximum definition. x, y and z are parameters
   double maximum( double x, double y, double z )
   {
      double max = x;   // assume x is largest     Enter three   real numbers: 99.32 37.3 27.1928
      if ( y > max )    // if y is larger,         Maximum is:   99.32
         max = y;       // assign y to max
                                                   Enter three   real numbers: 1.1 3.333 2.22
      if ( z > max )    // if z is larger,
                                                   Maximum is:   3.333
         max = z;       // assign z to max
      return max;       // max is largest value

   } // end function maximum
   Function prototype contains
      Function name
      Parameters (number and data type)
      Return type (void if returns nothing)
      Only needed if function definition after
       function call
   Prototype must match function definition
      Function prototype
         double maximum( double, double, double );
       Definition
         double maximum( double x, double y, double
            z )
         {
           …
         }
If the Function does not RETURN result, it is called void Function

       #include<iostream.h>
       void add2Nums(int,int);
       main()
       {       int a, b;
               cout<<“enter tow Number:”;
               cin >>a >> b;
               add2Nums(a, b)
               return 0;
       }
       void add2Nums(int x, int y)
       {
               cout<< x<< “+” << y << “=“ << x+y;
       }
If the function Does Not Take Arguments specify this with EMPT Y-LIST OR
    write void inside
     #include<iostream.h>
    void funA();
    void funB(void)
    main()
    {                                    Will be the same
          funA();                            in all cases
          funB();
          return 0;
    }
     void funA()
     {
          cout << “Function-A takes no arqumentsn”;
    }
    void funB()
    {
          cout << “Also Function-B takes No argumentsn”;
    }
   Local variables
      Known only in the function in which they are
       defined
      All variables declared inside a function are local
       variables
   Parameters
      Local variables passed to function when called (passing-
       parameters)
   Variables defined outside and before function main:
        Called global variables
       Can be accessible and used anywhere in the entire
        program
   Omitting the type of returned result defaults to int, but
    omitting a non-integer type is a Syntax Error
   If a Global variable defined again as a local variable in a
    function, then the Local-definition overrides the Global
    defining
   Function prototype, function definition, and function call
    must be consistent in:
        1- Number of arguments
        2- Type of those arguments
        3-Order of those arguments
#include<iostream.h>
int x,y; //Global Variables
int add2(int, int); //prototype
main()
{ int s;
  x = 11;
  y = 22;
  cout << “global x=” << x << endl;
  cout << “Global y=” << y << endl;
  s = add2(x, y);
  cout << x << “+” << y << “=“ << s;
  cout<<endl;
  cout<<“n---end of output---n”;
  return 0;
}                                      global x=11
int add2(int x1,int y1)
{ int x; //local variables             global y=22
  x=44;                                Local x=44
  cout << “nLocal x=” << x << endl;   11+22=33
  return x1+y1;
}
                                       ---end of output---
int sum(int x, int y)
{
   int result;
   result = x+y;
}
this function must return an integer value as indicated in the header
   definition (return result;) should be added
----------------------------------------------------------------------------------------
   -
int sum (int n)
{ if (n==0)
           return 0;
   else
           n+sum(n-1);
}
the result of n+sum(n-1) is not returned; sum returns an improper
   result, the else part should be written as:-
else return n+sum(n-1);
void f(float a);
{
  float a;
  cout<<a<<endl;
}
   ; found after function definition header.
 redefining the parameter a in the function
void f(float a)
{
   float a2 = a + 8.9;
  cout <<a2<<endl;
}
void product(void)
{
   int a, b, c, result;
   cout << “enter three integers:”;
   cin >> a >> b >> c;
   result = a*b*c;
   cout << “Result is” << result;
   return result;
}
 According to the definition it should not return a value , but in the block (body) it
   did & this is WRONG.
  Remove return Result;
       Call by value
    •      A copy of the value is passed
       Call by reference
    •      The caller passes the address of the value


