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

using namespace std;

# include "subset_sum.hpp"

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

int backup_one ( int n, int u[], int told )

//****************************************************************************80
//
//  Purpose:
//
//    BACKUP_ONE seeks the last 1 in the subarray U[0:TOLD-1].
//
//  Licensing:
//
//    I don't care what you do with this code.
//
//  Modified:
//
//    15 July 2017
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the full size of the U array.
//
//    Input, int U[N], the array to be checked.
//
//    Input, int TOLD, a value between 0 and N-1.
//
//    Output, int BACKUP_ONE, the highest index in U, between 0 and TOLD-1,
//    for which U is 1.  If no such value is found, T is -1.
//
{
  int i;
  int t;

  t = -1;
  
  for ( i = told - 1; 0 <= i; i-- )
  {
    if ( u[i] == 1 )
    {
      t = i;
      break;
    }
  }

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

int i4_max ( int i1, int i2 )

//****************************************************************************80
//
//  Purpose:
//
//    I4_MAX returns the maximum of two I4's.
//
//  Licensing:
//
//    I don't care what you do with this code.
//
//  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:
//
//    I don't care what you do with this code.
//
//  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_power ( int i, int j )

//****************************************************************************80
//
//  Purpose:
//
//    I4_POWER returns the value of I^J.
//
//  Licensing:
//
//    I don't care what you do with this code.
//
//  Modified:
//
//    01 April 2004
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int I, J, the base and the power.  J should be nonnegative.
//
//    Output, int I4_POWER, the value of I^J.
//
{
  int k;
  int value;

  if ( j < 0 )
  {
    if ( i == 1 )
    {
      value = 1;
    }
    else if ( i == 0 )
    {
      cerr << "\n";
      cerr << "I4_POWER - Fatal error!\n";
      cerr << "  I^J requested, with I = 0 and J negative.\n";
      exit ( 1 );
    }
    else
    {
      value = 0;
    }
  }
  else if ( j == 0 )
  {
    if ( i == 0 )
    {
      cerr << "\n";
      cerr << "I4_POWER - Fatal error!\n";
      cerr << "  I^J requested, with I = 0 and J = 0.\n";
      exit ( 1 );
    }
    else
    {
      value = 1;
    }
  }
  else if ( j == 1 )
  {
    value = i;
  }
  else
  {
    value = 1;
    for ( k = 1; k <= j; k++ )
    {
      value = value * i;
    }
  }
  return value;
}
//****************************************************************************80

int *i4_to_digits_binary ( int i, int n )

//****************************************************************************80
//
//  Purpose:
//
//    I4_TO_DIGITS_BINARY produces the binary digits of an I4.
//
//  Example:
//
//     I    N     C               Binary
//    --  ---   ---         ------------
//     0    1   0                      0
//     0    2   0, 0                  00
//     1    3   1, 0, 0              100
//     2    3   0, 1, 0              010
//     3    3   1, 1, 0              011
//     4    3   0, 0, 1              100
//     8    3   0, 0, 0           (1)000
//     8    5   0, 0, 0, 1, 0      01000
//    -8    5   0, 0, 0, 1, 0  (-) 01000
//
//     0    3   0, 0, 0
//     1    3   1, 0, 0
//     2    3   0, 1, 0
//     3    3   1, 1, 0
//     4    3   0, 0, 1
//     5    3   1, 0, 1
//     6    3   0, 1, 1
//     7    3   1, 1, 1
//
//  Licensing:
//
//    I don't care what you do with this code.
//
//  Modified:
//
//    19 December 2011
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int I, the integer to be analyzed.
//
//    Input, int N, the number of digits to determine.
//
//    Output, int I4_TO_DIGITS_BINARY[N], the first N binary digits of I.
//    Entry 0 is the units digit.
//
{
  int *c;
  int j;

  c = new int[n];

  i = abs ( i );

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

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

int *i4vec_copy_new ( int n, int a1[] )

//****************************************************************************80
//
//  Purpose:
//
//    I4VEC_COPY_NEW copies an I4VEC to a "new" I4VEC.
//
//  Discussion:
//
//    An I4VEC is a vector of I4's.
//
//  Licensing:
//
//    I don't care what you do with this code.
//
//  Modified:
//
//    04 July 2008
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of entries in the vectors.
//
//    Input, int A1[N], the vector to be copied.
//
//    Output, int I4VEC_COPY_NEW[N], the copy of A1.
//
{
  int *a2;
  int i;

  a2 = new int[n];

  for ( i = 0; i < n; i++ )
  {
    a2[i] = a1[i];
  }
  return a2;
}
//****************************************************************************80

int i4vec_dot_product ( int n, int x[], int y[] )

