-
In C++, a function may call itself
to define a recursive function.
-
Every recursive function consists of
one or more base cases and a general, recursive case.
-
Example: Power Function
//
Exponentiation program
#include <iostream.h>
int Power( int, int);
int main()
{
int number;
int exponent;
cin >> number
>> exponent;
cout <<
number << "^"
<< exponent << " = "
<< Power(number, exponent);
return 0;
}
//
Power recursive function
int Power (int x, int
n)
{
if (n <=
0)
return 1;
if (n ==
1)
return n;
return x
* Power(x, n-1);
}
-
The Power
function can be coded as a nonrecursive (iterative)
algorithm:
// Power iterative function
int Power (int x, int
n)
{
int pow
= 1;
for ( ;
n > 0; n--)
pow *= x;
return pow;
}
-
If there is no base case, or if the
base case is never executed, an infinite recursion occurs.
-
An Infinite
Recursion is when a recursive function calls
itself endlessly.
-
The factorial of a non-negative number
is defined as the product of all the values from 1 to the number:
n! = 1 * 2 * . . . * n
It can also be defined recursively
as
n! = 1
if n < 2
= n * (n -1)! if n >= 2
-
Example: Recursive Factorial Function
// Factorial Function
int Factorial ( int
n )
{
if ( n <
2)
return 1;
return n
* Factorial(n - 1);
}
-
The factorial function can also be
defined iteratively by a simple function. (The exercise is left to the
reader).
-
Many functions are much easier to define
recursively than they are iteratively.
