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

using namespace std;

# include "unicycle.hpp"

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

int i4_factorial ( int n )

//****************************************************************************80
//
//  Purpose:
//
//    I4_FACTORIAL computes the factorial of N.
//
//  Discussion:
//
//    factorial ( N ) = product ( 1 <= I <= N ) I
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    26 June 2008
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the argument of the factorial function.
//    If N is less than 1, the function value is returned as 1.
//    0 <= N <= 13 is required.
//
//    Output, int I4_FACTORIAL, the factorial of N.
//
{
  int i;
  int value;

  value = 1;

  if ( 13 < n )
  {
    cerr << "I4_FACTORIAL - Fatal error!\n";
    cerr << "  I4_FACTORIAL(N) cannot be computed as an integer\n";
    cerr << "  for 13 < N.\n";
    cerr << "  Input value N = " << n << "\n";
    exit ( 1 );
  }

  for ( i = 1; i <= n; i++ )
  {
    value = value * i;
  }

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

int i4_max ( int i1, int i2 )

//****************************************************************************80
//
//  Purpose:
//
//    I4_MAX returns the maximum of two I4's.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    13 October 1998
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int I1, I2, are two integers to be compared.
//
//    Output, int I4_MAX, the larger of I1 and I2.
//
{
  int value;

  if ( i2 < i1 )
  {
    value = i1;
  }
  else
  {
    value = i2;
  }
  return value;
}
//****************************************************************************80

int i4_min ( int i1, int i2 )

//****************************************************************************80
//
//  Purpose:
//
//    I4_MIN returns the minimum of two I4's.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    13 October 1998
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int I1, I2, two integers to be compared.
//
//    Output, int I4_MIN, the smaller of I1 and I2.
//
{
  int value;

  if ( i1 < i2 )
  {
    value = i1;
  }
  else
  {
    value = i2;
  }
  return value;
}
//****************************************************************************80

int i4_modp ( int i, int j )

//****************************************************************************80
//
//  Purpose:
//
//    I4_MODP returns the nonnegative remainder of I4 division.
//
//  Discussion:
//
//    If
//      NREM = I4_MODP ( I, J )
//      NMULT = ( I - NREM ) / J
//    then
//      I = J * NMULT + NREM
//    where NREM is always nonnegative.
//
//    The MOD function computes a result with the same sign as the
//    quantity being divided.  Thus, suppose you had an angle A,
//    and you wanted to ensure that it was between 0 and 360.
//    Then mod(A,360) would do, if A was positive, but if A
//    was negative, your result would be between -360 and 0.
//
//    On the other hand, I4_MODP(A,360) is between 0 and 360, always.
//
//        I         J     MOD  I4_MODP   I4_MODP Factorization
//
//      107        50       7       7    107 =  2 *  50 + 7
//      107       -50       7       7    107 = -2 * -50 + 7
//     -107        50      -7      43   -107 = -3 *  50 + 43
//     -107       -50      -7      43   -107 =  3 * -50 + 43
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    26 May 1999
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int I, the number to be divided.
//
//    Input, int J, the number that divides I.
//
//    Output, int I4_MODP, the nonnegative remainder when I is
//    divided by J.
//
{
  int value;

  if ( j == 0 )
  {
    cerr << "\n";
    cerr << "I4_MODP - Fatal error!\n";
    cerr << "  I4_MODP ( I, J ) called with J = " << j << "\n";
    exit ( 1 );
  }

  value = i % j;

  if ( value < 0 )
  {
    value = value + abs ( j );
  }

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

int i4_wrap ( int ival, int ilo, int ihi )

//****************************************************************************80
//
//  Purpose:
//
//    I4_WRAP forces an I4 to lie between given limits by wrapping.
//
//  Example:
//
//    ILO = 4, IHI = 8
//
//    I   Value
//
//    -2     8
//    -1     4
//     0     5
//     1     6
//     2     7
//     3     8
//     4     4
//     5     5
//     6     6
//     7     7
//     8     8
//     9     4
//    10     5
//    11     6
//    12     7
//    13     8
//    14     4
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    19 August 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int IVAL, an integer value.
//
//    Input, int ILO, IHI, the desired bounds for the integer value.
//
//    Output, int I4_WRAP, a "wrapped" version of IVAL.
//
{
  int jhi;
  int jlo;
  int value;
  int wide;

  jlo = i4_min ( ilo, ihi );
  jhi = i4_max ( ilo, ihi );

  wide = jhi + 1 - jlo;

  if ( wide == 1 )
  {
    value = jlo;
  }
  else
  {
    value = jlo + i4_modp ( ival - jlo, wide );
  }

