# include <cmath>
# include <cstdlib>
# include <ctime>
# include <iomanip>
# include <iostream>

using namespace std;

# include "toms515.hpp"

//****************************************************************************80

int binom ( int n, int k )

//****************************************************************************80
//
//  Purpose:
//
//    BINOM computes the binomial coefficient.
//
//  Discussion:
//
//    This is ACM algorithm 160 translated to Fortran.
//
//    It calculates the number of combinations of N things taken K at a time.
//
//  Modified:
//
//    01 April 2016
//
//  Author:
//
//    Bill Buckles, Matthew Lybanon
//
//  Reference:
//
//    Bill Buckles, Matthew Lybanon,
//    Algorithm 515: Generation of a Vector from the Lexicographical Index,
//    ACM Transactions on Mathematical Software,
//    Volume 3, Number 2, June 1977, pages 180-182.
//
//  Parameters:
//
//    Input, int N, K, the parameters for the binomial 
//    coefficient.
//
//    Output, int BINOM, the binomial coefficient.
//
{
  int i;
  int k1;
  int p;
  int r;

  k1 = k;
  p = n - k1;

  if ( k1 < p )
  {
    p = k1;
    k1 = n - p;
  }

  if ( p == 0 )
  {
    r = 1;
  }
  else
  {
    r = k1 + 1;
  }

  for ( i = 2; i <= p; i++ )
  {
    r = ( r * ( k1 + i ) ) / i;
  }

  return r;
}
//****************************************************************************80

int *comb ( int n, int p, int l )

//****************************************************************************80
//
//  Purpose:
//
//    COMB selects a subset of order P from a set of order N.
//
//  Discussion:
//
//    This subroutine finds the combination set of N things taken
//    P at a time for a given lexicographic index.
//
//  Modified:
//
//    01 April 2016
//
//  Author:
//
//    Bill Buckles, Matthew Lybanon
//
//  Reference:
//
//    Bill Buckles, Matthew Lybanon,
//    Algorithm 515: Generation of a Vector from the Lexicographical Index,
//    ACM Transactions on Mathematical Software,
//    Volume 3, Number 2, June 1977, pages 180-182.
//
//  Parameters:
//
//    Input, int N, the number of things in the set.
//
//    Input, int P, the number of things in each combination.
//    0 < P < N.
//
//    Input, int L, the lexicographic index of the 
//    desired combination.  1 <= L <= choose(N,P).
//
//    Output, int COMB[P], the combination set.
//
{
  int *c;
  int i;
  int k;
  int p1;
  int r;

  c = new int[p];
//
//  Special case: P = 1
//
  if ( p == 1 )
  {
    c[0] = l;
    return c;
  }
//
//  Initialize lower bound index.
//
  k = 0;
//
//  Select elements in ascending order.
//
  p1 = p - 1;
  c[0] = 0;

  for ( i = 1; i <= p1; i++ )
  {
//
//  Update lower bound as the previously selected element.
//
    if ( 1 < i )
    {
      c[i-1] = c[i-2];
    }
//
//  Check validity of each entry.
//
    for ( ; ; )
    {
      c[i-1] = c[i-1] + 1;
      r = binom ( n - c[i-1], p - i );
      k = k + r;

      if ( l <= k )
      {
        break;
      }
    }
    k = k - r;
  }

  c[p-1] = c[p1-1] + l - k;

  return c;
}
//****************************************************************************80

bool i4_choose_check ( int n, int k )