//****************************************************************************80
//
//  Purpose:
//
//    I4VEC_DOT_PRODUCT computes the dot product of two I4VEC's.
//
//  Discussion:
//
//    An I4VEC is a vector of I4's.
//
//  Licensing:
//
//    I don't care what you do with this code.
//
//  Modified:
//
//    19 December 2011
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the size of the array.
//
//    Input, int X[N], Y[N], the arrays.
//
//    Output, int I4VEC_DOT_PRODUCT, the dot product of X and Y.
//
{
  int i;
  int value;

  value = 0;
  for ( i = 0; i < n; i++ )
  {
    value = value + x[i] * y[i];
  }

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

void i4vec_print ( int n, int a[], string title )

//****************************************************************************80
//
//  Purpose:
//
//    I4VEC_PRINT prints an I4VEC.
//
//  Discussion:
//
//    An I4VEC is a vector of I4's.
//
//  Licensing:
//
//    I don't care what you do with this code.
//
//  Modified:
//
//    14 November 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of components of the vector.
//
//    Input, int A[N], the vector to be printed.
//
//    Input, string TITLE, a title.
//
{
  int i;

  cout << "\n";
  cout << title << "\n";
  cout << "\n";
  for ( i = 0; i < n; i++ )
  {
    cout << "  " << setw(8) << i
         << ": " << setw(8) << a[i]  << "\n";
  }
  return;
}
//****************************************************************************80

int subset_sum_count ( int n, int w[], int t, int ind_min, int ind_max )

//****************************************************************************80
//
//  Purpose:
//
//    SUBSET_SUM_COUNT counts solutions to the subset sum problem in a range.
//
//  Licensing:
//
//    I don't care what you do with this code.
//
//  Modified:
//
//    09 December 2010
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the size of the subset.
//
//    Input, int W[N], a set of weights.  The length of this
//    array must be no more than 31.
//
//    Input, int T, the target value.
//
//    Input, int IND_MIN, IND_MAX, the lower and upper
//    limits to be searched.  0 <= IND_MIN <= IND_MAX <= (2^N)-1.
//
//    Output, int SUBSET_SUM_COUNT, the number of distinct
//    solutions of the subset sum problem found within the given range.
//
{
  int *c;
  int ind;
  int ind_max2;
  int ind_min2;
  int solution_num;
//
//  Check the data.
//
  if ( n < 1 )
  {
    cerr << "\n";
    cerr << "SUBSET_SUM_COUNT - Fatal error!\n";
    cerr << "  N < 1.\n";
    exit ( 1 );
  }

  if ( 31 < n )
  {
    cerr << "\n";
    cerr << "SUBSET_SUM_COUNT - Fatal error!\n";
    cerr << "  31 < N.\n";
    exit ( 1 );
  }

  ind_min2 = i4_max ( ind_min, 0 );
  ind_max2 = i4_min ( ind_max, i4_power ( 2, n ) - 1 );
//
//  Run through the range.
//
  cout << "\n";
  cout << "  Searching from IND_MIN = " << ind_min2;
  cout << "  through IND_MAX = " << ind_max2 << "\n";

  solution_num = 0;

  for ( ind = ind_min2; ind <= ind_max2; ind++ )
  {
//
//  Convert INDEX into vector of indices in W.
//
    c = i4_to_digits_binary ( ind, n );
//
//  If the sum of those weights matches the target, return combination.
//
    if ( i4vec_dot_product ( n, c, w ) == t )
    {
      solution_num = solution_num + 1;
    }

    delete [] c;
  }

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

void subset_sum_count_test ( int n, int w[], int t, int ind_min, int ind_max )

//****************************************************************************80
//
//  Purpose:
//
//    SUBSET_SUM_COUNT_TEST tests SUBSET_SUM_COUNT.
//
//  Licensing:
//
//    I don't care what you do with this code.
//
//  Modified:
//
//    10 November 2015
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of weights.
//
//    Input, int W[N], a set of weights.  The length of this
//    array must be no more than 31.
//
//    Input, int T, the target value.
//
//    Input, int IND_MIN, IND_MAX, the lower and upper
//    limits to be searched.
//
{
  int solution_num;

  cout << "\n";
  cout << "SUBSET_SUM_COUNT_TEST:\n";
  cout << "  SUBSET_SUM_COUNT counts solutions to the subset sum problem.\n";
  cout << "\n";
  cout << "  Target value T = " << t << "\n";
  i4vec_print ( n, w, "  Weight vector W:" );

  solution_num = subset_sum_count ( n, w, t, ind_min, ind_max );

  cout << "\n";
  cout << "  Number of solutions = " << solution_num << "\n";