       Call by value
       Up to this point all the calls we have seen are call-by-value, a copy
        of the value (known) is passed from the caller-function to the called-
        function
       Any change to the copy does not affect the original value in the
        caller function
       Advantages, prevents side effect, resulting in reliable software
   Call By Reference
   We introduce reference-parameter, to perform call by reference. The caller
    gives the called function the ability to directly access the caller’s value, and to
    modify it.
   A reference parameter is an alias for it’s corresponding argument, it is stated in
    c++ by “flow the parameter’s type” in the function prototype by an
    ampersand(&) also in the function definition-header.
   Advantage: performance issue

                     void     function_name (type &);// prototype

                     main()
                     {
                               -----
                               ------
                     }
                     void function_name(type &parameter_name)
#include<iostream.h>
int squareVal(int); //prototype call by value function
void squareRef(int &); // prototype call by –reference function
int main()
{ int x=2; z=4;
   cout<< “x=“ << x << “before calling squareVal”;
   cout << “n” << squareVal(x) << “n”; // call by value
   cout<< “x=“ << x << “After returning”
   cout<< “z=“ << z << “before calling squareRef”;
   squareRef(z); // call by reference
   cout<< “z=“ << z<< “After returning squareRef”
   return 0;
}                                                  x=2 before calling squareVal
int squareVal(int a)                               4
{                                                  x=2 after returning
   return a*=a; // caller’s argument not modified z=4 before calling squareRef
}                                                  z=16 after returning squareRef
void squarRef(int &cRef)
{
   cRef *= cRef; // caller’s argument modified
}
   rand function generates an integer between 0 and RAND-
    MAX(~32767) a symbolic constant defined in <stdlib.h>
   You may use modulus operator (%) to generate numbers within a
    specifically range with rand.

//generate 10 random numbers open-range
int x;
for( int i=0; i<=10; i++){
   x=rand();
   cout<<x<<“ “;
}
             -------------------------------------------------------
//generate 10 integers between 0……..49
int x;
for( int i=0; i<10; i++){
   x=rand()%50;
   cout<<x<<“ “;
}
//generate 10 integers between 5…15
int x;
for ( int i=1; i<=10; i++){
  x= rand()%11 + 5;
  cout<<x<<“ “;
}
               ------------------------------------

//generate 100 number as simulation of rolling a
  dice
int x;
for (int i=1; i<=100; i++){
  x= rand%6 + 1;
  cout<<x<<“ “;
}
    the rand( ) function will generate the same set of random
    numbers each time you run the program .
   To force NEW set of random numbers with each new run
    use the randomizing process
   Randomizing is accomplished with the standard library
    function srand(unsigned integer); which needs a
    header file <stdlib.h>

Explanation of signed and unsigned integers:
 int is stored in at least two-bytes of memory and can
  have positive & negative values
 unsigned int also stored in at least two-bytes of
  memory but it can have only positive values 0…..65535
#include<iostream.h>
#include<iomanip.h>
#include<stdlib.h>
int main()
{
   int i;
   unsigned num;
   // we will enter a different number each time we run
   cin>>num;
   srand(num);
   for(i=1; i<=5; i++)
        cout<<setw(10)<< 1+rand()%6;
   return 0;
}

                  Output for Multiple Runs
19   6   1   1   4   2   1
18   6   1   5   1   4   4             Different-set of Random
 3   1   2   5   6   2   4               numbers
 0   1   5   5   3   5   5
 3   1   2   5   6   3   4
#include<iostream.h>
#include<iomanip.h>
#include<stdlib.h>
int main()
{
   int i;

    for(i=1; i<=5; i++)
        cout<<setw(10)<< 1+rand()%6;
    return 0;
}



                    Output for Multiple Runs
5   3   3   5   4    2
5   3   3   5   4    2                   Same set of numbers for
5   3   3   5   4    2
5   3   3   5   4    2
                                           each run
6   5   3   3   5    4
 Main calls another function…..normal
 A function calls another function2….normal
 A function calls itself ?! Possible?? YES

A recursive function is one that call itself.
   A recursive function is called to solve a problem
   The function knows to solve only the simplest cases
    or so-called base-cases
   Thus if the function called with a base-case, it simply
    returns a result. But if it is called with more complex
    problem, the function divides the problem into two
    conceptual pieces, one knows how to do, and another
    doesn't know what to do.
   The second case/piece must resemble the original
    problem, but be a slightly simpler/smaller version of
    the original problem
   Thus the function launches (calls) a fresh
    copy of itself to work on the smaller
    problem –this is related as a Recursive-
    call/recursive step.

