1. Programming fundamentals 2 Chapter 1: Functions (Sub-Algorithms)
Miss:Hanan Hardan

2. Contents Algorithm Design Sub-Algorithms C++ Functions
Definition
Types of Functions
Examples
Function Prototype
Scope of Variables
Call by Value / Call by Reference

3. Top-Down Algorithm Design
Topics to cover here:
Top-Down Design approach
Structured Programming
Sub-algorithms (a breadth look)

4. Top-Down Algorithm Design
1) Top-Down Design
The problem is divided into its major sub-problems
Solve the sub-problems to derive the solution to the original problem.
2) Structured Design:
Dividing the problem into smaller sub-problems is called “structured design”, “top-down design”,
“step-wise refinement”, and “modular Programming”
3) Structured Programming: The process of implementing a structured design is called “structured programming”

5. Structured Programming & Structure Chart
The main goal of structured programming is
to write error-free code
to reuse any possible code that has already been written and tested (this is called reusability)
to have many sub-problems that are related.

6. Sub-algorithms
A sub-algorithm is a block of instructions that is executed when it is called from some other point of the algorithm.
The top-down algorithm design needs
- to write the sub-algorithm definitions
- to write an algorithm that calls the sub-algorithms
(i.e. includes a CALL statement for each one) .
Sub-algorithms are of two type:
- Sub-algorithms that do not return a value
- Sub-algorithms that return a value
* The sub-algorithm is called function in C++.

7. The Sub-algorithm Definition
a) Definition of a sub-algorithm that does not return a value
1- Sub-algorithm without arguments:
SUBALGORITHM subalgorithm-name ( )
Statements
END subalgorithm-name
where, ( ) is the empty list.

8. The Sub-algorithm Definition
2- Sub-algorithm with arguments:
SUBALGORITHM subalgorithm-name (parameter-list)
Statements
END subalgorithm-name
where, Parameter-list is a list that contains one or more parameters that are passed to the sub-algorithm.

9. The Call to a Sub-algorithm
The call to a sub-algorithm that does not return a value is given in the CALL statement which has the following syntax:
subalgorithm-name (Actual parameters)
Examples:
draw_circle ( )
sum(4,7)
sum(x,y)

10. The Call to a Sub-algorithm
Interpretation of the sub-algorithm call
Suppose that algorithm Figure calls the sub-algorithm draw_circle using the call statement
CALL draw_circle ( )
Then the flow of control between sub-algorithms will be as follows (see the next diagram):
The flow of control in algorithm Figure stops on this statement to initiate the execution of the sub-algorithm draw_circle
after this sub-algorithm has finished executing, the next statement in the calling algorithm will be executed.

11. The Call to a Sub-algorithm
Algorithm Figure Sub-algorithm draw_circle
ALGORITHM Figure
CALL draw_circle ( )
------
END Figure
SUBALGORITHM draw_circle ( )
------
END draw_circle
call
return

12. The Call to a function (C++)
program Figure Function draw_circle
void main(){
draw_circle ( );
------ }
call
void draw_circle ( ) {
------ }
return

13. Example 1: Syntax ( in Algorithm ): Syntax ( in C++ ):
SubAlgorithm print_box ()
output “* * * * * * *\n”
output “* “ , 50 , “ * \n”
End print_box
Algorithm Test
begin
print_box ()
output “\n”
End Test
void print_box () {
cout << “* * * * * * *\n” ;
cout << “* “ << 50 << “ * \n” ; }
void main()
print_box ();
cout<<endl;

14. Example 2: Syntax ( in Algorithm ): Syntax ( in C++ ):
SubAlgorithm print_box ( n)
output “* * * * * * *\n”
output “* “ , n , “ * \n”
End print_box
Algorithm Test
Begin
Output “ Enter integer number"
Input a
print_box (a)
print_box (5)
End Test
void print_box (int n) {
cout << “* * * * * * *\n” ;
cout << “* “ << n << “ * \n” ; }
void main()
int a;
cout<<"\n Enter integer number";
cin>>a;
print_box (a);
cout<<endl;
print_box (5);

15. The Sub-algorithm Definition
b) Definition of a sub-algorithm that returns a value:
1- Sub-algorithm without arguments:
ftype SUBALGORITHM subalgorithm-name ( )
Statements
END subalgorithm-name
Notes:
- ftype: is any data type that the result of a subalgortihm can have. If the subalgorithm does not return any result, then no type is specified.
-( ) empty list.
- If the subalgorithm has a type, then the Statements in the body of the subalgorithm should have return statement, usually it is the last statement.