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

void i4vec_indicator ( int n, int a[] )

//****************************************************************************80
//
//  Purpose:
//
//    I4VEC_INDICATOR sets an I4VEC to the indicator vector.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    25 February 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of elements of A.
//
//    Output, int A[N], the initialized array.
//
{
  int i;

  for ( i = 0; i < n; i++ )
  {
    a[i] = i + 1;
  }
  return;
}
//****************************************************************************80

int *i4vec_indicator_new ( int n )

//****************************************************************************80
//
//  Purpose:
//
//    I4VEC_INDICATOR_NEW sets an I4VEC to the indicator vector.
//
//  Discussion:
//
//    An I4VEC is a vector of I4's.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    03 June 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of elements of A.
//
//    Output, int I4VEC_INDICATOR_NEW[N], the array.
//
{
  int *a;
  int i;

  a = new int[n];

  for ( i = 0; i < n; i++ )
  {
    a[i] = i + 1;
  }
  return a;
}
//****************************************************************************80

void i4vec_reverse ( int n, int a[] )

//****************************************************************************80
//
//  Purpose:
//
//    I4VEC_REVERSE reverses the elements of an I4VEC.
//
//  Discussion:
//
//    An I4VEC is a vector of I4's.
//
//  Example:
//
//    Input:
//
//      N = 5,
//      A = ( 11, 12, 13, 14, 15 ).
//
//    Output:
//
//      A = ( 15, 14, 13, 12, 11 ).
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    22 September 2005
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of entries in the array.
//
//    Input/output, int A[N], the array to be reversed.
//
{
  int i;
  int j;

  for ( i = 0; i < n / 2; i++ )
  {
    j        = a[i];
    a[i]     = a[n-1-i];
    a[n-1-i] = j;
  }

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

void perm_check ( int n, int p[] )

//****************************************************************************80
// 
//  Purpose:
//
//    PERM_CHECK checks a representation of a permutation.
// 
//  Discussion:
// 
//    The routine is given N and P, a vector of length N.
//    P is a legal represention of a permutation of the integers from
//    1 to N if and only if every integer from 1 to N occurs
//    as a value of P(I) for some I between 1 and N.
// 
//  Licensing:
// 
//    This code is distributed under the MIT license.
// 
//  Modified:
// 
//    25 July 2011
// 
//  Author:
// 
//    John Burkardt
// 
//  Parameters:
// 
//    Input, int N, the number of values being permuted.
//    N must be positive.
// 
//    Input, int P[N], the array to check.
// 
{
  int i;
  int ifind;
  int iseek;

  if ( n < 1 )
  {
    cerr << "\n";
    cerr << "PERM_CHECK - Fatal error!\n";
    cerr << "  Input N = " << n << " < 1.\n";
    exit ( 1 );
  }

  for ( i = 0; i < n; i++ )
  {
    if ( p[i] < 1 || n < p[i] )
    {
      cerr << "\n";
      cerr << "PERM_CHECK - Fatal error!\n";
      cerr << "  P[" << i << "] = " << p[i] << "\n";
      cerr << "  but 1 <= p[i] <= " << n << " is required.\n";
      exit ( 1 );
    }
  }

  for ( iseek = 1; iseek <= n; iseek++ )
  {
    ifind = -1;
    for ( i = 0; i < n; i++ )
    {
      if ( p[i] == iseek )
      {
        ifind = i;
        break;
      }
    }

    if ( ifind == -1 )
    {
      cerr << "\n";
      cerr << "PERM_CHECK - Fatal error!\n";
      cerr << "  Could not locate the value " << iseek << "\n";
      exit ( 1 );
    }
  }
  return;
}
//****************************************************************************80

int perm_enum ( int n )