   The function keeps dividing each new sub
    problem into two conceptual pieces until
    eventually terminates after converging on
    the base-case.
   The function thus recognize the base-case
    and returns a result to the previous copy of
    the way up the line until original call of the
    function returns the final result to main.
5!                                   Final value=120
                         5!
                                5!=5*24=120 returned
     5*4!                     5*4!
                                       4!=4*6=24 returned
       4*3!                     4*3!
                                              3!=3*2=6 returned
              3*2!                     3*2!
                                                   2!=2*1=2 returned
                 2*1!                      2*1!
                                                              1
                     1                         1
//Recursive factorial Function
#include<iostream.h>
#include<iomonip.h>
unsigned lion factorial(unsigned long);//prototype
int main()
{
   int num;
   cout<<“enter a positive integer:”;
   cin>>num;
   cout<<“factorial=“<<factorial(num);
   return 0;
}
unsigned long factorial(unsigned long n)
{
   if ( n <= 1) //the base case
        return 1;
   else
        return n * factorial (n - 1);
}
   Function overloading
       Functions with same name and different
        parameters
       Should perform similar tasks
            I.e., function to square ints and function to square floats
             int square( int x) {return x * x;}
             float square(float x) { return x * x; }
   A call-time c++ complier selects the proper function by
    examining the number, type and order of the parameters
User defined functions