16. The Sub-algorithm Definition
b) Definition of a sub-algorithm that returns a value:
2- Sub-algorithm without arguments:
ftype SUBALGORITHM subalgorithm-name (parameter-list)
Statements
END subalgorithm-name
Notes:
- ftype: is any data type that the result of a subalgortihm can have. If the subalgorithm does not return any result, then no type is specified.
- parameter-list: includes one or more arguments.
- If the subalgorithm has a type, then the Statements in the body of the subalgorithm should have return statement, usually it is the last statement.

17. The Call to a Sub-algorithm
The call to a sub-algorithm that returns a value is given as follows:
- The name of the sub-algorithm is given within the
OUTPUT statement
assignment statement
Examples:
result  Sum (x, y )
output Sum (x, y )

18. Example: Syntax ( in Algorithm ): Syntax ( in C++ ):
INT SubAlgorithm sum ()
x5
y7
return x+y
End sum
Algorithm Test
Begin
Output “sum=“ ,sum()
a  sum()
Output “sum=“ , a
End Test
int sum () {
int x=5, y=7 ;
return x+y ; }
void main()
int a;
cout<<“sum=“<<sum()<<endl;
a=sum();
cout<<“sum=“<<a<<endl;

19. Example: Syntax ( in Algorithm ): Syntax ( in C++ ):
INT SubAlgorithm Rect_area (L, W)
a  L * W
return a
End Rect_area
Algorithm Test
Begin
Output “ Enter 2 integer number"
Input a ,b
Output “area==“, Rect_area(a,b)
z  Rect_area(3,2)
Output “area=“ , z
End Test
int Rect_area (int L, int W) {
int a ;
a = L * W ;
return a ; }
void main()
int a,b,z;
cout<<"\n Enter 2 integer number";
cin>>a>>b; cout<<“area==“<<Rect_area(a,b)<<endl;
z=Rect_area(3,2);
cout<<“area=“<<z<<endl;

20. Function - Summary Function Definition:
User defined function is a code segment (block) that perform an specific action.
Function Syntax: Return_DT F_name ( list of formal parameters) { Action_ body ; }

21. Types of Functions Function are of 4 types:
1- A function that doesn’t return a value without argument
-Return_DT is void Action_body doesn’t contain return statement.
Syntax:
void function-name ( )
{ local declarations // this is optional
executable statements }

22. Example: function that doesn’t return a value without arguments
void print_O ( )
{ cout << “ ** “ << endl;
cout << “ * * “ << endl;
cout << “ ** “ << endl; }

23. 2- A function that doesn’t return a value with arguments
Types of Functions
2- A function that doesn’t return a value with arguments
-Return_DT is void Action_body doesn’t contain return statement.
Syntax:
void function-name(argument_list)
{ local declarations // this is optional
executable statements }

24. Example: function that doesn’t return a value with arguments
void print_box (int n)
{ cout << “* * * * * * *\n” ;
cout << “* “ << n << “ * \n” ;
cout << “* * * * * * *\n” ; }

25. 3- A function that returns a result of any type without arguments
Types of Functions
3- A function that returns a result of any type without arguments
-Return_DT is any type -Action_body contains return statement.
Syntax:
<any type> function-name( )
{ local declarations // this is optional
executable statements }

26. Example: function that return a value without arguments
int sum ()
{ int x=5, y=7 ;
return x+y ; }

27. 4- A function that returns a result of any type with arguments
Types of Functions
4- A function that returns a result of any type with arguments
-Return_DT is any type -Action_body contains return statement.
Syntax:
<any type> function-name(argument_list )
{ local declarations // this is optional
executable statements }

28. Example: function that return a value with arguments
int Rect_area (int L, int W)
{ int a ;
a = L * W ;
return a ; }

29. Calling (invoking) Function:
a) The call to a Function that does not return a value is given in the following syntax:
F_name (Actual parameters);
e.g. draw_circle ( );
e.g. sum(4,7);
b) The call to a Function that returns a value is given as follows:
- The name of the functio is given within the output statement
e.g cout<<sum(x,y);
- The name of the Function is given within the
assignment statement
e.g. result = sum (x, y );