//****************************************************************************80
// 
//  Purpose:
//
//    PERM_ENUM enumerates the permutations on N digits.
// 
//  Licensing:
// 
//    This code is distributed under the MIT license.
// 
//  Modified:
// 
//    24 July 2011
// 
//  Author:
// 
//    John Burkardt
// 
//  Parameters:
// 
//    Input, int N, the number of values being permuted.
//    N must be nonnegative.
// 
//    Output, int PERM_ENUM, the number of distinct elements.
// 
{
  int value;

  value = i4_factorial ( n );

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

int *perm_inverse ( int n, int p[] )

//****************************************************************************80
// 
//  Purpose:
//
//    PERM_INVERSE computes the inverse of a permutation.
// 
//  Licensing:
// 
//    This code is distributed under the MIT license.
// 
//  Modified:
// 
//    25 July 2011
// 
//  Author:
// 
//    John Burkardt
// 
//  Reference:
// 
//    Donald Kreher, Douglas Simpson,
//    Combinatorial Algorithms,
//    CRC Press, 1998,
//    ISBN: 0-8493-3988-X,
//    LC: QA164.K73.
// 
//  Parameters:
// 
//    Input, int N, the number of values being permuted.
//    N must be positive.
// 
//    Input, int P[N], describes the permutation.
//    P(I) is the item which is permuted into the I-th place
//    by the permutation.
// 
//    Output, int PERM_INVERSE[N], the inverse permutation.
// 
{
  int i;
  int *pinv;
// 
//  Check.
// 
  perm_check ( n, p );

  pinv = new int[n];

  for ( i = 0; i < n; i++ )
  {
    pinv[p[i]-1] = i + 1;
  }

  return pinv;
}
//****************************************************************************80

bool perm_is_unicycle ( int n, int p[] )

//****************************************************************************80
//
//  Purpose:
//
//    PERM_IS_UNICYCLE is TRUE if a permutation is a unicycle.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    16 June 2012
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of objects in the permutation.
//
//    Input, int P[N], the permutation.
//
//    Output, bool PERM_IS_UNICYCLE, is TRUE if the permutation is a unicycle.
//
{
  int i;
  int j;
  bool value;

  value = false;

  perm_check ( n, p );
//
//  From 1, you must be able to take N-1 steps without reaching 1...
//
  i = 1;
  for ( j = 1; j <= n - 1; j++ )
  {
    i = p[i-1];
    if ( i == 1 )
    {
      return value;
    }
  }
//
//  ...and the N-th step must reach 1.
//
  i = p[i-1];
  if ( i == 1 )
  {
    value = true;
  }

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

void perm_lex_next ( int n, int p[], int &rank )

//****************************************************************************80
// 
//  Purpose:
//
//    PERM_LEX_NEXT computes the lexicographic permutation successor.
// 
//  Example:
// 
//    RANK  Permutation
// 
//       0  1 2 3 4
//       1  1 2 4 3
//       2  1 3 2 4
//       3  1 3 4 2
//       4  1 4 2 3
//       5  1 4 3 2
//       6  2 1 3 4
//       ...
//      23  4 3 2 1
// 
//  Licensing:
// 
//    This code is distributed under the MIT license.
// 
//  Modified:
// 
//    26 July 2011
// 
//  Author:
// 
//    John Burkardt
// 
//  Reference:
// 
//    Donald Kreher, Douglas Simpson,
//    Combinatorial Algorithms,
//    CRC Press, 1998,
//    ISBN: 0-8493-3988-X,
//    LC: QA164.K73.
// 
//  Parameters:
// 
//    Input, int N, the number of values being permuted.
//    N must be positive.
// 
//    Input/output, int P[N], describes the permutation.
//    P(I) is the item which is permuted into the I-th place
//    by the permutation.
// 
//    Input/output, int &RANK, the rank.
//    If RANK = -1 on input, then the routine understands that this is
//    the first call, and that the user wishes the routine to supply
//    the first element in the ordering, which has RANK = 0.
//    In general, the input value of RANK is increased by 1 for output,
//    unless the very last element of the ordering was input, in which
//    case the output value of RANK is 0.
// 
{
  int i;
  int j;
  int temp;
// 
//  Return the first element.
// 
  if ( rank == -1 )
  {
    i4vec_indicator ( n, p );
    rank = 0;
    return;
  }
// 
//  Check.
// 
  perm_check ( n, p );
// 
//  Seek I, the highest index for which the next element is bigger.
// 
  i = n - 1;