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User defined functions

  • 1. Introduction  Function Definition  Void function  Global Vs Local variables  Random Number Generator  Recursion  Function Overloading  Sample Code
  • 2. Experience has shown that the best way to develop and maintain large programs is to construct it from smaller pieces(Modules)  This technique Called “Divide and Conquer” Bad Development Approach Wise Development Approach main() main() •Easer To { { ----- ----- Design ---- ----- Build } ----- Debug ----- Extend function f1() . Modify { . Understand --- . Reuse --- ---- Better Organization } ----- ----- function f2() Return 0; { } --- --- }
  • 3. In FORTRAN Modules Known as Subprograms  In Pascal Modules known as Procedures & Functions  In C++ Modules Known as Functions & Classes  Programs use new and “prepackaged” modules  New: programmer-defined functions and classes  Prepackaged: from the standard library
  • 4. Functions invoked by a function–call-statement which consist of it’s name and information it needs (arguments)  Boss To Worker Analogy  A Boss (the calling/caller function) asks a worker (the called function) to perform a task and return result when it is done. Boss Main Worker Worker Worker Function Z Function A Function B Worker Worker Note: usual main( ) Calls other Function B1 Function B2 functions, but other functions can call each other
  • 5. • Functions called by writing functionName (argument); or functionName(argument1, argument2, …); • Example cout << sqrt( 900.0 ); • sqrt (square root) function • The preceding statement would print 30 • All functions in math library return a double  Function Arguments can be: - Constant sqrt(9); - Variable sqrt(x); - Expression sqrt( x*9 + y) ; sqrt( sqrt(x) ) ;
  • 6. • Calling/invoking a function – sqrt(x); – Parentheses an operator used to call function • Pass argument x • Function gets its own copy of arguments – After finished, passes back result Function Name argument Output 3 cout<< sqrt(9); Parentheses used to enclose argument(s)
  • 7. Math Library Functions Revisited Method Description Example ceil( x ) rounds x to the smallest integer ceil( 9.2 ) is 10.0 not less than x ceil( -9.8 ) is -9.0 cos( x ) trigonometric cosine of x cos( 0.0 ) is 1.0 (x in radians) exp( x ) exponential function ex exp( 1.0 ) is 2.71828 exp( 2.0 ) is 7.38906 fabs( x ) absolute value of x fabs( 5.1 ) is 5.1 fabs( 0.0 ) is 0.0 fabs( -8.76 ) is 8.76 floor( x ) rounds x to the largest integer floor( 9.2 ) is 9.0 not greater than x floor( -9.8 ) is -10.0 fmod( x, y ) remainder of x/y as a floating- fmod( 13.657, 2.333 ) is 1.992 point number log( x ) natural logarithm of x (base e) log( 2.718282 ) is 1.0 log( 7.389056 ) is 2.0 log10( x ) logarithm of x (base 10) log10( 10.0 ) is 1.0 log10( 100.0 ) is 2.0 pow( x, y ) x raised to power y (xy) pow( 2, 7 ) is 128 pow( 9, .5 ) is 3 sin( x ) trigonometric sine of x sin( 0.0 ) is 0 (x in radians) sqrt( x ) square root of x sqrt( 900.0 ) is 30.0 sqrt( 9.0 ) is 3.0 tan( x ) trigonometric tangent of x tan( 0.0 ) is 0 (x in radians) Fig. 3.2 Math library functions.
  • 8. Functions  Modularize a program  Software reusability  Call function multiple times  Local variables  Known only in the function in which they are defined  All variables declared in function definitions are local variables  Parameters  Local variables passed to function when called  Provide outside information
  • 9. Function prototype  Tells compiler argument type and return type of function  int square( int );  Function takes an int and returns an int  Explained in more detail later  Calling/invoking a function  square(x);  Parentheses an operator used to call function  Pass argument x  Function gets its own copy of arguments  After finished, passes back result
  • 10. Syntax format for function definition returned-value-type function-name (parameter-list) { Declarations of local variables and Statements }  Parameter list  Comma separated list of arguments  Data type needed for each argument  If no arguments, use void or leave blank  Return-value-type  Data type of result returned (use void if nothing returned)
  • 11. Example function int square( int y ) { return y * y; }  return keyword  Returns data, and control goes to function’s caller  If no data to return, use return;  Function ends when reaches right brace  Control goes to caller  Functions cannot be defined inside other functions
  • 12. // Creating and using a programmer-defined function. #include <iostream.h> Function prototype: specifies int square( int ); // function prototype data types of arguments and return values. square int main() expects an int, and returns { an int. // loop 10 times and calculate and output // square of x each time for ( int x = 1; x <= 10; x++ ) cout << square( x ) << " "; // function call Parentheses () cause function to be called. cout << endl; When done, it returns the result. return 0; // indicates successful termination } // end main // square function definition returns square of an integer int square( int y ) // y is a copy of argument to function { return y * y; // returns square of y as an int Definition of square. y is a copy of the argument passed. } // end function square Returns y * y, or y squared. 1 4 9 16 25 36 49 64 81 100
