9 December  2013  10:50:29.654 AM      
 
COMBO_PRB
  FORTRAN77 version
  Test the COMBO library.
 
TEST01
  Balanced sequences:
 
  BAL_SEQ_ENUM enumerates,
  BAL_SEQ_RANK ranks,
  BAL_SEQ_SUCCESSOR lists,
  BAL_SEQ_UNRANK unranks.
 
  For N =        5
  the number of balanced sequences is       42
 
      0   0 0 0 0 0 1 1 1 1 1
      1   0 0 0 0 1 0 1 1 1 1
      2   0 0 0 0 1 1 0 1 1 1
      3   0 0 0 0 1 1 1 0 1 1
      4   0 0 0 0 1 1 1 1 0 1
      5   0 0 0 1 0 0 1 1 1 1
      6   0 0 0 1 0 1 0 1 1 1
      7   0 0 0 1 0 1 1 0 1 1
      8   0 0 0 1 0 1 1 1 0 1
      9   0 0 0 1 1 0 0 1 1 1
     10   0 0 0 1 1 0 1 0 1 1
     11   0 0 0 1 1 0 1 1 0 1
     12   0 0 0 1 1 1 0 0 1 1
     13   0 0 0 1 1 1 0 1 0 1
     14   0 0 1 0 0 0 1 1 1 1
     15   0 0 1 0 0 1 0 1 1 1
     16   0 0 1 0 0 1 1 0 1 1
     17   0 0 1 0 0 1 1 1 0 1
     18   0 0 1 0 1 0 0 1 1 1
     19   0 0 1 0 1 0 1 0 1 1
     20   0 0 1 0 1 0 1 1 0 1
     21   0 0 1 0 1 1 0 0 1 1
     22   0 0 1 0 1 1 0 1 0 1
     23   0 0 1 1 0 0 0 1 1 1
     24   0 0 1 1 0 0 1 0 1 1
     25   0 0 1 1 0 0 1 1 0 1
     26   0 0 1 1 0 1 0 0 1 1
     27   0 0 1 1 0 1 0 1 0 1
     28   0 1 0 0 0 0 1 1 1 1
     29   0 1 0 0 0 1 0 1 1 1
     30   0 1 0 0 0 1 1 0 1 1
     31   0 1 0 0 0 1 1 1 0 1
     32   0 1 0 0 1 0 0 1 1 1
     33   0 1 0 0 1 0 1 0 1 1
     34   0 1 0 0 1 0 1 1 0 1
     35   0 1 0 0 1 1 0 0 1 1
     36   0 1 0 0 1 1 0 1 0 1
     37   0 1 0 1 0 0 0 1 1 1
     38   0 1 0 1 0 0 1 0 1 1
     39   0 1 0 1 0 0 1 1 0 1
     40   0 1 0 1 0 1 0 0 1 1
     41   0 1 0 1 0 1 0 1 0 1
 
  The element of rank       21
 
     0 0 1 0 1 1 0 0 1 1
 
  Element to be ranked:
 
         1:            0
         2:            0
         3:            1
         4:            0
         5:            1
         6:            1
         7:            0
         8:            0
         9:            1
        10:            1
 
  Computed rank:       21
 
TEST02
  BAL_SEQ_TO_TABLEAU converts a balanced
  sequence to a tableau;
  TABLEAU_TO_BAL_SEQ converts a tableau
  to a balanced sequence.
 
  "Random" balanced sequence:
 
     0 0 1 1 0 0 1 1
 
  Corresponding tableau
 
     1 2 5 6
     3 4 7 8
 
  Corresponding balanced sequence:
 
         1:            0
         2:            0
         3:            1
         4:            1
         5:            0
         6:            0
         7:            1
         8:            1
 
TEST03
  BELL_NUMBERS computes Bell numbers.
 
         N        BELL(N)    BELL_NUMBERS(N)
 
         0             1             1
         1             1             1
         2             2             2
         3             5             5
         4            15            15
         5            52            52
         6           203           203
         7           877           877
         8          4140          4140
         9         21147         21147
        10        115975        115975
 