  for ( ; ; )
  {
    if ( i <= 0 )
    {
      break;
    }

    if ( p[i-1] <= p[i] )
    {
      break;
    }
    i = i - 1;
  }
// 
//  If no I could be found, then we have reach the final permutation,
//  N, N-1, ..., 2, 1.  Time to start over again.
// 
  if ( i == 0 )
  {
    i4vec_indicator ( n, p );
    rank = -1;
  }
  else
  {
// 
//  Otherwise, look for the the highest index after I whose element
//  is bigger than I''s.  We know that I+1 is one such value, so the
//  loop will never fail.
// 
    j = n;
    while ( p[j-1] < p[i-1] )
    {
      j = j - 1;
    }
// 
//  Interchange elements I and J.
// 
    temp = p[i-1];
    p[i-1] = p[j-1];
    p[j-1] = temp;
// 
//  Reverse the elements from I+1 to N.
// 
    i4vec_reverse ( n - i, p+i );

    rank = rank + 1;
  }

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

int perm_lex_rank ( int n, int p[] )

//****************************************************************************80
// 
//  Purpose:
//
//    PERM_LEX_RANK computes the lexicographic rank of a permutation.
// 
//  Discussion:
// 
//    The original code altered the input permutation.
// 
//  Licensing:
// 
//    This code is distributed under the MIT license.
// 
//  Modified:
// 
//    25 July 2011
// 
//  Author:
// 
//    John Burkardt
// 
//  Reference:
// 
//    Donald Kreher, Douglas Simpson,
//    Combinatorial Algorithms,
//    CRC Press, 1998,
//    ISBN: 0-8493-3988-X,
//    LC: QA164.K73.
// 
//  Parameters:
// 
//    Input, int N, the number of values being permuted.
//    N must be positive.
// 
//    Input, int P[N], describes the permutation.
//    P[I] is the item which is permuted into the I-th place
//    by the permutation.
// 
//    Output, int PERM_LEX_RANK, the rank of the permutation.
// 
{
  int i;
  int j;
  int *pcopy;
  int rank;
// 
//  Check.
// 
  perm_check ( n, p );

  rank = 0;
  pcopy = new int[n];

  for ( i = 0; i < n; i++ )
  {
    pcopy[i] = p[i];
  }

  for ( j = 0; j < n; j++ )
  {
    rank = rank + ( pcopy[j] - 1 ) * i4_factorial ( n - 1 - j );
    for ( i = j + 1; i < n; i++ )
    {
      if ( pcopy[j] < pcopy[i] )
      {
        pcopy[i] = pcopy[i] - 1;
      }
    }
  }
  delete [] pcopy;

  return rank;
}
//****************************************************************************80

int *perm_lex_unrank ( int n, int rank )

//****************************************************************************80
// 
//  Purpose:
//
//    PERM_LEX_UNRANK computes the permutation of given lexicographic rank.
// 
//  Licensing:
// 
//    This code is distributed under the MIT license.
// 
//  Modified:
// 
//    17 June 2012
// 
//  Author:
// 
//    John Burkardt
// 
//  Reference:
// 
//    Donald Kreher, Douglas Simpson,
//    Combinatorial Algorithms,
//    CRC Press, 1998,
//    ISBN: 0-8493-3988-X,
//    LC: QA164.K73.
// 
//  Parameters:
// 
//    Input, int N, the number of values being permuted.
//    N must be positive.
// 
//    Input, int RANK, the rank of the permutation.
// 
//    Output, int PERM_LEX_UNRANK[N], describes the permutation.
// 
{
  int d;
  int i;
  int j;
  int nperm;
  int *p;
  int rank_copy;
// 
//  Check.
// 
  if ( n < 1 )
  {
    cout << "\n";
    cout << "PERM_LEX_UNRANK - Fatal error!\n";
    cout << "  Input N is illegal.\n";
    exit ( 1 );
  }