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

void subset_sum_count_tests ( )

//****************************************************************************80
//
//  Purpose:
//
//    SUBSET_SUM_COUNT_TESTS tests SUBSET_SUM_COUNT_TEST.
//
//  Licensing:
//
//    I don't care what you do with this code.
//
//  Modified:
//
//    10 November 2015
//
//  Author:
//
//    John Burkardt
//
{
  int ind_max;
  int ind_min;
  int n;
  int t;
  int test;
  int test_num = 9;
  int *w;
  static int w01[8] = { 15, 22, 14, 26, 32, 9, 16, 8 };
  static int w02[8] = { 15, 22, 14, 26, 32, 9, 16, 8 };
  static int w03[8] = { 15, 22, 14, 26, 32, 9, 16, 8 };
  static int w04[10] = { 267,  493,  869,  961, 1000, 1153, 1246, 1598, 1766, 1922 };
  static int w05[21] = {518533, 1037066, 2074132, 1648264, 796528, 
             1593056,  686112, 1372224,  244448, 488896, 
              977792, 1955584, 1411168,  322336, 644672, 
             1289344,   78688,  157376,  314752, 629504, 
             1259008};
  static int w06[10] = { 41, 34, 21, 20,  8,  7,  7,  4,  3,  3 };
  static int w07[9] = { 81, 80, 43, 40, 30, 26, 12, 11, 9 };
  static int w08[6] = { 1, 2, 4, 8, 16, 32};
  static int w09[10] = { 25, 27, 3, 12, 6, 15, 9, 30, 21, 19 };

  cout << "\n";
  cout << "SUBSET_SUM_COUNT_TESTS:\n";
  cout << "  SUBSET_SUM_COUNT_TEST calls SUBSET_SUM_COUNT\n";
  cout << "  with particular problem data.\n";

  for ( test = 1; test <= test_num; test++ )
  {
    if ( test == 1 )
    {
      n = 8;
      w = i4vec_copy_new ( n, w01 );
      t = 53;
      ind_min = 0;
      ind_max = i4_power ( 2, n ) - 1;
    }
    else if ( test == 2 )
    {
      n = 8;
      w = i4vec_copy_new ( n, w02 );
      t = 53;
      ind_min = 68;
      ind_max = i4_power ( 2, n ) - 1;
    }
    else if ( test == 3 )
    {
      n = 8;
      w = i4vec_copy_new ( n, w03 );
      t = 53;
      ind_min = 167;
      ind_max = i4_power ( 2, n ) - 1;
    }
    else if ( test == 4 )
    {
      n = 10;
      w = i4vec_copy_new ( n, w04 );
      t = 5842;
      ind_min = 0;
      ind_max = i4_power ( 2, n ) - 1;
    }
    else if ( test == 5 )
    {
      n = 21;
      w = i4vec_copy_new ( n, w05 );
      t = 2463098;
      ind_min = 0;
      ind_max = i4_power ( 2, n ) - 1;
    }
    else if ( test == 6 )
    {
      n = 10;
      w = i4vec_copy_new ( n, w06 );
      t = 50;
      ind_min = 0;
      ind_max = i4_power ( 2, n ) - 1;
    }
    else if ( test == 7 )
    {
      n = 9;
      w = i4vec_copy_new ( n, w07 );
      t = 100;
      ind_min = 0;
      ind_max = i4_power ( 2, n ) - 1;
    }
    else if ( test == 8 )
    {
      n = 6;
      w = i4vec_copy_new ( n, w08 );
      t = 22;
      ind_min = 0;
      ind_max = i4_power ( 2, n ) - 1;
    }
    else if ( test == 9 )
    {
      n = 10;
      w = i4vec_copy_new ( n, w09 );
      t = 50;
      ind_min = 0;
      ind_max = i4_power ( 2, n ) - 1;
    }

    subset_sum_count_test ( n, w, t, ind_min, ind_max );

    delete [] w;
  }

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

int *subset_sum_find ( int n, int w[], int t, int ind_min, int ind_max, 
  int &ind )