TEST04
  I4_CHOOSE computes binomial coefficients.
      -1      -1       0
      -1       0       0
      -1       1       0
      -1       2       0
      -1       3       0
      -1       4       0
      -1       5       0
       0      -1       0
       0       0       1
       0       1       0
       0       2       0
       0       3       0
       0       4       0
       0       5       0
       1      -1       0
       1       0       1
       1       1       1
       1       2       0
       1       3       0
       1       4       0
       1       5       0
       2      -1       0
       2       0       1
       2       1       2
       2       2       1
       2       3       0
       2       4       0
       2       5       0
       3      -1       0
       3       0       1
       3       1       3
       3       2       3
       3       3       1
       3       4       0
       3       5       0
       4      -1       0
       4       0       1
       4       1       4
       4       2       6
       4       3       4
       4       4       1
       4       5       0
       5      -1       0
       5       0       1
       5       1       5
       5       2      10
       5       3      10
       5       4       5
       5       5       1
 
TEST05
  CYCLE_TO_PERM converts a permutation from
  cycle to array form;
  PERM_TO_CYCLE converts a permutation from
  array to cycle form.
 
  "Random" permutation:
 
   1   2   3   4   5   6   7
   4   5   1   2   3   6   7
 
  Corresponding cycle form:
  Number of cycles is        3
 
       4   2   5   3   1
       6
       7
 
  Corresponding permutation:
 
   1   2   3   4   5   6   7
   4   5   1   2   3   6   7
 
TEST06
  For a distribution of M indistinguishable
  objects among K distinguishable slots:
 
  DIST_ENUM enumerates them;
  DIST_NEXT produces the "next" one.
 
  Number of:
    indistinguishable objects =        5
    distinguishable slots =            3
    distributions is                  21
 
        1    0    0    5
        2    0    1    4
        3    0    2    3
        4    0    3    2
        5    0    4    1
        6    0    5    0
        7    1    0    4
        8    1    1    3
        9    1    2    2
       10    1    3    1
       11    1    4    0
       12    2    0    3
       13    2    1    2
       14    2    2    1
       15    2    3    0
       16    3    0    2
       17    3    1    1
       18    3    2    0
       19    4    0    1
       20    4    1    0
       21    5    0    0
 
TEST07:
  I4_FACTORIAL evaluates the factorial function.
 
     X       Exact F       FACTORIAL(X)
 
   1           1           1
   2           2           2
   3           6           6
   4          24          24
   5         120         120
   6         720         720
   7        5040        5040
   8       40320       40320
   9      362880      362880
  10     3628800     3628800
  11    39916800    39916800
  12   479001600   479001600
 
TEST08
  Gray codes:
 
  GRAY_CODE_ENUM enumerates,
  GRAY_CODE_RANK ranks,
  GRAY_CODE_SUCCESSOR lists,
  GRAY_CODE_UNRANK unranks.
 
  For N =        5
  the number of Gray code elements is       32
 
        0    0    0    0    0    0
        1    0    0    0    0    1
        2    0    0    0    1    1
        3    0    0    0    1    0
        4    0    0    1    1    0
        5    0    0    1    1    1
        6    0    0    1    0    1
        7    0    0    1    0    0
        8    0    1    1    0    0
        9    0    1    1    0    1
       10    0    1    1    1    1
       11    0    1    1    1    0
       12    0    1    0    1    0
       13    0    1    0    1    1
       14    0    1    0    0    1
       15    0    1    0    0    0
       16    1    1    0    0    0
       17    1    1    0    0    1
       18    1    1    0    1    1
       19    1    1    0    1    0
       20    1    1    1    1    0
       21    1    1    1    1    1
       22    1    1    1    0    1
       23    1    1    1    0    0
       24    1    0    1    0    0
       25    1    0    1    0    1
       26    1    0    1    1    1
       27    1    0    1    1    0
       28    1    0    0    1    0
       29    1    0    0    1    1
       30    1    0    0    0    1
       31    1    0    0    0    0
 
  The element of rank       16
 
        1    1    0    0    0
 
  Element to be ranked:
 
         1:            1
         2:            1
         3:            0
         4:            0
         5:            0
 
  Computed rank:       16
 
TEST09
  Integer vectors:
 
  I4VEC_SORT_INSERT_A ascending sorts;
  I4VEC_SEARCH_BINARY_A searches a ascending sorted vector.
 
  Before ascending sort:
 
         1:            6
         2:            7
         3:            1
         4:            0
         5:            4
         6:            3
         7:            2
         8:            1
         9:            5
        10:            8
 
  After ascending sort:
 
         1:            0
         2:            1
         3:            1
         4:            2
         5:            3
         6:            4
         7:            5
         8:            6
         9:            7
        10:            8
 
  Now search for an instance of the value        5
 
  The value occurs at index =        7
 
TEST10
  Integer vectors:
 
  I4VEC_SORT_INSERT_D descending sorts;
  I4VEC_SEARCH_BINARY_D searches a descending
  sorted vector.
 