  nperm = perm_enum ( n );

  if ( rank < 0 || nperm < rank )
  {
    cout << "\n";
    cout << "PERM_LEX_UNRANK - Fatal error!\n";
    cout << "  The input rank is illegal.\n";
    exit ( 1 );
  }

  rank_copy = rank;

  p = new int[n];

  p[n-1] = 1;

  for ( j = 1; j <= n - 1; j++ )
  {
    d = ( rank_copy % i4_factorial ( j + 1 ) ) / i4_factorial ( j );
    rank_copy = rank_copy - d * i4_factorial ( j );
    p[n-j-1] = d + 1;

    for ( i = n - j + 1; i <= n; i++ )
    {
      if ( d < p[i-1] )
      {
        p[i-1] = p[i-1] + 1;
      }
    }
  }
  return p;
}
//****************************************************************************80

void perm_print ( int n, int p[], string title )

//****************************************************************************80
//
//  Purpose:
//
//    PERM_PRINT prints a permutation.
//
//  Discussion:
//
//    The permutation is assumed to be zero-based.
//
//  Example:
//
//    Input:
//
//      P = 6 1 2 0 4 2 5
//
//    Printed output:
//
//      "This is the permutation:"
//
//      0 1 2 3 4 5 6
//      6 1 2 0 4 2 5
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    17 June 2012
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of objects permuted.
//
//    Input, int P[N], the permutation, in standard index form.
//
//    Input, string TITLE, a title.
//    If no title is supplied, then only the permutation is printed.
//
{
  int i;
  int ihi;
  int ilo;
  int inc = 20;

  if ( s_len_trim ( title ) != 0 )
  {
    cout << "\n";
    cout << title << "\n";

    for ( ilo = 0; ilo < n; ilo = ilo + inc )
    {
      ihi = ilo + inc;
      if ( n < ihi ) 
      {
        ihi = n;
      }
      cout << "\n";
      cout << "  ";
      for ( i = ilo; i < ihi; i++ )
      {
        cout << setw(4) << i + 1;
      }
      cout << "\n";
      cout << "  ";
      for ( i = ilo; i < ihi; i++ )
      {
        cout << setw(4) << p[i];
      }
      cout << "\n";
    }
  }
  else
  {
    for ( ilo = 0; ilo < n; ilo = ilo + inc )
    {
      ihi = ilo + inc;
      if ( n < ihi ) 
      {
        ihi = n;
      }
      cout << "  ";
      for ( i = ilo; i < ihi; i++ )
      {
        cout << setw(4) << p[i];
      }
      cout << "\n";
    }
  }

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

int *perm_random ( int n, int &seed )

//****************************************************************************80
//
//  Purpose:
//
//    PERM_RANDOM selects a random permutation of N objects.
//
//  Discussion:
//
//    The routine assumes the objects are labeled 1, 2, ... N.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    12 May 2002
//
//  Author:
//
//    John Burkardt.
//
//  Reference:
//
//    Albert Nijenhuis, Herbert Wilf,
//    Combinatorial Algorithms for Computers and Calculators,
//    Second Edition,
//    Academic Press, 1978,
//    ISBN: 0-12-519260-6,
//    LC: QA164.N54.
//
//  Parameters:
//
//    Input, int N, the number of objects to be permuted.
//
//    Input/output, int &SEED, a seed for the random number
//    generator.
//
//    Output, int PERM_RANDOM[N], a permutation of ( 1, 2, ..., N ),
//    in standard index form.
//
{
  int i;
  int j;
  int *p;
  int t;

  p = i4vec_indicator_new ( n );

  for ( i = 0; i < n - 1; i++ )
  {
    j = i4_uniform_ab ( i, n - 1, seed );

    t = p[i];
    p[i] = p[j];
    p[j] = t;
  }

  return p;
}
//****************************************************************************80

int s_len_trim ( string s )