30. Example #include <iostream> using namespace std;
int Max (int Value1, int Value2) {
if (Value1 > Value2)
return Value1;
else
return Value2; }
void main() {
int a, b;
cout<<"\nPlease Enter the values of a and b: ";
cin>>a>>b;
cout<<"\n the maximum one is: "<<Max(a,b)<<endl;
Function Definition
Calling the function in an expression like cout<<, condition, assignment statements

31. Example #include <iostream> using namespace std;
int Max (int Value1, int Value2) {
if (Value1 > Value2)
return Value1;
else
return Value2; }
void main() {
int a, b, c;
cout<<"\nPlease Enter the values of a and b: ";
cin>>a>>b;
c=Max(a,b);
cout<<"\n the maximum one is: "<<c<<endl;

32. Example #include <iostream> using namespace std;
int Sum (int A, int B) {
return (A+B); }
void main() {
int N1, N2, S;
cout<<"\n Please Enter N1 and N2: ";
cin>>N1>>N2;
S = Sum(N1,N2);
cout<<"\nSum= "<<S<<endl;

33. Example #include <iostream> using namespace std;
bool Positive (int Num) {
if (Num > 0)
return true;
else
return false; }
void main() {
int Number;
cout<<"\nEnter Number: ";
cin>> Number;
if (Positive(Number))
cout<<"\n the number is positive";
cout<<"\n the number is negative";
cout<<endl;

34. Example #include <iostream> using namespace std;
float Area (int R) {
return (3.14 * R * R ); }
void main() {
int Radius;
cout<<"Enter the Redius: ";
cin>>Radius;
cout<<"\nCircle Area is: "<<Area(Radius);
cout<<endl;

35. Example #include <iostream> using namespace std;
long Power(int Base, int Exp) {
int M=1;
for(int i=1; i<=Exp; i++)
M*=Base;
return M; }
void main() {
int B, E;
cout<<"\nEnter Base: ";
cin>>B;
cout<<"\nEnter Exponent: ";
cin>>E;
cout<<"\n Result= "<<Power(B,E);
cout<<endl;

36. Example #include <iostream> using namespace std;
long Fact (int Num) {
int F = 1, i = Num;
while (i>=1){
F *= i;
i--; }
return F; }
void main() {
int Number;
cout<<"Enter an integer number: ";
cin>>Number;
cout<<endl<<Number<<"!= "<<Fact(Number);
cout<<endl;

37. Example No Return Statement #include <iostream>
using namespace std;
void Print(char Ch, int n) {
for (int i=1; i<=n; i++)
cout<<Ch;
cout<<endl; }
void main() {
char Sym;
int Number;
cout<<"\nEnter the Symbol: ";
cin>>Sym;
cout<<"\nHow many times: ";
cin>>Number;
Print(Sym,Number);
No Return
Statement

38. Example #include <iostream> using namespace std;
int Mul(int V1, int V2) {
return V1 * V2; }
void Result() {
cout<<"\n5 x 9 = "<<Mul(5,9);
cout<<"\n4 x 7 = "<<Mul(4,7);
cout<<"\n6 x 4 = "<<Mul(6,4)<<endl; }
void main() {
Result() ; }

39. The Function Prototype
Like other identifiers in C++, function must be declared before it can be referenced.
To declare a function, we can insert a function prototype before the main function.
The function prototype provides all information that the C++ compiler needs to know to translate calls to the function correctly.
A function prototype tells the compiler the
- data type of the function
- the function name
- information about the arguments that the function expects.
Examples: void draw_circle ( );
int m ( ) ;
void print_box (int) ;
int Rect_area (int , int);

40. Function Prototype #include <iostream.h> int Mul(int, int);
int Add(int, int);
void Show();
void main() {
Show(); }
int Mul(int X, int Y) { return X*Y; }
int Add(int X, int Y) { return X+Y; }
void Show() {
int A=10, B=20;
cout<<Add(A,B)<<'\t'<<Mul(A,B)<<endl; }
Function Prototype contains only data types
But may contain identifiers.

