1. Basic Scientific Programming
Recursion

2. Recursion


All of the examples considered thus far
involved a main program referencing a
subprogram or one subprogram
referencing another.
A subprogram may also reference itself,
this is called Recursion.

3. Ex: n!


n! = 1 * 2* 3* … * n
0! = 1
1! = 1
2! = 1 * 2 = 2
3! = 2! * 3 = 2*3 = 6
4! = 3! * 4 = 6*4 = 24
It is clear that once one factorial has been
calculated, it can be used to calculate the
next one.
n! = n * (n-1)!

4. 
A function is defined recursively if the
definition consists of two parts:


A base case: in which the value of the
function is specified for one or more values
of the argument(s) 0! = 1
A recursive step: in which the function’s
value for a current value of argument is
defined in terms of a previously defined
function value.
n>0 n! = n* (n-1)!

5. 4!

4! = 4 * 3!
3! = 3 * 2!
2! = 2 * 1!
1! = 1* 0!
0! =1

6. 4!

4!=4*3!=4*6=24
3!= 3*2!=3*2=6
2!=2*1!=2*1=2
1!=1*0!=1 * 1 = 1
0! =1

7. Notes


Subprograms may be declared to be
recursive by attaching the word
RECURSIVE at the beginning of the
subprogram heading.
For a recursive function, a RESULT
clause must be attached at the end of
the function heading.

8. Notes


Return value will be assigned to the
result variable instead of the function
name.
The type of the function is specified by
declaring the type of the result variable.

9. 
Recursive function factorial(n) result(fact)
integer:: fact
integer,intent(in)::n
if(n==0) then
fact = 1
else
fact = factorial(n-1) * n
end if
End Function factorial

10. 


Fact = 1
do I = 1,5
fact = fact * I
end do
Nonrecursive programs may execute more
rapidly and utilize less memory than
corresponding recursive programs.
For some problems, recursion is the most
natural and straightforward technique.

11. Ex:

Recursive function f(n) result(f_value)
integer:: f_value
integer,intent(in) :: N
if(n==0) then
f_value = 0
else
f_value = n+ f(n-1)
end if
end function f
!Find f(5), f(0)

12. Ex:

recursive function f(num1,num2) result(f_val)
integer:: f_value
integer,intent(in):: num1,num2
if (num1>num2) then
f_val = 0
Else if(num2==num1+1) then
f_val = 1
Else
f_val = f(num1+1,num2-1) + 2
End if
end function f !! F(2,2), F(1,5), F(8,3)

13. xn

Recursive function f(x,n) result(x2n)
integer:: x2n
integer,intent(in):: x,n
if(n==0)
x2n = 1
else
x2n = f(x,n-1) * x
end if
end function f