1. C++ Programming Lecture 12 Functions – Part IVBy
Ghada Al-Mashaqbeh
The Hashemite University
Computer Engineering Department

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Outline
Introduction.
Recursion.
Reference parameters and variables.
Functions call by reference and call by value.
Examples.
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Recursion I
Recursive functions
Are functions that calls themselves.
Can only solve a base case.
If not base case, the function breaks the problem into a slightly smaller, slightly simpler, problem that resembles the original problem and
Launches a new copy of itself to work on the smaller problem, slowly converging towards the base case
Makes a call to itself inside the return statement
Eventually the base case gets solved and then that value works its way back up to solve the whole problem.
The recursion step executes while the original call to the function is still open (not finished yet).
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Recursion II
Example: factorial
n! = n * ( n – 1 ) * ( n – 2 ) * … * 1
Can be solved either iteratively or recursively:
Iteratively:
int factorial = 1;
for (int count = n; count >= 1; count--)
factorial *= count;
Recursively:
Recursive relationship ( n! = n * ( n – 1 )! )
5! = 5 * 4!
4! = 4 * 3!…
Base case (1! = 0! = 1)
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5. Example Using Recursion: The Fibonacci Series
Each number sum of two previous ones
Example of a recursive formula:
fib(n) = fib(n-1) + fib(n-2)
C++ code for fibonacci function
long fibonacci( long n ) {
if ( n == 0 || n == 1 ) // base case
return n;
else return fibonacci( n - 1 ) + fibonacci( n – 2 ); }
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6. Example Using Recursion: The Fibonacci Series
Diagram of Fibonacci function
f( 3 )
f( 1 )
f( 2 )
f( 0 )
return 1
return 0
return +
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7. 2.1 Call function fibonacci 2.2 Output results.
1 // Fig. 3.15: fig03_15.cpp
2 // Recursive fibonacci function
3 #include <iostream> 4
5 using std::cout;
6 using std::cin;
7 using std::endl; 8
9 unsigned long fibonacci( unsigned long ); 10
11 int main()
12 {
unsigned long result, number; 14
cout << "Enter an integer: ";
cin >> number;
result = fibonacci( number );
cout << "Fibonacci(" << number << ") = " << result << endl;
return 0;
20 } 21
22 // Recursive definition of function fibonacci
23 unsigned long fibonacci( unsigned long n )
24 {
25 if ( n == 0 || n == 1 ) // base case
return n;
27 else // recursive case
return fibonacci( n - 1 ) + fibonacci( n - 2 );
29 }
1. Function prototype
1.1 Initialize variables
2. Input an integer
2.1 Call function fibonacci
2.2 Output results.
3. Define fibonacci recursively
Only the base cases return values. All other cases call the fibonacci function again.

8. Program Output Enter an integer: 0 Fibonacci(0) = 0
Enter an integer: 6
Fibonacci(6) = 8
Enter an integer: 20
Fibonacci(20) = 6765
Program Output
Enter an integer: 30
Fibonacci(30) =
Enter an integer: 35
Fibonacci(35) =

9. Recursion vs. Iteration
Repetition
Iteration: explicit loop
Recursion: repeated function calls
Termination
Iteration: loop condition fails
Recursion: base case recognized
Both can have infinite loops
Balance between performance (iteration) and good software engineering (recursion).
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Reference Variables I
Reference variable is an alias to some variable.
& (ampersand) is used to signify a reference
E.g:
int x = 0;
int &y = x; //y is a reference to an integer which is x
Here y is an alias to the variable x since the address of y is equal to the address of x.
So, modifying either x or y both variables will have the same modified value since both of them refer to the same memory location or address.
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11. Reference Variables II
Reference variables must be initialized within the same statement that defines them, if not it will be a syntax error.
Reference variables must be initialized with a variable only, constants and expressions are not allowed  syntax error.
You cannot reassign the reference variable to another variable since you simply copy the value of the new variable in the old one and you still working on the old one and this is considered as a logical error.
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Call By Reference I
Two types of function call:
Call by value
Copy of data passed to function.
Changes to copy do not change the original found in the caller.
Used to prevent unwanted side effects.
Call by reference
Function can directly access data.
Changes affect the original found in the caller.
No copy exist (reduce overhead), however, it is dangerous since the original value is overwritten.
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Call By Reference II
Function arguments can be passed by reference.
In both the function header and prototype you must proceed the reference variable by &.
In the function call just type the name of the variable that you want to pass.
Inside the function body use the reference variable by its name without &.
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Call By Reference III
Again the reference argument must be a variable (constants or expressions are not allowed  syntax error
E.g.:
void change( int &variable )
{ variable += 3; }
Adds 3 to the input variable which also affects the original variable (passed as argument to function change in the caller).
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Call By Reference IV
Note that till now we have talked about the function arguments or parameters to be reference variables. But what about the return result? Can we make it a reference variable?
If the function return a reference variable this means that it returns an alias to a variable inside that function.
If this variable is not static (i.e. automatic) then this variable will be destroyed when the function ends.
So, this function will return a reference to an undefined variable which is called dangling reference.
Such thing is considered as a logical error.
As possible avoid the usage of reference return results even to static variables.
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1 // Fig. 3.20: fig03_20.cpp
2 // Comparing call-by-value and call-by-reference
3 // with references.
4 #include <iostream> 5
6 using std::cout;
7 using std::endl; 8
9 int squareByValue( int );
10 void squareByReference( int & ); 11
12 int main()
13 {
14 int x = 2, z = 4; 15
16 cout << "x = " << x << " before squareByValue\n"
<< "Value returned by squareByValue: "
<< squareByValue( x ) << endl
<< "x = " << x << " after squareByValue\n" << endl; 20
21 cout << "z = " << z << " before squareByReference" << endl;
22 squareByReference( z );
23 cout << "z = " << z << " after squareByReference" << endl; 24
25 return 0;
26 } 27
28 int squareByValue( int a )
29 {
30 return a *= a; // caller's argument not modified
31 }
Notice the use of the & operator
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33 void squareByReference( int &cRef )
34 {
35 cRef *= cRef; // caller's argument modified
36 }
x = 2 before squareByValue
Value returned by squareByValue: 4
x = 2 after squareByValue
z = 4 before squareByReference
z = 16 after squareByReference
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Additional Notes
This lecture covers the following material from the textbook:
Fourth Edition
Chapter 3: Sections 3.12, 3.13, 3.14, 3.17
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