41. Scope of Variables (1) Global variables:
- Those variables that are declared before the main function.
- These are visible from any point of the code, inside and outside any function.
(2) Local variables:
- These are declared inside a block or a function.
- The scope of local variables is limited to the same
nesting level in which they are declared.

42. Example of Local and Global Variables
// File: global.cpp
#include <iostream.h>
int x = 7 ; // global variables
int fun1 (int ); // function prototype
void main ( )
{ int z ; // local variable in main
cout << “The global variable: “ << x ;
z = fun1 ( 5 ) ; // calling add function
cout << “ The result is “ << z << endl ; }
int fun1 ( int a )
{ int r ; // local variable in fun1
r = a * a * a ;
return r ; }

43. Example2 of Local and Global Variables
#include <iostream>
using namespace std;
int x = 7; // global variable
void main() {
int x = 5;
cout << "main "<< x<< endl;
int x = 3;
cout << "in block "<< x<< endl;
cout << "global "<< ::x<< endl; }
Output:
main 5
in block 3
global 7

44. More about global and local variables
When you use the same variable name for both a local and a global variable, the local variable is used in a block or a function instead of the global variable, this operation is called “Masking”.
Each variable has a life time, which is the time this variable remains seen by the program.
The lifetime of a global variable extends through the execution of the whole program, while the lifetime of a local variable only last until the end of the function or the block where this local variable is defined.

45. Functions and Passing Parameters
The mechanisms of passing parameters:
(1) Call by value:
- During the function call, the value of the argument is
found and passed to the function.
- Any modification inside the function does not affect the
argument.
(2) Call by reference:
- During the function call, the address of the variable is
passed to the function.
- Any modification made on the parameter inside the
function will have effect in the passed variable outside it.

46. Difference between Function Definitions for Call by Value and Call by Reference
For call by value, we declare the arguments of the function as usual.
Example:
int func1 ( int , int ); // function prototype
For call by reference, the type of the argument is followed by the symbol (&) to specify that the variable has to be passed by reference.
void func2 ( int & , int & ); // function prototype

47. Call by value
When calling, the value of actual parameter will be copied to the formal parameter.
#include <iostream.h>
void Increment(int);
void main() {
int A = 10;
Increment(A);
cout<<A<<endl; }
void Increment(int X) { ++X; }

48. Call By reference
When calling, the reference formal parameter will be an alternative name to the actual parameter.
#include <iostream.h>
void Increment(int&);
void main() {
int A = 10;
Increment(A);
cout<<A<<endl; }
void Increment(int &X) { ++X; }

49. Call By reference
When calling, the pointer formal parameter will points to the actual parameter.
#include <iostream.h>
void Increment(int*);
void main() {
int A = 10;
Increment(&A);
cout<<A<<endl; }
void Increment(int *X) { ++*X; }

50. Example 1: Call by Value // File: calls1.cpp
#include <iostream.h>
// function prototype: the arguments to be passed by value
int add (int , int );
void main ( )
{ int x, y , z ; // local variables in main
cout << “ Enter two integers: “ ;
cin >> x >> y ;
cout << “ x = “ << x << “ y = “ << y << endl;
z = add ( x , y ) ; // calling add function
cout << “ The result is “ << z ;
cout <<“After call “<< “ x = “ << x << “ y = “ << y << endl; }
int add ( int a , int b )
{ return a + b ; }

51. Execution of Example 1
The user will be prompted to enter two integers.
The user enters, for example, 10 and 20 that are saved in x and y respectively.
When function add is called, the value of x and y are passed to the function.
The function add takes the values 10 and 20 and links them to a and b respectively.
The function will return the result which is 30.
The output:
Enter two integers:
x = y = 20
The result is 30
After call x = 10 y = 20

52. Example 2: Call by Reference
// File: calls2.cpp
#include <iostream.h>
// function prototype: the arguments to be passed by reference
void duplicate (int & , int & , int & );
void main ( )
{ int x, y , z ; // local variables in main
cout << “ Enter three integers: “ ;
cin >> x >> y >> z ;
cout << “ Before call: “ << “ x = “ << x << “ y = “ << y
<< “ z = “ << z <<endl;
duplicate ( x , y , z ) ; // calling duplicate function
cout <<“ After call: << “ x = “ << x << “ y = “ << y
<< “ z = “ << z <<endl; }
void duplicate ( int & a , int & b , int & c )
{ a *= 2 ;
b *= 2 ;
c *= 2 ; }