//****************************************************************************80
//
//  Purpose:
//
//    S_LEN_TRIM returns the length of a string to the last nonblank.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    05 July 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, string S, a string.
//
//    Output, int S_LEN_TRIM, the length of the string to the last nonblank.
//    If S_LEN_TRIM is 0, then the string is entirely blank.
//
{
  int n;

  n = s.length ( );

  while ( 0 < n )
  {
    if ( s[n-1] != ' ' )
    {
      return n;
    }
    n = n - 1;
  }

  return n;
}
//****************************************************************************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
}
//****************************************************************************80

void unicycle_check ( int n, int u[] )

//****************************************************************************80
//
//  Purpose:
//
//    UNICYCLE_CHECK checks that a vector represents a unicycle.
//
//  Discussion:
//
//    A unicycle is a permutation with a single cycle.  This might be called
//    a cyclic permutation, except that that name is used with at least two
//    other meanings.  So, to be clear, a unicycle is a permutation of N
//    objects in which each object is returned to itself precisely after 
//    N applications of the permutation.
//
//    This routine verifies that each of the integers from 1
//    to N occurs among the N entries of the permutation.
//
//    Any permutation of the integers 1 to N describes a unicycle.
//    The permutation ( 3, 4, 2, 1 ) indicates that the unicycle
//    sends 3 to 4, 4 to 2, 2 to 1 and 1 to 3.  This is the sequential
//    description of a unicycle.
//
//    The standard sequence "rotates" the permutation so that it begins
//    with 1.  The above sequence becomes a standard sequence when
//    written as ( 1, 3, 4, 2 ).
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    17 June 2012
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of entries.
//
//    Input, int U[N], the unicycle sequence vector
//
{
  bool error;
  int i;
  int iseek;

  for ( iseek = 1; iseek <= n; iseek++ )
  {
    error = true;

    for ( i = 0; i < n; i++ )
    {
      if ( u[i] == iseek )
      {
        error = false;
        break;
      }
    }

    if ( error )
    {
      cout << "\n";
      cout << "\n";
      cout << "UNICYCLE_CHECK - Fatal error!\n";
      cout << "  The input array does not represent\n";
      cout << "  a unicycle.  In particular, the\n";
      cout << "  array is missing the value " << iseek << "\n";
      exit ( 1 );
    }
  }
  return;
}
//****************************************************************************80

int unicycle_enum ( int n )

//****************************************************************************80
//
//  Purpose:
//
//    UNICYCLE_ENUM enumerates the unicycles.
//
//  Discussion:
//
//    Each standard sequence corresponds to a unique unicycle.  Since the
//    first element of a standard sequence is always 1, the number of standard
//    sequences, and hence the number of unicycles, is (n-1)!.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    17 June 2012
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the order of the unicyle.
//
//    Output, int UNICYCLE_ENUM, the number of unicycles.
//
{
  int num;

  num = i4_factorial ( n - 1 );

  return num;
}
//****************************************************************************80

int *unicycle_index ( int n, int u[] )

//****************************************************************************80
//
//  Purpose:
//
//    UNICYCLE_INDEX returns the index form of a unicycle.
//
//  Example:
//
//    N = 4
//
//    U       = 1 3 4 2
//    U_INDEX = 3 1 4 2
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    17 June 2012
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the order of the unicycles.
//
//    Input, int U[N], the unicycle sequence vector.
//
//    Output, int UNICYCLE_INDEX[N], the unicycle index vector.
//
{
  int i;
  int ip1;
  int *u_index;

  u_index = new int[n];

  for ( i = 0; i < n; i++ )
  {
    ip1 = i4_wrap ( i + 1, 0, n - 1 );
    u_index[u[i]-1] = u[ip1];
  }
  
  return u_index;
}
//****************************************************************************80

void unicycle_index_print ( int n, int u_index[], string title )