  Before descending sort:
 
         1:            6
         2:            7
         3:            1
         4:            0
         5:            4
         6:            3
         7:            2
         8:            1
         9:            5
        10:            8
 
  After descending sort:
 
         1:            8
         2:            7
         3:            6
         4:            5
         5:            4
         6:            3
         7:            2
         8:            1
         9:            1
        10:            0
 
  Now search for an instance of the value        5
 
  The value occurs at index =        4
 
TEST11
  KNAPSACK_REORDER reorders the knapsack data.
  KNAPSACK_01 solves the 0/1 knapsack problem.
 
  Object, Profit, Mass, "Profit Density"
 
       1   24.000   12.000    2.000
       2   13.000    7.000    1.857
       3   23.000   11.000    2.091
       4   15.000    8.000    1.875
       5   16.000    9.000    1.778
 
  After reordering by Profit Density:
 
  Object, Profit, Mass, "Profit Density"
 
       1   23.000   11.000    2.091
       2   24.000   12.000    2.000
       3   15.000    8.000    1.875
       4   13.000    7.000    1.857
       5   16.000    9.000    1.778
 
  Total mass restriction is  26.000
 
  Object, Density, Choice, Profit, Mass
 
     1  2.091  1.000 23.000 11.000
     2  2.000  0.000  0.000  0.000
     3  1.875  1.000 15.000  8.000
     4  1.857  1.000 13.000  7.000
     5  1.778  0.000  0.000  0.000
 
  Total:             51.000 26.000
 
TEST12
  KNAPSACK_REORDER reorders the knapsack data.
  KNAPSACK_RATIONAL solves the rational knapsack problem.
 
  Object, Profit, Mass, "Profit Density"
 
     1 24.000 12.000  2.000
     2 13.000  7.000  1.857
     3 23.000 11.000  2.091
     4 15.000  8.000  1.875
     5 16.000  9.000  1.778
 
  After reordering by Profit Density:
 
  Object, Profit, Mass, "Profit Density"
 
     1 23.000 11.000  2.091
     2 24.000 12.000  2.000
     3 15.000  8.000  1.875
     4 13.000  7.000  1.857
     5 16.000  9.000  1.778
 
  Total mass restriction is  26.000
 
  Object, Density, Choice, Profit, Mass
 
     1  2.091  1.000 23.000 11.000
     2  2.000  1.000 24.000 12.000
     3  1.875  0.375  5.625  3.000
     4  1.857  0.000  0.000  0.000
     5  1.778  0.000  0.000  0.000
 
  Total:             52.625 26.000
 
TEST13
  K-subsets of an N set,
  using the colexicographic ordering:
 
  KSUBSET_COLEX_RANK ranks,
  KSUBSET_COLEX_SUCCESSOR lists,
  KSUBSET_COLEX_UNRANK unranks.
  KSUBSET_ENUM enumerates,
 
  For N =        5
  the number of K subsets is       10
 
        0    3    2    1
        1    4    2    1
        2    4    3    1
        3    4    3    2
        4    5    2    1
        5    5    3    1
        6    5    4    1
        7    5    4    2
        8    5    4    3
 
  The element of rank        5
 
        5    3    1
 
  The rank of the element:
 
        5    3    1
 
  is computed as        5
 
TEST14
  K-subsets of an N set,
  using the lexicographic ordering:
 
  KSUBSET_ENUM enumerates,
  KSUBSET_LEX_RANK ranks,
  KSUBSET_LEX_SUCCESSOR lists,
  KSUBSET_LEX_UNRANK unranks.
 
  For N =        5
  the number of K subsets is       10
 
    0    1    2    3
    1    1    2    4
    2    1    2    5
    3    1    3    4
    4    1    3    5
    5    1    4    5
    6    2    3    4
    7    2    3    5
    8    2    4    5
    9    3    4    5
 
  The element of rank        5
 
    1    4    5
 
  The rank of the element:
 
    1    4    5
 
  is computed as        5
 
TEST15
  K-subsets of an N set,
  using the revolving door ordering:
 
  KSUBSET_ENUM enumerates,
  KSUBSET_REVDOOR_RANK ranks,
  KSUBSET_REVDOOR_SUCCESSOR lists,
  KSUBSET_REVDOOR_UNRANK unranks.
 