53. Execution of Example 2
The user will be prompted to enter three integers.
The user enters, for example, 10, 20, and 30 that are saved in x, y, and z respectively.
When function duplicate is called, the addresses of x, y, and z are passed to the function.
The addresses of x, y, and z are linked to the parameters of the function a, b, and c. The function will duplicate each parameter and save the result in the same parameter. Thus,
a becomes 20 hence x becomes 20 also
b becomes 40 hence x becomes 40 also
c becomes 60 hence x becomes 60 also
After the call we see that the values of x, y, and z are changed.
The output:
Enter three integers:
Before call: x = y = z = 30
After call: x = y = z = 60

54. Overloading
Overloading, is the operation of defining several functions of the same name, but in different signatures.
The signature of the function includes, the return data type of the function, the function name, number of parameters passed to it, and the data types of these parameters.

55. Overloading – Example1 Output: hello # * * * * * integer 2 char &
#include <iostream> using namespace std; void print () { cout << "hello" << endl; } void print (char x) cout << x << endl; void print (char a, int b) for (int i=1; i<=b; i++) cout << a<<" "; cout << endl;
void print (int x, char y) { cout << "integer " << x<< " char " << y<< endl; } void main() print (); print ('#'); print ('*', 5); print (2, '&');
Output:
hello #
* * * * *
integer 2 char &

56. Overloading – Example2 Output: Result = 16 Result2 = 30.25
#include <iostream> using namespace std; int square (int x) { return x * x; } float square (float x)
void main() { int a = 4, result; float b = 5.5, result2; result = square (a); result2 = square (b); cout<< "Result = "<< result<<endl; cout<< "Result2 = "<< result2<<endl; }
Output:
Result = 16
Result2 = 30.25

57. Important Note - Overloading
Suppose you have defined these two functions:
int max (int x, int y) {
if (x > y)
return x;
else
return y; }
bool max (int a, int b)
if (a > b)
return true;
return false;
In this case the compiler will result this syntax error: Cannot overload functions distinguished by return type alone. This means, that you cannot define the same function name twice or more, with the same number of parameters and the same types, but the only different is the return type. There should be difference in the parameters as well.

58. Template
Assume you have this program: #include <iostream> using namespace std; void swapping (int a, int b) { int temp; temp = a; a = b; b = temp; cout << a << " " << b<< endl; } void swapping (char a, char b) char temp;
void main() {
swapping (2, 5);
swapping ('$', '*'); }
Output:
5 2
* $
This is another example of overloading, but you may need to add other functions with other data
types as well.
In such cases we can define a template function, that we can send to it any data types we need.

59. Template - Example Output: 5 2 3.66 5.6 * $ Ali Ahmad
Assume you have this program: #include <iostream> using namespace std; template <class T> void swapping (T a, T b) { T temp; temp = a; a = b; b = temp; cout << a << " " << b<< endl; } void main() swapping (2, 5); swapping (5.6, 3.66); swapping ('$', '*'); swapping ("Ahmad", "Ali");
Output:
5 2
* $
Ali Ahmad
In this example, we only needed to define the function swapping once, and we could call it several types using different data types for the parameters.

60. Template – Example2
#include <iostream> using namespace std; template <class T> T square (T a) { return a * a; } void main() int x = square (2); float y = square (3.5); double z = square ( ); long e = square ( ); cout << "x = "<< x << endl; cout << "y = "<< y << endl; cout << "z = "<< z << endl; cout << "e = "<< e << endl;

61. Setting default values for parameters in a function
Assume you have this program: #include <iostream> using namespace std; void print (char x, char y, char z) { cout << x << " " << y << " "<< z; } void main() print '$', '%');
Note here that each time you call function print, you will have to send values to the three parameters defined in it.
Sometimes, we need to give default values to parameters, so that if the call statement ignored sending them, the default value will be considered.