//****************************************************************************80
//
//  Purpose:
//
//    SUBSET_SUM seeks a subset of a set that has a given sum.
//
//  Discussion:
//
//    This function tries to compute a target value as the sum of
//    a selected subset of a given set of weights.
//
//    This function works by brute force, that is, it tries every
//    possible subset to see if it sums to the desired value.
//
//    Given N weights, every possible selection can be described by
//    one of the N-digit binary numbers from 0 to 2^N-1.
//
//    This function includes a range, which allows the user to
//    control which subsets are to be checked.  Thus, if there are
//    N weights, specifying a range of [ 0, 2^N-1] indicates that
//    all subsets should be checked.  On the other hand, this full
//    range could be broken down into smaller subranges, each of
//    which could be checked independently.
//
//    It is possible that, in the given range, there may be multiple
//    solutions of the problem.  This function will only return
//    one such solution, if found.  However, the function may be called
//    again, with an appropriate restriction of the range, to continue
//    the search for other solutions.
//
//  Example:
//
//    w = [ 1, 2, 4, 8, 16, 32 ];
//    t = 22;
//    r = [ 0, 2^6 - 1 ];
//
//    call subset_sum ( w, t, r, c, ind )
//
//    c = [ 2, 3, 5 ]
//    index = 22
//
//  Licensing:
//
//    I don't care what you do with this code.
//
//  Modified:
//
//    09 December 2010
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the size of the subset.
//
//    Input, int W[N], a set of weights.  The length of this
//    array must be no more than 31.
//
//    Input, int T, the target value.
//
//    Input, int IND_MIN, IND_MAX, the lower and upper
//    limits to be searched.  0 <= IND_MIN <= IND_MAX <= (2^N)-1.
//
//    Output, int &IND, the index of the solution.
//    If IND is -1, no solution was found in the range.
//
//    Output, int SUBSET_SUM_FIND[N], indicates the solution, assuming
//    that IND is not -1.  In that case, the sum T is made by selecting
//    those weights W(I) for which C(I) is 1.  In fact,
//    T = sum ( 1 <= I <= N ) C(I) * W(I).
//
{
  int *c;
  int ind_max2;
  int ind_min2;
//
//  Check the data.
//
  if ( n < 1 )
  {
    cerr << "\n";
    cerr << "SUBSET_SUM_COUNT - Fatal error!\n";
    cerr << "  N < 1.\n";
    exit ( 1 );
  }

  if ( 31 < n )
  {
    cerr << "\n";
    cerr << "SUBSET_SUM_COUNT - Fatal error!\n";
    cerr << "  31 < N.\n";
    exit ( 1 );
  }

  ind_min2 = i4_max ( ind_min, 0 );
  ind_max2 = i4_min ( ind_max, i4_power ( 2, n ) - 1 );
//
//  Run through the range.
//
  cout << "\n";
  cout << "  Searching from IND_MIN = " << ind_min2;
  cout << "  through IND_MAX = " << ind_max2 << "\n";

  for ( ind = ind_min2; ind <= ind_max2; ind++ )
  {
//
//  Convert INDEX into vector of indices in W.
//
    c = i4_to_digits_binary ( ind, n );
//
//  If the sum of those weights matches the target, return combination.
//
    if ( i4vec_dot_product ( n, c, w ) == t )
    {
      return c;
    }

    delete [] c;
  }

  ind = - 1;

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

int subset_sum_find_test ( int n, int w[], int t, int ind_min, int ind_max )

//****************************************************************************80
//
//  Purpose:
//
//    SUBSET_SUM_FIND_TEST tests SUBSET_SUM_FIND.
//
//  Licensing:
//
//    I don't care what you do with this code.
//
//  Modified:
//
//    10 Novemer 2015
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of weights.
//
//    Input, int W[N], a set of weights.  The length of this
//    array must be no more than 31.
//
//    Input, int T, the target value.
//
//    Input, int IND_MIN, IND_MAX, the lower and upper
//    limits to be searched.
//
//    Output, int SUBSET_SUM_FIND_TEST, the index of a solution, if found,
//    or the value -1 otherwise.
//
{
  int *c;
  int ind;

  cout << "\n";
  cout << "SUBSET_SUM_FIND_TEST:\n";
  cout << "  SUBSET_SUM_FIND seeks a subset of W that sums to T.\n";
  cout << "\n";
  cout << "  Target value T = " << t << "\n";
  i4vec_print ( n, w, "  Weight vector W:" );

  c = subset_sum_find ( n, w, t, ind_min, ind_max, ind );

  if ( ind == -1 )
  {
    cout << "\n";
    cout << "  No solution was found.\n";
  }
  else
  {
    cout << "\n";
    cout << "  Solution index = " << ind << "\n";
    i4vec_print ( n, c, "  Solution:" );
  }
  delete [] c;

