program main

!*****************************************************************************80
!
!! matrix_chain_dynamic_test() tests matrix_chain_dynamic().
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    23 April 2024
!
!  Author:
!
!    John Burkardt
!
  implicit none

  integer catalan_number
  integer cost
  integer, allocatable :: dims(:)
  integer n

  call timestamp ( )
  write ( *, '(a)' ) ''
  write ( *, '(a)' ) 'matrix_chain_dynamic_test():'
  write ( *, '(a)' ) '  Fortran90 version'
  write ( *, '(a)' ) '  Test matrix_chain_dynamic().'

  n = 4
  allocate ( dims(1:n+1) )
  dims = (/ 40, 20, 30, 10, 30 /)
  call matrix_chain_dynamic ( n, dims, cost )
  write ( *, '(a)' ) ''
  write ( *, '(a,i2)' ) '  n = ', n
  call i4vec_transpose_print ( n + 1, dims, '  dims():' )
  write ( *, '(a,i8)' ) '  minimal cost = ', cost
  write ( *, '(a,i4)' ) '  Number of possible orderings = ', catalan_number ( n - 1 )
  deallocate ( dims )

  n = 4
  allocate ( dims(1:n+1) )
  dims = (/ 1, 2, 3, 4, 3 /)
  call matrix_chain_dynamic ( n, dims, cost )
  write ( *, '(a)' ) ''
  write ( *, '(a,i2)' ) '  n = ', n
  call i4vec_transpose_print ( n + 1, dims, '  dims():' )
  write ( *, '(a,i8)' ) '  minimal cost = ', cost
  write ( *, '(a,i4)' ) '  Number of possible orderings = ', catalan_number ( n - 1 )
  deallocate ( dims )

  n = 2
  allocate ( dims(1:n+1) )
  dims = (/ 10, 20, 30 /)
  call matrix_chain_dynamic ( n, dims, cost )
  write ( *, '(a)' ) ''
  write ( *, '(a,i2)' ) '  n = ', n
  call i4vec_transpose_print ( n + 1, dims, '  dims():' )
  write ( *, '(a,i8)' ) '  minimal cost = ', cost
  write ( *, '(a,i4)' ) '  Number of possible orderings = ', catalan_number ( n - 1 )
  deallocate ( dims )

  n = 3
  allocate ( dims(1:n+1) )
  dims = (/ 10, 30, 5, 60 /)
  call matrix_chain_dynamic ( n, dims, cost )
  write ( *, '(a)' ) ''
  write ( *, '(a,i2)' ) '  n = ', n
  call i4vec_transpose_print ( n + 1, dims, '  dims():' )
  write ( *, '(a,i8)' ) '  minimal cost = ', cost
  write ( *, '(a,i4)' ) '  Number of possible orderings = ', catalan_number ( n - 1 )
  deallocate ( dims )

  n = 1
  allocate ( dims(1:n+1) )
  dims = (/ 10, 20 /)
  call matrix_chain_dynamic ( n, dims, cost )
  write ( *, '(a)' ) ''
  write ( *, '(a,i2)' ) '  n = ', n
  call i4vec_transpose_print ( n + 1, dims, '  dims():' )
  write ( *, '(a,i8)' ) '  minimal cost = ', cost
  write ( *, '(a,i4)' ) '  Number of possible orderings = ', catalan_number ( n - 1 )
  deallocate ( dims )

  n = 0
  allocate ( dims(1:n+1) )
  dims = (/ 40 /)
  call matrix_chain_dynamic ( n, dims, cost )
  write ( *, '(a)' ) ''
  write ( *, '(a,i2)' ) '  n = ', n
  call i4vec_transpose_print ( n + 1, dims, '  dims():' )
  write ( *, '(a,i8)' ) '  minimal cost = ', cost
  write ( *, '(a,i4)' ) '  Number of possible orderings = ', catalan_number ( n - 1 )
  deallocate ( dims )
!
!  Terminate.
!
  write ( *, '(a)' ) ''
  write ( *, '(a)' ) 'matrix_chain_dynamic_test():'
  write ( *, '(a)' ) '  Normal end of execution.'
  write ( *, '(a)' ) ''
  call timestamp ( )

  stop 0
end
subroutine i4vec_transpose_print ( n, a, title )

!*****************************************************************************80
!
!! i4vec_transpose_print() prints an I4VEC "transposed".
!
!  Discussion:
!
!    An I4VEC is a vector of I4's.
!
!  Example:
!
!    A = (/ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 /)
!    TITLE = 'My vector:  '
!
!    My vector:
!        1    2    3    4    5
!        6    7    8    9   10
!       11
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    02 June 2015
!
!  Author:
!
!    John Burkardt
!
!  Input:
!
!    integer N, the number of components of the vector.
!
!    integer A(N), the vector to be printed.
!
!    character ( len = * ) TITLE, a title.
!
  implicit none

  integer n

  integer a(n)
  integer ihi
  integer ilo
  character ( len = * ) title

  if ( 0 < len_trim ( title ) ) then
    write ( *, '(a)' ) ' '
    write ( *, '(a)' ) trim ( title )
  end if

  if ( 0 < n ) then
    do ilo = 1, n, 5
      ihi = min ( ilo + 5 - 1, n )
      write ( *, '(5i12)' ) a(ilo:ihi)
    end do
  else
    write ( *, '(a)' ) '  (empty vector)'
  end if

  return
end
subroutine timestamp ( )

!*****************************************************************************80
!
!! timestamp() prints the current YMDHMS date as a time stamp.
!
!  Example:
!
!    31 May 2001   9:45:54.872 AM
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    15 August 2021
!
!  Author:
!
!    John Burkardt
!
  implicit none

  character ( len = 8 ) ampm
  integer d
  integer h
  integer m
  integer mm
  character ( len = 9 ), parameter, dimension(12) :: month = (/ &
    'January  ', 'February ', 'March    ', 'April    ', &
    'May      ', 'June     ', 'July     ', 'August   ', &
    'September', 'October  ', 'November ', 'December ' /)
  integer n
  integer s
  integer values(8)
  integer y

  call date_and_time ( values = values )

  y = values(1)
  m = values(2)
  d = values(3)
  h = values(5)
  n = values(6)
  s = values(7)
  mm = values(8)

  if ( h < 12 ) then
    ampm = 'AM'
  else if ( h == 12 ) then
    if ( n == 0 .and. s == 0 ) then
      ampm = 'Noon'
    else
      ampm = 'PM'
    end if
  else
    h = h - 12
    if ( h < 12 ) then
      ampm = 'PM'
    else if ( h == 12 ) then
      if ( n == 0 .and. s == 0 ) then
        ampm = 'Midnight'
      else
        ampm = 'AM'
      end if
    end if
  end if

  write ( *, '(i2.2,1x,a,1x,i4,2x,i2,a1,i2.2,a1,i2.2,a1,i3.3,1x,a)' ) &
    d, trim ( month(m) ), y, h, ':', n, ':', s, '.', mm, trim ( ampm )

  return
end