62. Setting default values for parameters in a function
Assume you have this program: #include <iostream> using namespace std; void print (char x, char y, char z = ‘*’) { cout << x << " " << y << " "<< z; } void main() print '$', '%'); print '$');
$ $ *

63. Setting default values for parameters in a function
Assume you have this program: #include <iostream> using namespace std; void print (char x, char y = ‘#’, char z = ‘*’) { cout << x << " " << y << " "<< z; } void main() print '$', '%'); print '$'); print
$ $ # *

64. Setting default values for parameters in a function
Assume you have this program: #include <iostream> using namespace std; void print (char x = ‘&’, char y = ‘#’, char z = ‘*’) { cout << x << " " << y << " "<< z; } void main() print '$', '%'); print '$'); print print ();
$ $ # * & # *

65. Setting default values for parameters in a function – Example 2
Assume you have this program: #include <iostream> using namespace std; void print (char x , int y =1) { for (int i=1; i<=y; i++) cout << x <<" "; cout << endl; } void main() print 5); print ('#'); #

66. Setting default values for parameters in a function – Example 2
Suppose you have written the function print in the following way: void print (int y =1, char x ) { for (int i=1; i<=y; i++) cout << x <<" "; cout << endl; }
Note here, that the first parameter has a default value, while the second doesn’t. C++ will not allow you do order the parameters this way. Always make sure that the parameters with default values are listed at the end of the parameters. This program will result the following syntax error: Default argument not at end of parameter list

67. Static Variables
Consider the following program: #include <iostream> using namespace std; void test () { int x =1; x++; cout << "x = "<< x<< endl; } void main() test();
In the function test, x is defined as a local variable within the function. Its lifetime will extend until the end of the function execution, as was discussed earlier. So, when this program is executed, each time test() is called, x is redefined and initialized with 1, and then incremented. The output in this case will be: x = 2

68. Static Variables Output: x=2 x=3 x=4
Consider changing a little bit on the program, by specifying the local variable x, as static. #include <iostream> using namespace std; void test () { static int x =1; x++; cout << "x = "<< x<< endl; } void main() test();
Static keyword, that proceeds the declaration of the variable x, will expand its life time. x is still a local variable that can be accessed only within the function test, but its lifetime won’t end by the end of this function. The first time test() is called, x is declared and initialized with 1, and then incremented. The second time test() is called, x, won’t be declared and initialized again, since it is static it has reserved its final value in the previous call, which was 2, so when it is incremented it will become 3. The life time of a static variable, will end when the execution of the whole program is finished.
Output:
x=2
x=3
x=4

69. Recursion
A Recursive Function, is a function that keeps calling itself until it reaches to its base case (or stopping condition)

70. Factorial example using loop
#include <iostream> using namespace std; void main () { int y, fact =1; cin >> y; for (int i=y; i>=1; i--) fact *=i; cout << fact <<endl; }

71. Factorial example using Recursion
#include <iostream> using namespace std; int Fact (int N) { if (N<=1) return 1; else return N * Fact(N-1); } void main() { cout<<Fact(5)<<endl;

72. Example 2
#include <iostream> using namespace std; int Fun (int N) { int Z; if (N<=1) Z=1; else Z= Fun(N-1) + Fun(N-3); return Z; } void main() { cout<< Fun(5)<<endl;

73. Example 3
#include <iostream> using namespace std; void exercise (int x) { if (x > 0 && x < 10) cout << x << " "; exercise (x + 1); } void main () exercise (5);

74. Example 4
Write a recursive function named, sumSquares, that returns the sum of the squares of the numbers from 0 to num, in which num is a nonnegative int variable.

75. Example 4: Cont. First, let’s solve this problem using For loop.
#include <iostream>
using namespace std;
void main ()
{ int num, sum = 0;
cin >> num;
for (int i=num; i>=0; i--)
sum = sum + i*i;
cout << "Sum = "<< sum << endl; }

76. Example 4: Cont. Now, solve the problem using recursive function.
#include <iostream>
using namespace std;
int sumSquare (int x)
{ if (x == 0)
return 0; // Base case #1
else
if (x == 1)
return 1; //Base case #2
return x * x + sumSquare (x-1);}
void main ()
{ int num;
cin >> num;
cout << "Sum = "<< sumSquare(num) << endl; }

77. Homework
Q1: Write a recursive function that finds and returns the sum of the elements in an int array. Write a program to test your function. Q2: Write a recursive function that returns both the smallest and the largest element in an integer array. Write a program to test your function.