//****************************************************************************80
//
//  Purpose:
//
//    I4_CHOOSE_CHECK reports whether the binomial coefficient can be computed.
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    28 March 2016
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, K, the binomial parameters.
//
//    Output, bool I4_CHOOSE_CHECK is:
//    TRUE, if C(N,K) < maximum integer.
//    FALSE, otherwise.
//
{
  bool check;
  double choose_nk_log;
  const int i4_huge = 2147483647;
  double i4_huge_log;

  i4_huge_log = log ( ( double ) ( i4_huge ) );

  choose_nk_log = 
      lgamma ( ( double ) ( n + 1 ) ) 
    - lgamma ( ( double ) ( k + 1 ) ) 
    - lgamma ( ( double ) ( n - k + 1 ) );

  check = ( choose_nk_log < i4_huge_log );
        
  return check;
}
//****************************************************************************80

int i4_uniform_ab ( int a, int b, int &seed )

//****************************************************************************80
//
//  Purpose:
//
//    I4_UNIFORM_AB returns a scaled pseudorandom I4 between A and B.
//
//  Discussion:
//
//    The pseudorandom number should be uniformly distributed
//    between A and B.
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    02 October 2012
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    Paul Bratley, Bennett Fox, Linus Schrage,
//    A Guide to Simulation,
//    Second Edition,
//    Springer, 1987,
//    ISBN: 0387964673,
//    LC: QA76.9.C65.B73.
//
//    Bennett Fox,
//    Algorithm 647:
//    Implementation and Relative Efficiency of Quasirandom
//    Sequence Generators,
//    ACM Transactions on Mathematical Software,
//    Volume 12, Number 4, December 1986, pages 362-376.
//
//    Pierre L'Ecuyer,
//    Random Number Generation,
//    in Handbook of Simulation,
//    edited by Jerry Banks,
//    Wiley, 1998,
//    ISBN: 0471134031,
//    LC: T57.62.H37.
//
//    Peter Lewis, Allen Goodman, James Miller,
//    A Pseudo-Random Number Generator for the System/360,
//    IBM Systems Journal,
//    Volume 8, Number 2, 1969, pages 136-143.
//
//  Parameters:
//
//    Input, int A, B, the limits of the interval.
//
//    Input/output, int &SEED, the "seed" value, which should NOT be 0.
//    On output, SEED has been updated.
//
//    Output, int I4_UNIFORM, a number between A and B.
//
{
  int c;
  const int i4_huge = 2147483647;
  int k;
  float r;
  int value;

  if ( seed == 0 )
  {
    cerr << "\n";
    cerr << "I4_UNIFORM_AB - Fatal error!\n";
    cerr << "  Input value of SEED = 0.\n";
    exit ( 1 );
  }
//
//  Guarantee A <= B.
//
  if ( b < a )
  {
    c = a;
    a = b;
    b = c;
  }

  k = seed / 127773;

  seed = 16807 * ( seed - k * 127773 ) - k * 2836;

  if ( seed < 0 )
  {
    seed = seed + i4_huge;
  }

  r = ( float ) ( seed ) * 4.656612875E-10;
//
//  Scale R to lie between A-0.5 and B+0.5.
//
  r = ( 1.0 - r ) * ( ( float ) a - 0.5 ) 
    +         r   * ( ( float ) b + 0.5 );
//
//  Use rounding to convert R to an integer between A and B.
//
  value = round ( r );
//
//  Guarantee A <= VALUE <= B.
//
  if ( value < a )
  {
    value = a;
  }
  if ( b < value )
  {
    value = b;
  }

  return value;
}
//****************************************************************************80

void timestamp ( )

//****************************************************************************80
//
//  Purpose:
//
//    TIMESTAMP prints the current YMDHMS date as a time stamp.
//
//  Example:
//
//    31 May 2001 09:45:54 AM
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    08 July 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    None
//
{
# define TIME_SIZE 40

  static char time_buffer[TIME_SIZE];
  const struct std::tm *tm_ptr;
  std::time_t now;

  now = std::time ( NULL );
  tm_ptr = std::localtime ( &now );

  std::strftime ( time_buffer, TIME_SIZE, "%d %B %Y %I:%M:%S %p", tm_ptr );

  std::cout << time_buffer << "\n";

  return;
# undef TIME_SIZE
}