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

void subset_sum_find_tests ( )

//****************************************************************************80
//
//  Purpose:
//
//    SUBSET_SUM_FIND_TESTS tests SUBSET_SUM_FIND_TEST.
//
//  Licensing:
//
//    I don't care what you do with this code.
//
//  Modified:
//
//    10 November 2015
//
//  Author:
//
//    John Burkardt
//
{
  int ind;
  int ind_max;
  int ind_min;
  int n;
  int t;
  int test;
  int test_num = 9;
  int *w;
  static int w01[8] = { 15, 22, 14, 26, 32, 9, 16, 8 };
  static int w02[8] = { 15, 22, 14, 26, 32, 9, 16, 8 };
  static int w03[8] = { 15, 22, 14, 26, 32, 9, 16, 8 };
  static int w04[10] = { 267,  493,  869,  961, 1000, 1153, 1246, 1598, 1766, 1922 };
  static int w05[21] = {518533, 1037066, 2074132, 1648264, 796528, 
             1593056,  686112, 1372224,  244448, 488896, 
              977792, 1955584, 1411168,  322336, 644672, 
             1289344,   78688,  157376,  314752, 629504, 
             1259008};
  static int w06[10] = { 41, 34, 21, 20,  8,  7,  7,  4,  3,  3 };
  static int w07[9] = { 81, 80, 43, 40, 30, 26, 12, 11, 9 };
  static int w08[6] = { 1, 2, 4, 8, 16, 32};
  static int w09[10] = { 25, 27, 3, 12, 6, 15, 9, 30, 21, 19 };

  cout << "\n";
  cout << "SUBSET_SUM_FIND_TESTS:\n";
  cout << "  SUBSET_SUM_FIND_TEST calls SUBSET_SUM_FIND\n";
  cout << "  with particular problem data.\n";

  for ( test = 1; test <= test_num; test++ )
  {
    if ( test == 1 )
    {
      n = 8;
      w = i4vec_copy_new ( n, w01 );
      t = 53;
      ind_min = 0;
      ind_max = i4_power ( 2, n ) - 1;
    }
    else if ( test == 2 )
    {
      n = 8;
      w = i4vec_copy_new ( n, w02 );
      t = 53;
      ind_min = ind + 1;
      ind_max = i4_power ( 2, n ) - 1;
    }
    else if ( test == 3 )
    {
      n = 8;
      w = i4vec_copy_new ( n, w03 );
      t = 53;
      ind_min = ind + 1;
      ind_max = i4_power ( 2, n ) - 1;
    }
    else if ( test == 4 )
    {
      n = 10;
      w = i4vec_copy_new ( n, w04 );
      t = 5842;
      ind_min = 0;
      ind_max = i4_power ( 2, n ) - 1;
    }
    else if ( test == 5 )
    {
      n = 21;
      w = i4vec_copy_new ( n, w05 );
      t = 2463098;
      ind_min = 0;
      ind_max = i4_power ( 2, n ) - 1;
    }
    else if ( test == 6 )
    {
      n = 10;
      w = i4vec_copy_new ( n, w06 );
      t = 50;
      ind_min = 0;
      ind_max = i4_power ( 2, n ) - 1;
    }
    else if ( test == 7 )
    {
      n = 9;
      w = i4vec_copy_new ( n, w07 );
      t = 100;
      ind_min = 0;
      ind_max = i4_power ( 2, n ) - 1;
    }
    else if ( test == 8 )
    {
      n = 6;
      w = i4vec_copy_new ( n, w08 );
      t = 22;
      ind_min = 0;
      ind_max = i4_power ( 2, n ) - 1;
    }
    else if ( test == 9 )
    {
      n = 10;
      w = i4vec_copy_new ( n, w09 );
      t = 50;
      ind_min = 0;
      ind_max = i4_power ( 2, n ) - 1;
    }

    ind = subset_sum_find_test ( n, w, t, ind_min, ind_max );

    delete [] w;
  }

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

void subset_sum_next ( int s, int n, int v[], bool &more, int u[], int &t )
 