  • 13. #include<iostream.h> int square(int); // prototype Output int cube(int); // prototype 1 square=1 main() 1 cube=1 { int i; 2 square=4 for (int i=1;i<=10;i++){ 2 cube=8 . . cout<< i<< “square=“ << square(i) << endl; . cout<< i<< “cube=“ <<cube(i) << endl; . } // end for 10 square=100 return 0; 10 cube=1000 } // end main function int square(int y) //function definition { return y*y; // returned Result } int cube(int y) //function definition { return y*y*y; // returned Result }
  • 14. // Finding the maximum of three floating-point (real) numbers. #include <iostream.h> double maximum( double, double, double ); // function prototype int main() { double number1, number2; double number3; Function maximum takes 3 arguments (all double) and cout << "Enter three real numbers: "; returns a double. cin >> number1 >> number2 >> number3; // number1, number2 and number3 are arguments to the maximum function call cout << "Maximum is: " << maximum( number1, number2, number3 ) << endl; return 0; // indicates successful termination } // end main // function maximum definition. x, y and z are parameters double maximum( double x, double y, double z ) { double max = x; // assume x is largest Enter three real numbers: 99.32 37.3 27.1928 if ( y > max ) // if y is larger, Maximum is: 99.32 max = y; // assign y to max Enter three real numbers: 1.1 3.333 2.22 if ( z > max ) // if z is larger, Maximum is: 3.333 max = z; // assign z to max return max; // max is largest value } // end function maximum
  • 15. Function prototype contains  Function name  Parameters (number and data type)  Return type (void if returns nothing)  Only needed if function definition after function call  Prototype must match function definition  Function prototype double maximum( double, double, double );  Definition double maximum( double x, double y, double z ) { … }
  • 16. If the Function does not RETURN result, it is called void Function #include<iostream.h> void add2Nums(int,int); main() { int a, b; cout<<“enter tow Number:”; cin >>a >> b; add2Nums(a, b) return 0; } void add2Nums(int x, int y) { cout<< x<< “+” << y << “=“ << x+y; }
  • 17. If the function Does Not Take Arguments specify this with EMPT Y-LIST OR write void inside #include<iostream.h> void funA(); void funB(void) main() { Will be the same funA(); in all cases funB(); return 0; } void funA() { cout << “Function-A takes no arqumentsn”; } void funB() { cout << “Also Function-B takes No argumentsn”; }
  • 18. Local variables  Known only in the function in which they are defined  All variables declared inside a function are local variables  Parameters  Local variables passed to function when called (passing- parameters)  Variables defined outside and before function main:  Called global variables  Can be accessible and used anywhere in the entire program
  • 19. Omitting the type of returned result defaults to int, but omitting a non-integer type is a Syntax Error  If a Global variable defined again as a local variable in a function, then the Local-definition overrides the Global defining  Function prototype, function definition, and function call must be consistent in: 1- Number of arguments 2- Type of those arguments 3-Order of those arguments
  • 20. #include<iostream.h> int x,y; //Global Variables int add2(int, int); //prototype main() { int s; x = 11; y = 22; cout << “global x=” << x << endl; cout << “Global y=” << y << endl; s = add2(x, y); cout << x << “+” << y << “=“ << s; cout<<endl; cout<<“n---end of output---n”; return 0; } global x=11 int add2(int x1,int y1) { int x; //local variables global y=22 x=44; Local x=44 cout << “nLocal x=” << x << endl; 11+22=33 return x1+y1; } ---end of output---
  • 21. int sum(int x, int y) { int result; result = x+y; } this function must return an integer value as indicated in the header definition (return result;) should be added ---------------------------------------------------------------------------------------- - int sum (int n) { if (n==0) return 0; else n+sum(n-1); } the result of n+sum(n-1) is not returned; sum returns an improper result, the else part should be written as:- else return n+sum(n-1);
  • 22. void f(float a); { float a; cout<<a<<endl; }  ; found after function definition header.  redefining the parameter a in the function void f(float a) { float a2 = a + 8.9; cout <<a2<<endl; }
  • 23. void product(void) { int a, b, c, result; cout << “enter three integers:”; cin >> a >> b >> c; result = a*b*c; cout << “Result is” << result; return result; }  According to the definition it should not return a value , but in the block (body) it did & this is WRONG.   Remove return Result;
  • 24. Call by value • A copy of the value is passed  Call by reference • The caller passes the address of the value  Call by value  Up to this point all the calls we have seen are call-by-value, a copy of the value (known) is passed from the caller-function to the called- function  Any change to the copy does not affect the original value in the caller function  Advantages, prevents side effect, resulting in reliable software
