How to resolve the algorithm Catalan numbers step by step in the Fortran programming language

Published on 12 May 2024 09:40 PM
#Fortran

How to resolve the algorithm Catalan numbers step by step in the Fortran programming language

Table of Contents

Problem Statement

Catalan numbers are a sequence of numbers which can be defined directly: Or recursively: Or alternatively (also recursive):

Implement at least one of these algorithms and print out the first 15 Catalan numbers with each. Memoization   is not required, but may be worth the effort when using the second method above.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Catalan numbers step by step in the Fortran programming language

Source code in the fortran programming language

program main
  !=======================================================================================
  implicit none

  !=== Local data
  integer                      :: n

  !=== External procedures
  double precision, external   :: catalan_numbers         
  
  !=== Execution =========================================================================

  write(*,'(1x,a)')'==============='
  write(*,'(5x,a,6x,a)')'n','c(n)'
  write(*,'(1x,a)')'---------------'

  do n = 0, 14
    write(*,'(1x,i5,i10)') n, int(catalan_numbers(n))
  enddo

  write(*,'(1x,a)')'==============='

  !=======================================================================================
end program main
!BL
!BL
!BL
double precision recursive function catalan_numbers(n) result(value)
  !=======================================================================================
  implicit none

  !=== Input, ouput data
  integer, intent(in)          :: n

  !=== Execution =========================================================================

  if ( n .eq. 0 ) then
    value = 1
  else 
    value = ( 2.0d0 * dfloat(2 * n - 1) / dfloat( n + 1 ) ) * catalan_numbers(n-1)
  endif

  !=======================================================================================
end function catalan_numbers

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