//****************************************************************************80
//
//  Purpose:
//  
//    SUBSET_SUM_NEXT seeks, one at a time, subsets of V that sum to S.
//
//  Licensing:
//
//    I don't care what you do with this code.
//
//  Modified:
//
//    15 July 2017
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int S, the desired sum.
//
//    Input, int N, the number of values.
//
//    Input, int V[N], the values.
//    These must be nonnegative, and sorted in ascending order.  
//    Duplicate values are allowed.
//
//    Input/output, bool &MORE, should be set to FALSE before the first call.
//    Thereafter, on output, MORE is TRUE if a solution is being returned,
//    and FALSE if there are no more solutions.
//
//    Input/output, int U[N], should be set to 0 before the 
//    first call.  On output with MORE TRUE, U indexes the selected entries
//    of V that form a solution.
//
//    Input/output, int &T, should be set to -1 before the first 
//    call.  On output, if MORE is true, T is the highest index of the selected 
//    values, although this is of little interest to the user.
//
{
  int i;
  int su;

  if ( ! more )
  {
    t = -1;
    for ( i = 0; i < n; i++ )
    {
      u[i] = 0;
    }
  }
  else
  {
    more = false;
    u[t] = 0;

    t = backup_one ( n, u, t );
    
    if ( t < 0 )
    {
      return;
    }

    u[t] = 0;
    t = t + 1;
    u[t] = 1;   
  }
    
  while ( true )
  {
    su = i4vec_dot_product ( n, u, v );
  
    if ( su < s && t < n - 1 )
    {
      t = t + 1;
      u[t] = 1;
    }
    else
    {
      if ( su == s )
      {
        more = true;
        return;
      }

      u[t] = 0;

      t = backup_one ( n, u, t );
      
      if ( t < 0 )
      {
        break;
      }

      u[t] = 0;
      t = t + 1;
      u[t] = 1; 
    }
  }

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

void subset_sum_next_test ( int s, int n, int v[] )

//****************************************************************************80
//
//  Purpose:
//
//    SUBSET_SUM_NEXT_TEST tests the SUBSET_SUM_NEXT library.
//
//  Licensing:
//
//    I don't care what you do with this code.
//
//  Modified:
//
//    15 July 2017
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int S, the desired sum.
//
//    Input, int N, the number of values.
//
//    Input, int V[N], the values.
//    These must be nonnegative, and sorted in ascending order.  
//    Duplicate values are allowed.
//
{
  int i;
  int k;
  bool more;
  bool plus;
  int t;
  int *u;

  cout << "\n";
  cout << "SUBSET_SUM_NEXT_TEST:\n";
  cout << "  SUBSET_SUM_NEXT finds the next subset of the values V\n";
  cout << "  which sum to the desired total S.\n";

  more = false;
  u = new int[n];
  for ( i = 0; i < n; i++ )
  {
    u[i] = 0;
  }
  t = -1;
  
  cout << "\n";
  cout << "  Desired sum S = " << s << "\n";
  cout << "  Number of targets = " << n << "\n";
  cout << "  Targets:";
  for ( i = 0; i < n; i++ )
  {
    cout << " " << v[i];
  }
  cout << "\n";
  cout << "\n";

  k = 0;
  
  while ( true )
  {
    subset_sum_next ( s, n, v, more, u, t );
    if ( ! more )
    {
      break;
    }
    k = k + 1;
    cout << "  " << k << ":  " << s << " =";
    plus = false;
    for ( i = 0; i < n; i++ )
    {
      if ( u[i] != 0 )
      {
        if ( plus )
        {
          cout << " +";
        }
        cout << " " << v[i];
        plus = true;
      }
    }
    cout << "\n";
  }
   
  delete [] u;

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

void subset_sum_next_tests ( )

//****************************************************************************80
//
//  Purpose:
//
//    SUBSET_SUM_NEXT_TESTS calls SUBSET_SUM_NEXT_TEST with various values.
//
//  Licensing:
//
//    I don't care what you do with this code.
//
//  Modified:
//
//    15 July 2017
//
//  Author:
//
//    John Burkardt
//
{
  int n;
  int s;
  int *v;
  static int v01[5] = { 1, 2, 3, 5, 7 };
  static int v02[9] = { 1, 2, 3, 4, 5, 6, 7, 8, 9 };
  static int v03[9] = { 1, 2, 3, 3, 5, 6, 7, 8, 9 };
  static int v04[5] = { 1, 2, 3, 5, 7 };
  static int v05[10] = { 267, 493, 869, 961, 1000, 1153, 1246, 1598, 1766, 1922 };

  cout << "\n";
  cout << "SUBSET_SUM_NEXT_TESTS:\n";
  cout << "  SUBSET_SUM_NEXT_TEST solves the subset sum problem\n";
  cout << "  for specific values of S, N and V.\n";
  