  • 25. Call By Reference  We introduce reference-parameter, to perform call by reference. The caller gives the called function the ability to directly access the caller’s value, and to modify it.  A reference parameter is an alias for it’s corresponding argument, it is stated in c++ by “flow the parameter’s type” in the function prototype by an ampersand(&) also in the function definition-header.  Advantage: performance issue void function_name (type &);// prototype main() { ----- ------ } void function_name(type &parameter_name)
  • 26. #include<iostream.h> int squareVal(int); //prototype call by value function void squareRef(int &); // prototype call by –reference function int main() { int x=2; z=4; cout<< “x=“ << x << “before calling squareVal”; cout << “n” << squareVal(x) << “n”; // call by value cout<< “x=“ << x << “After returning” cout<< “z=“ << z << “before calling squareRef”; squareRef(z); // call by reference cout<< “z=“ << z<< “After returning squareRef” return 0; } x=2 before calling squareVal int squareVal(int a) 4 { x=2 after returning return a*=a; // caller’s argument not modified z=4 before calling squareRef } z=16 after returning squareRef void squarRef(int &cRef) { cRef *= cRef; // caller’s argument modified }
  • 27. rand function generates an integer between 0 and RAND- MAX(~32767) a symbolic constant defined in <stdlib.h>  You may use modulus operator (%) to generate numbers within a specifically range with rand. //generate 10 random numbers open-range int x; for( int i=0; i<=10; i++){ x=rand(); cout<<x<<“ “; } ------------------------------------------------------- //generate 10 integers between 0……..49 int x; for( int i=0; i<10; i++){ x=rand()%50; cout<<x<<“ “; }
  • 28. //generate 10 integers between 5…15 int x; for ( int i=1; i<=10; i++){ x= rand()%11 + 5; cout<<x<<“ “; } ------------------------------------ //generate 100 number as simulation of rolling a dice int x; for (int i=1; i<=100; i++){ x= rand%6 + 1; cout<<x<<“ “; }
  • 29. the rand( ) function will generate the same set of random numbers each time you run the program .  To force NEW set of random numbers with each new run use the randomizing process  Randomizing is accomplished with the standard library function srand(unsigned integer); which needs a header file <stdlib.h> Explanation of signed and unsigned integers:  int is stored in at least two-bytes of memory and can have positive & negative values  unsigned int also stored in at least two-bytes of memory but it can have only positive values 0…..65535
  • 30. #include<iostream.h> #include<iomanip.h> #include<stdlib.h> int main() { int i; unsigned num; // we will enter a different number each time we run cin>>num; srand(num); for(i=1; i<=5; i++) cout<<setw(10)<< 1+rand()%6; return 0; } Output for Multiple Runs 19 6 1 1 4 2 1 18 6 1 5 1 4 4 Different-set of Random 3 1 2 5 6 2 4 numbers 0 1 5 5 3 5 5 3 1 2 5 6 3 4
  • 31. #include<iostream.h> #include<iomanip.h> #include<stdlib.h> int main() { int i; for(i=1; i<=5; i++) cout<<setw(10)<< 1+rand()%6; return 0; } Output for Multiple Runs 5 3 3 5 4 2 5 3 3 5 4 2 Same set of numbers for 5 3 3 5 4 2 5 3 3 5 4 2 each run 6 5 3 3 5 4
  • 32.  Main calls another function…..normal  A function calls another function2….normal  A function calls itself ?! Possible?? YES A recursive function is one that call itself.
  • 33. A recursive function is called to solve a problem  The function knows to solve only the simplest cases or so-called base-cases  Thus if the function called with a base-case, it simply returns a result. But if it is called with more complex problem, the function divides the problem into two conceptual pieces, one knows how to do, and another doesn't know what to do.  The second case/piece must resemble the original problem, but be a slightly simpler/smaller version of the original problem
  • 34. Thus the function launches (calls) a fresh copy of itself to work on the smaller problem –this is related as a Recursive- call/recursive step.  The function keeps dividing each new sub problem into two conceptual pieces until eventually terminates after converging on the base-case.  The function thus recognize the base-case and returns a result to the previous copy of the way up the line until original call of the function returns the final result to main.
  • 35. 5! Final value=120 5! 5!=5*24=120 returned 5*4! 5*4! 4!=4*6=24 returned 4*3! 4*3! 3!=3*2=6 returned 3*2! 3*2! 2!=2*1=2 returned 2*1! 2*1! 1 1 1
  • 36. //Recursive factorial Function #include<iostream.h> #include<iomonip.h> unsigned lion factorial(unsigned long);//prototype int main() { int num; cout<<“enter a positive integer:”; cin>>num; cout<<“factorial=“<<factorial(num); return 0; } unsigned long factorial(unsigned long n) { if ( n <= 1) //the base case return 1; else return n * factorial (n - 1); }
  • 37. Function overloading  Functions with same name and different parameters  Should perform similar tasks  I.e., function to square ints and function to square floats int square( int x) {return x * x;} float square(float x) { return x * x; }  A call-time c++ complier selects the proper function by examining the number, type and order of the parameters