//****************************************************************************80
//
//  Purpose:
//
//    UNICYCLE_INDEX_PRINT prints a unicycle given in index form.
//
//  Example:
//
//    Input:
//
//      U_INDEX = 7 1 4 5 2 3 6
//
//    Printed output:
//
//      1 2 3 4 5 6 7
//      7 1 4 5 2 3 6
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    13 June 2012
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the order of the unicycle.
//
//    Input, int U_INDEX(N), the unicycle index vector.
//
//    Input, string TITLE, a title.
//
{
  int i;
  int ihi;
  int ilo;
  int inc = 20;

  if ( 0 < s_len_trim ( title ) )
  {
    cout << "\n";
    cout << title << "\n";
  }

  for ( ilo = 0; ilo < n; ilo = ilo + inc )
  {
    ihi = i4_min ( n, ilo + inc - 1 );
    cout << "\n";
    cout << "  ";
    for ( i = ilo; i < ihi; i++ )
    {
      cout << setw(4) << i + 1;
    }
    cout << "\n";
    cout << "  ";
    for ( i = ilo; i < ihi; i++ )
    {
      cout << setw(4) << u_index[i];
    }
    cout << "\n";
  }
  return;
}
//****************************************************************************80

int *unicycle_index_to_sequence ( int n, int u_index[] )

//****************************************************************************80
//
//  Purpose:
//
//    UNICYCLE_INDEX_TO_SEQUENCE converts a unicycle from index to sequence form.
//
//  Example:
//
//    N = 4
//
//    U_INDEX = 3 1 4 2
//    U       = 1 3 4 2
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    13 June 2012
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the order of the unicycles.
//
//    Output, int U_INDEX(N), the unicycle index vector.
//
//    Input, int U(N), the unicycle sequence vector.
//
{
  int i;
  int j;
  int *u;

  u = new int[n];

  u[0] = 1;
  i = 1;

  for ( j = 1; j < n; j++ )
  {
    i = u_index[i-1];
    u[j] = i;

    if ( i == 1 )
    {
      cout << "\n";
      cout << "UNICYCLE_INDEX_TO_SEQUENCE - Fatal error!\n";
      cout << "  The index vector does not represent a unicycle.\n";
      cout << "  On step " << j << " u_index(" << i << ") = 1.\n";
      exit ( 1 );
    }
  }
  
  return u;
}
//****************************************************************************80

int *unicycle_inverse ( int n, int u[] )

//****************************************************************************80
//
//  Purpose:
//
//    UNICYCLE_INVERSE returns the inverse of a unicycle.
//
//  Example:
//
//    N = 4
//
//    U         = 1 3 4 2
//    U_INVERSE = 1 2 4 3
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    17 June 2012
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the order of the unicycles.
//
//    Input, int U[N], the unicycle sequence vector.
//
//    Output, int UNICYCLE_INVERSE[N], the inverse unicycle.
//
{
  int i;
  int *u_inverse;

  u_inverse = new int[n];

  u_inverse[0] = 1;
  for ( i = 1; i < n; i++ )
  {
    u_inverse[i] = u[n-i];
  }
  return u_inverse;
}
//****************************************************************************80

void unicycle_next ( int n, int u[], int &rank )

//****************************************************************************80
//
//  Purpose:
//
//    UNICYCLE_NEXT generates unicycles in lexical order, one at a time.
//
//  Example:
//
//    N = 4
//
//    1   1 2 3 4
//    2   1 2 4 3
//    3   1 3 2 4
//    4   1 3 4 2
//    5   1 4 2 3
//    6   1 4 3 2
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    17 June 2012
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the order of the unicycles.
//
//    Input/output, int U[N]; on first call with MORE = FALSE,
//    this value is not used.  Otherwise, the input value is the previous
//    unicycle.  The output value is the next unicycle.
//
//    Input/output, int &RANK, the rank.
//    If RANK = -1 on input, then the routine understands that this is
//    the first call, and that the user wishes the routine to supply
//    the first element in the ordering, which has RANK = 0.
//    In general, the input value of RANK is increased by 1 for output,
//    unless the very last element of the ordering was input, in which
//    case the output value of RANK is -1.
//
{
  int i;
  int *p;

  p = new int[n-1];

  if ( rank == -1 )
  {
    u[0] = 1;
  }
  else
  {
    for ( i = 0; i < n - 1; i++ )
    {
      p[i] = u[i+1] - 1;
    }
  }

  perm_lex_next ( n - 1, p, rank );
 
  for ( i = 0; i < n - 1; i++ )
  {
    u[i+1] = p[i] + 1;
  }
  delete [] p;

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

void unicycle_print ( int n, int u[], string title )