  For N =        5
  the number of K subsets is       10
 
    0    1    2    3
    1    1    3    4
    2    2    3    4
    3    1    2    4
    4    1    4    5
    5    2    4    5
    6    3    4    5
    7    1    3    5
    8    2    3    5
    9    1    2    5
 
  The element of rank        5
 
    2    4    5
 
  The rank of the element:
 
    2    4    5
 
  is computed as        5
 
TEST16
  MARRIAGE arranges a set of stable marriages
  given a set of preferences.
 
  Man, Wife's rank, Wife
 
       1       3       1
       2       4       4
       3       3       5
       4       2       3
       5       3       2
 
  Woman, Husband's rank, Husband
 
       1       2       1
       2       2       5
       3       2       4
       4       2       2
       5       3       3
 
  Correct result:
 
  M:W 1  2  3  4  5
   1  +  .  .  .  .
   2  .  .  .  +  .
   3  .  .  .  .  +
   4  .  .  +  .  .
   5  .  +  .  .  .
 
TEST17
  MOUNTAIN computes mountain numbers.
 
   Y    MXY
 
   0     42   0  14   0   5   0   2   0   1   0   1
   1      0  42   0  14   0   5   0   2   0   1   0
   2     90   0  28   0   9   0   3   0   1   0   0
   3      0  48   0  14   0   4   0   1   0   0   0
   4     75   0  20   0   5   0   1   0   0   0   0
   5      0  27   0   6   0   1   0   0   0   0   0
 
TEST18
  Partitions of N with NPART parts
  in reverse standard form:
 
  NPART_ENUM enumerates,
  NPART_RSF_LEX_RANK ranks,
  NPART_RSF_LEX_SUCCESSOR lists;
  NPART_RSF_LEX_UNRANK unranks.
 
  For N =       12
  and NPART =        3
  the number of partitions is       12
 
    0    1    1   10
    1    1    2    9
    2    1    3    8
    3    1    4    7
    4    1    5    6
    5    2    2    8
    6    2    3    7
    7    2    4    6
    8    2    5    5
    9    3    3    6
   10    3    4    5
   11    4    4    4
 
  The element of rank        4
 
    1    5    6
 
  The rank of the element:
 
    1    5    6
 
  is computed as        4
 
TEST19
  Partitions of N with NPART parts
  in reverse standard form:
 
  NPART_RSF_LEX_RANDOM produces random examples.
    1    4    7
    4    4    4
    3    4    5
    2    4    6
    2    2    8
    1    2    9
    1    5    6
    1    3    8
    1    2    9
    2    5    5
 
TEST20
  Partitions of N with NPART parts
  in standard form:
 
  NPART_ENUM enumerates,
  NPART_SF_LEX_SUCCESSOR lists.
 
  For N =       12
  and NPART =        3
  the number of partitions is       12
 
    0    4    4    4
    1    5    4    3
    2    5    5    2
    3    6    3    3
    4    6    4    2
    5    6    5    1
    6    7    3    2
    7    7    4    1
    8    8    2    2
    9    8    3    1
   10    9    2    1
   11   10    1    1
 
TEST21
  NPART_TABLE tabulates partitions
  of N with NPART parts;
  PART_TABLE tabulates partitions of N.
 
    I P(I)  P(I,0) P(I,1) P(I,2) P(I,3) P(I,4) P(I,5)
 
    0    1    1    0*****32767*****   11
    1    1    0    1    0    0    0    0
    2    2    0    1    1    0    0    0
    3    3    0    1    1    1    0    0
    4    5    0    1    2    1    1    0
    5    7    0    1    2    2    1    1
    6   11    0    1    3    3    2    1
    7   15    0    1    3    4    3    2
    8   22    0    1    4    5    5    3
    9   30    0    1    4    7    6    5
   10   42    0    1    5    8    9    7
 
TEST22
  PART_SUCCESSOR produces partitions of N,
  PART_ENUM enumerates.
 
  Partitions of N =        8
 
  For N =        8
  the number of partitions is       22
 
   0     1  1  1  1  1  1  1  1
   1     2  1  1  1  1  1  1
   2     2  2  1  1  1  1
   3     2  2  2  1  1
   4     2  2  2  2
   5     3  1  1  1  1  1
   6     3  2  1  1  1
   7     3  2  2  1
   8     3  3  1  1
   9     3  3  2
  10     4  1  1  1  1
  11     4  2  1  1
  12     4  2  2
  13     4  3  1
  14     4  4
  15     5  1  1  1
  16     5  2  1
  17     5  3
  18     6  1  1
  19     6  2
  20     7  1
  21     8
 
TEST23
  PART_SUCCESSOR produces partitions of N,
  PART_SF_CONJUGATE produces the conjugate of a partition.
 
