#! /usr/bin/env python
#
def vector_next ( n, x_min, x_max, x, more ):

#*****************************************************************************80
#
## VECTOR_NEXT returns the "next" integer vector between two ranges.
#
#  Discussion:
#
#    We consider all integer vectors of dimension N satisfying:
#
#      X_MIN(1:N) <= X(1:N) <= X_MAX(1:N).
#
#    This routine returns, one at a time, and in right-to-left
#    lexicographic order, all these vectors.
#
#  Example:
#
#    N = 3
#    X_MIN:   2   2   0
#    X_MAX:   4   3   1
#
#    #  X(1)  X(2)  X(3)
#
#    1    2     2     0
#    2    3     2     0
#    3    4     2     0
#    4    2     3     0
#    5    3     3     0
#    6    4     3     0
#    7    2     2     1
#    8    3     2     1
#    9    4     2     1
#   10    2     3     1
#   11    3     3     1
#   12    4     3     1
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    08 May 2015
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer N, the number of components in the vector.
#
#    Input, integer X_MIN(N), X_MAX(N), the minimum and maximum
#    values allowed in each component.
#
#    Input, integer X(N).  On first call, with
#    MORE = FALSE, the input value of X is not important.  On subsequent calls,
#    the input value of X should be the output value from the previous call.
#
#    Input, logical MORE.  On input, if the user has set MORE
#    FALSE, the user is requesting the initiation of a new sequence
#    of values.  If MORE is TRUE, then the user is requesting "more"
#    values in the current sequence.
#
#    Output, integer X(N).  If MORE = TRUE, the value of X will be the "next"
#    vector in the reverse lexicographical list of vectors.  However, on
#    output with MORE = FALSE, the vector X is meaningless, because there
#    are no more vectors in the list.
#
#    Output, logical MORE.  If MORE is TRUE,
#    then another value was found and returned in X, but if MORE is
#    FALSE, then there are no more values in the sequence, and X is
#    NOT the next value.
#
  if ( not more ):

    for i in range ( 0, n ):
      x[i] = x_min[i]
    more = True

  else:

    i = 0

    while ( True ):

      if ( x[i] < x_max[i] ):
        x[i] = x[i] + 1
        more = True
        break
      else:
        x[i] = x_min[i]
        i = i + 1
        if ( n <= i ):
          more = False
          break

  return x, more

def vector_next_test ( ):

#*****************************************************************************80
#
## VECTOR_NEXT_TEST tests VECTOR_NEXT.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    08 May 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform

  n_max = 3

  x_min = np.array ( [ 1, 4, 3 ] )
  x_max = np.array ( [ 2, 6, 4 ] )

  print ( '' )
  print ( 'VECTOR_NEXT_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  VECTOR_NEXT generates all vectors X such that:' )
  print ( '  X_MIN(1:N) <= X(1:N) <= X_MAX(1:N)' )

  for n in range ( 2, n_max + 1 ):

    more = False

    print ( '' )
    print ( '  X_MIN: ', end = '' )
    for i in range ( 0, n ):
      print ( '  %4d' % ( x_min[i] ), end = '' )
    print ( '' )

    k = 0
    x = np.zeros ( n )

    while ( True ):

      x, more = vector_next ( n, x_min, x_max, x, more )

      if ( not more ):
        break

      k = k + 1

      print ( '  X(%2d): ' % ( k ), end = '' )
      for i in range ( 0, n ):
        print ( '  %4d' % ( x[i] ), end = '' )
      print ( '' )

    print ( '  X_MAX: ', end = '' )
    for i in range ( 0, n ):
      print ( '  %4d' % ( x_max[i] ), end = '' )
    print ( '' )
#
#  Terminate.
#
  print ( '' )
  print ( 'VECTOR_NEXT_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  vector_next_test ( )
  timestamp ( )