//****************************************************************************80
//
//  Purpose:
//
//    UNICYCLE_PRINT prints a unicycle given in sequence form.
//
//  Example:
//
//    Input:
//
//      U = 7 1 4 5 2 3 6
//
//    Printed output:
//
//      7 1 4 5 2 3 6
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    17 June 2012
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the order of the unicycle.
//
//    Input, int U[N], the unicycle sequence vector.
//
//    Input, string TITLE, a title.
//
{
  int i;
  int ihi;
  int ilo;
  int inc = 20;

  if ( s_len_trim ( title ) != 0 )
  {
    cout << "\n";
    cout << title << "\n";
    cout << "\n";
  }

  for ( ilo = 0; ilo < n; ilo = ilo + inc )
  {
    ihi = ilo + inc;
    if ( n < ihi ) 
    {
      ihi = n;
    }
    cout << "  ";
    for ( i = ilo; i < ihi; i++ )
    {
      cout << setw(4) << u[i];
    }
    cout << "\n";
  }
  return;
}
//****************************************************************************80

int *unicycle_random ( int n, int &seed )

//****************************************************************************80
//
//  Purpose:
//
//    UNICYCLE_RANDOM selects a random unicycle of N objects.
//
//  Discussion:
//
//    The routine assumes the objects are labeled 1, 2, ... N.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    17 June 2012
//
//  Author:
//
//    John Burkardt.
//
//  Reference:
//
//    Albert Nijenhuis, Herbert Wilf,
//    Combinatorial Algorithms for Computers and Calculators,
//    Second Edition,
//    Academic Press, 1978,
//    ISBN: 0-12-519260-6,
//    LC: QA164.N54.
//
//  Parameters:
//
//    Input, int N, the number of objects to be permuted.
//
//    Input/output, int &SEED, a seed for the random number
//    generator.
//
//    Output, int UNICYCLE_RANDOM[N], a unicycle in sequence form.
//
{
  int i;
  int j;
  int *u;
  int t;

  u = i4vec_indicator_new ( n );

  for ( i = 1; i < n; i++ )
  {
    j = i4_uniform_ab ( i, n - 1, seed );
    t = u[i];
    u[i] = u[j];
    u[j] = t;
  }

  return u;
}
//****************************************************************************80

int unicycle_rank ( int n, int u[] )

//****************************************************************************80
//
//  Purpose:
//
//    UNICYCLE_RANK computes the rank of a unicycle.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    17 June 2012
//
//  Author:
//
//    John Burkardt.
//
//  Parameters:
//
//    Input, int N, the order of the unicycle.
//
//    Input, int U[N], a unicycle in sequence form.
//
//    Output, int UNICYLE_RANK, the rank of the unicycle.
//
{
  int i;
  int *p;
  int rank;

  p = new int[n-1];

  for ( i = 0; i < n - 1; i++ )
  {
    p[i] = u[i+1] - 1;
  }

  rank = perm_lex_rank ( n - 1, p );

  delete [] p;

  return rank;
}
//****************************************************************************80

int *unicycle_unrank ( int n, int rank )

//****************************************************************************80
//
//  Purpose:
//
//    UNICYCLE_UNRANK "unranks" a unicycle.
//
//  Discussion:
//
//    That is, given a rank, it computes the corresponding unicycle.
//
//    The value of the rank should be between 0 and (N-1)!-1.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    17 June 2012
//
//  Author:
//
//    John Burkardt.
//
//  Reference:
//
//    Dennis Stanton, Dennis White,
//    Constructive Combinatorics,
//    Springer, 1986,
//    ISBN: 0387963472,
//    LC: QA164.S79.
//
//  Parameters:
//
//    Input, int N, the number of elements in the set.
//
//    Input, int RANK, the desired rank of the permutation.
//
//    Output, int UNICYCLE_UNRANK[N], the unicycle.
//
{
  int i;
  int *p;
  int *u;

  p = perm_lex_unrank ( n - 1, rank );

  u = new int[n];

  u[0] = 1;
  for ( i = 0; i < n - 1; i++ )
  {
    u[i+1] = p[i] + 1;
  }
  delete [] p;

  return u;
}