  Partitions of N =        8
   0      1  1  1  1  1  1  1  1
  Con:    8
   1      2  1  1  1  1  1  1
  Con:    7  1
   2      2  2  1  1  1  1
  Con:    6  2
   3      2  2  2  1  1
  Con:    5  3
   4      2  2  2  2
  Con:    4  4
   5      3  1  1  1  1  1
  Con:    6  1  1
   6      3  2  1  1  1
  Con:    5  2  1
   7      3  2  2  1
  Con:    4  3  1
   8      3  3  1  1
  Con:    4  2  2
   9      3  3  2
  Con:    3  3  2
  10      4  1  1  1  1
  Con:    5  1  1  1
  11      4  2  1  1
  Con:    4  2  1  1
  12      4  2  2
  Con:    3  3  1  1
  13      4  3  1
  Con:    3  2  2  1
  14      4  4
  Con:    2  2  2  2
  15      5  1  1  1
  Con:    4  1  1  1  1
  16      5  2  1
  Con:    3  2  1  1  1
  17      5  3
  Con:    2  2  2  1  1
  18      6  1  1
  Con:    3  1  1  1  1  1
  19      6  2
  Con:    2  2  1  1  1  1
  20      7  1
  Con:    2  1  1  1  1  1  1
  21      8
  Con:    1  1  1  1  1  1  1  1
 
TEST24
  PART_SF_MAJORIZE determines if one partition
  majorizes another.
 
  Partitions of N =        8
 
  A:    2  2  2  1  1
  B:    3  1  1  1  1  1
  C:    2  2  1  1  1  1
 
  A compare B:       -2
  B compare C:        1
  C compare A:       -1
  C compare C:        0
 
TEST25
  PARTITION_GREEDY partitions an integer vector into
  two subsets with nearly equal sum.
 
 
Data set #1 partitioned:
 
            10
       9
       8
             7
             5
       5
             3
       3
             2
       2
 
  Sums:
 
    27    27
 
 
  Data set #2 partitioned:
 
        1003
   885
   854
         771
   734
         486
         281
   121
          83
    62
 
  Sums:
 
  2656  2624
 
TEST26
  Partitions of N with maximum element NMAX:
 
  PARTN_SUCCESSOR lists;
  PARTN_ENUM enumerates.
 
  For N =       11
  and NMAX =        4
  the number of partitions is       11
 
   0     4  1  1  1  1  1  1  1
   1     4  2  1  1  1  1  1
   2     4  2  2  1  1  1
   3     4  2  2  2  1
   4     4  3  1  1  1  1
   5     4  3  2  1  1
   6     4  3  2  2
   7     4  3  3  1
   8     4  4  1  1  1
   9     4  4  2  1
  10     4  4  3
 
  Repeat, but list RSF conjugated partitions.
 
   0     1  1  1  8
   1     1  1  2  7
   2     1  1  3  6
   3     1  1  4  5
   4     1  2  2  6
   5     1  2  3  5
   6     1  2  4  4
   7     1  3  3  4
   8     2  2  2  5
   9     2  2  3  4
  10     2  3  3  3
 
TEST27
  Permutations of the integers:
 
  PERM_INV computes an inverse permutation,
  PERM_MUL multiplies two permutations.
 
  The permutation P is
 
   1   2   3   4
   3   1   2   4
 
  The inverse permutation Q is
 
   1   2   3   4
   2   3   1   4
 
  The product R = P * Q is
 
   1   2   3   4
   1   2   3   4
 
TEST28
  Permutations of the integers,
  using the lexicographic ordering:
 
  PERM_ENUM enumerates,
  PERM_LEX_RANK ranks,
  PERM_LEX_SUCCESSOR lists,
  PERM_LEX_UNRANK unranks.
 
  For N =        4
  the number of permutations is       24
 
    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
    7    2    1    4    3
    8    2    3    1    4
    9    2    3    4    1
   10    2    4    1    3
   11    2    4    3    1
   12    3    1    2    4
   13    3    1    4    2
   14    3    2    1    4
   15    3    2    4    1
   16    3    4    1    2
   17    3    4    2    1
   18    4    1    2    3
   19    4    1    3    2
   20    4    2    1    3
   21    4    2    3    1
   22    4    3    1    2
   23    4    3    2    1
 
  The element of rank       12
   3   1   2   4
 
  The rank of the element:
 
   1   2   3   4
   3   1   2   4
 
is computed as       12
 
TEST29
  Permutations of the integers
  using the Trotter-Johnson ordering:
 
  PERM_ENUM enumerates,
  PERM_TJ_RANK ranks,
  PERM_TJ_SUCCESSOR lists,
  PERM_TJ_UNRANK unranks.
 