  s = 9;
  n = 5;
  v = i4vec_copy_new ( n, v01 );
  subset_sum_next_test ( s, n, v );
  delete [] v;
  
  s = 8;
  n = 9;
  v = i4vec_copy_new ( n, v02 );
  subset_sum_next_test ( s, n, v );
  delete [] v;
//
//  What happens with a repeated target?
//
  s = 8;
  n = 9;
  v = i4vec_copy_new ( n, v03 );
  subset_sum_next_test ( s, n, v );
  delete [] v;
//
//  What happens with a target that needs all the values?
//
  s = 18;
  n = 5;
  v = i4vec_copy_new ( n, v04 );
  subset_sum_next_test ( s, n, v );
  delete [] v;
//
//  A larger S.
//
  s = 5842;
  n = 10;
  v = i4vec_copy_new ( n, v05 );
  subset_sum_next_test ( s, n, v );
  delete [] v;
//
//  Terminate.
//
  cout << "\n";
  cout << "SUBSET_SUM_NEXT_TESTS:\n";
  cout << "  Normal end of execution.\n";
  
  return;
}
//****************************************************************************80

int *subset_sum_table ( int t, int n, int w[] )

//****************************************************************************80
//
//  Purpose:
//
//    SUBSET_SUM_TABLE sets a subset sum table.
//
//  Discussion:
//
//    The subset sum problem seeks to construct the value T by summing a 
//    subset of the values W.
//
//    This function seeks a solution by constructing a table TABLE of length T,
//    so that TABLE(I) = J means that the sum I can be constructed, and that
//    the last member of the sum is an entry of W equal to J.
//
//  Licensing:
//
//    I don't care what you do with this code.
//
//  Modified:
//
//    11 November 2015
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int T, the target value.
//
//    Input, int N, the number of weights.
//
//    Input, int W[N], the weights.
//
//    Output, int SUBSET_SUM_TABLE[T], the subset sum table.  TABLE(I) is 
//    0 if the target value I cannot be formed.  It is J if the value I can 
//    be formed, with the last term in the sum being the value J.
//
{
  int i;
  int j;
  int *table;

  table = new int[t+1];

  for ( i = 0; i <= t; i++ )
  {
    table[i] = 0;
  }

  for ( i = 0; i < n; i++ )
  {
    for ( j = t - w[i]; 0 <= j; j-- )
    {
      if ( j == 0 )
      {
        if ( table[w[i]] == 0 )
        {
          table[w[i]] = w[i];
        }
      }
      else if ( table[j] != 0 && table[j+w[i]] == 0 )
      {
        table[j+w[i]] = w[i];
      }
    }
  }
  
  return table;
}
//****************************************************************************80

void subset_sum_table_test ( int t, int n, int w[] )

//****************************************************************************80
//
//  Purpose:
//
//    SUBSET_SUM_TABLE_TEST tests SUBSET_SUM_TABLE.
//
//  Licensing:
//
//    I don't care what you do with this code.
//
//  Modified:
//
//    12 Novemer 2015
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of weights.
//
//    Input, int W[N], a set of weights.
//
//    Input, int T, the target value.
//
{
  int i;
  int *list;
  int m;
  int *table;

  cout << "\n";
  cout << "SUBSET_SUM_TABLE_TEST:\n";
  cout << "  SUBSET_SUM_TABLE seeks a subset of W that sums to T.\n";
  cout << "\n";
  cout << "  Target value T = " << t << "\n";
  i4vec_print ( n, w, "  Weight vector W:" );

  table = subset_sum_table ( t, n, w );

  m = subset_sum_table_to_list_length ( t, table );

  cout << "\n";

  if ( m == 0 )
  {
    cout << "  No solution was found.\n";
  }
  else
  {
    list = subset_sum_table_to_list ( t, table, m );
    cout << "  " << t << " = ";
    for ( i = 0; i < m; i++ )
    {
      if ( 0 < i )
      {
        cout << " + ";
      }
      cout << list[i];
    }
    cout << "\n";
    delete [] list;
  }
  delete [] table;

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

void subset_sum_table_tests ( )

//****************************************************************************80
//
//  Purpose:
//
//    SUBSET_SUM_TABLE_TESTS tests SUBSET_SUM_TABLE_TEST.
//
//  Licensing:
//
//    I don't care what you do with this code.
//
//  Modified:
//
//    12 November 2015
//
//  Author:
//
//    John Burkardt
//
{
  int n;
  int t;
  int test;
  int test_num = 7;
  int *w;
  static int w01[8] = { 15, 22, 14, 26, 32, 9, 16, 8 };
  static int w02[10] = { 267,  493,  869,  961, 1000, 1153, 1246, 1598, 1766, 1922 };
  static int w03[21] = {
              518533, 1037066, 2074132, 1648264, 796528, 
             1593056,  686112, 1372224,  244448, 488896, 
              977792, 1955584, 1411168,  322336, 644672, 
             1289344,   78688,  157376,  314752, 629504, 
             1259008};
  static int w04[10] = { 41, 34, 21, 20,  8,  7,  7,  4,  3,  3 };
  static int w05[9] = { 81, 80, 43, 40, 30, 26, 12, 11, 9 };
  static int w06[6] = { 1, 2, 4, 8, 16, 32};
  static int w07[10] = { 25, 27, 3, 12, 6, 15, 9, 30, 21, 19 };

  cout << "\n";
  cout << "SUBSET_SUM_TABLE_TESTS:\n";
  cout << "  SUBSET_SUM_TABLE_TEST calls SUBSET_SUM_TABLE\n";
  cout << "  with particular problem data.\n";

  for ( test = 1; test <= test_num; test++ )
  {
    if ( test == 1 )
    {
      t = 53;
      n = 8;
      w = i4vec_copy_new ( n, w01 );
    }
    else if ( test == 2 )
    {
      t = 5842;
      n = 10;
      w = i4vec_copy_new ( n, w02 );
    }
    else if ( test == 3 )
    {
      t = 2463098;
      n = 21;
      w = i4vec_copy_new ( n, w03 );
    }
    else if ( test == 4 )
    {
      t = 50;
      n = 10;
      w = i4vec_copy_new ( n, w04 );
    }
    else if ( test == 5 )
    {
      t = 100;
      n = 9;
      w = i4vec_copy_new ( n, w05 );
    }
    else if ( test == 6 )
    {
      t = 22;
      n = 6;
      w = i4vec_copy_new ( n, w06 );
    }
    else if ( test == 7 )
    {
      t = 50;
      n = 10;
      w = i4vec_copy_new ( n, w07 );
    }

    subset_sum_table_test ( t, n, w );

    delete [] w;
  }

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

int *subset_sum_table_to_list ( int t, int table[], int m )

//****************************************************************************80
//
//  Purpose:
//
//    SUBSET_SUM_TABLE_TO_LIST converts a subset sum table to a list.
//
//  Discussion:
//
//    The subset sum problem seeks to construct the value T by summing a 
//    subset of the values W.
//
//    This function takes a table computed by subset_sum_table() and converts
//    it to the corresponding list of values that form the sum.
//
//  Licensing:
//
//    I don't care what you do with this code.
//
//  Modified:
//
//    11 November 2015
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int T, the target value.
//
//    Input, int TABLE[T], the subset sum table.
//
//    Input, int M, the number of items in the list.
//
//    Output, int LIST[M], the weights that sum to T.
//
{
  int i;
  int *list;
//
//  Create list.
//
  list = new int[m];
//
//  Populate list.
//
  i = t;
  m = 0;
  while ( 0 < i )
  {
    list[m] = table[i];
    m = m + 1;
    i = i - table[i];
  }
  return list;
}
//****************************************************************************80

int subset_sum_table_to_list_length ( int t, int table[] )

//****************************************************************************80
//
//  Purpose:
//
//    SUBSET_SUM_TABLE_TO_LIST_LENGTH returns the length of a table list.
//
//  Discussion:
//
//    The subset sum problem seeks to construct the value T by summing a 
//    subset of the values W.
//
//    This function takes a table computed by subset_sum_table() and converts
//    it to the corresponding list of values that form the sum.
//
//  Licensing:
//
//    I don't care what you do with this code.
//
//  Modified:
//
//    12 November 2015
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, integer T, the target value.
//
//    Input, integer TABLE[T], the subset sum table.
//
//    Output, int SUBSET_SUM_TABLE_TO_LIST_LENGTH, the number of items in the list.
//    If M == 0, then no solution was found and the list is empty.
//
{
  int i;
  int m;
//
//  Determine length of list.
//
  i = t;
  m = 0;
  while ( 0 < i )
  {
    m = m + 1;
    i = i - table[i];
  }
  return m;
}
//****************************************************************************80

void timestamp ( )

//****************************************************************************80
//
//  Purpose:
//
//    TIMESTAMP prints the current YMDHMS date as a time stamp.
//
//  Example:
//
//    31 May 2001 09:45:54 AM
//
//  Licensing:
//
//    I don't care what you do with this code.
//
//  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
}