  For N =        4
  the number of permutations is       24
 
    0    1    2    3    4
    1    1    2    4    3
    2    1    4    2    3
    3    4    1    2    3
    4    4    1    3    2
    5    1    4    3    2
    6    1    3    4    2
    7    1    3    2    4
    8    3    1    2    4
    9    3    1    4    2
   10    3    4    1    2
   11    4    3    1    2
   12    4    3    2    1
   13    3    4    2    1
   14    3    2    4    1
   15    3    2    1    4
   16    2    3    1    4
   17    2    3    4    1
   18    2    4    3    1
   19    4    2    3    1
   20    4    2    1    3
   21    2    4    1    3
   22    2    1    4    3
   23    2    1    3    4
 
  The element of rank   12
   4   3   2   1
 
  The rank of the element:
 
   1   2   3   4
   4   3   2   1
 
  is computed as       12
 
TEST30
  Pruefer codes:
 
  PRUEFER_ENUM enumerates,
  PRUEFER_RANK ranks,
  PRUEFER_SUCCESSOR lists,
  PRUEFER_UNRANK unranks.
 
  For N =        4
  the number of Pruefer codes is       16
 
    0    1    1
    1    1    2
    2    1    3
    3    1    4
    4    2    1
    5    2    2
    6    2    3
    7    2    4
    8    3    1
    9    3    2
   10    3    3
   11    3    4
   12    4    1
   13    4    2
   14    4    3
   15    4    4
 
  The element of rank        8
 
    3    1
 
  The rank of the element:
 
    3    1
 
  is computed as        8
 
TEST31
  PRUEFER_TO_TREE converts a Pruefer code to
  a tree;
  TREE_TO_PRUEFER converts a tree to a Pruefer
  code.
 
  Random Pruefer code of rank       27
    2    1    3
 
  Edge list for the corresponding tree:
 
    1    5    2
    2    4    1
    3    2    3
    4    3    1
 
  Corresponding Pruefer code:
    2    1    3
 
  Random Pruefer code of rank      119
    5    4    5
 
  Edge list for the corresponding tree:
 
    1    3    5
    2    2    4
    3    4    5
    4    5    1
 
  Corresponding Pruefer code:
    5    4    5
 
  Random Pruefer code of rank      103
    5    1    4
 
  Edge list for the corresponding tree:
 
    1    3    5
    2    5    1
    3    2    4
    4    4    1
 
  Corresponding Pruefer code:
    5    1    4
 
  Random Pruefer code of rank       70
    3    5    1
 
  Edge list for the corresponding tree:
 
    1    4    3
    2    3    5
    3    5    1
    4    2    1
 
  Corresponding Pruefer code:
    3    5    1
 
  Random Pruefer code of rank       51
    3    1    2
 
  Edge list for the corresponding tree:
 
    1    5    3
    2    4    1
    3    3    2
    4    2    1
 
  Corresponding Pruefer code:
    3    1    2
 
TEST32
  QUEENS produces nonattacking queens
  on a chessboard.
  BACKTRACK supervises a backtrack search.
 
   8   4   1   3   6   2   7   5
   8   3   1   6   2   5   7   4
   8   2   5   3   1   7   4   6
   8   2   4   1   7   5   3   6
   7   5   3   1   6   8   2   4
   7   4   2   8   6   1   3   5
   7   4   2   5   8   1   3   6
   7   3   8   2   5   1   6   4
   7   3   1   6   8   5   2   4
   7   2   6   3   1   4   8   5
   7   2   4   1   8   5   3   6
   7   1   3   8   6   4   2   5
   6   8   2   4   1   7   5   3
   6   4   7   1   8   2   5   3
   6   4   7   1   3   5   2   8
   6   4   2   8   5   7   1   3
   6   4   1   5   8   2   7   3
   6   3   7   4   1   8   2   5
   6   3   7   2   8   5   1   4
   6   3   7   2   4   8   1   5
   6   3   5   8   1   4   2   7
   6   3   5   7   1   4   2   8
   6   3   1   8   5   2   4   7
   6   3   1   8   4   2   7   5
   6   3   1   7   5   8   2   4
   6   2   7   1   4   8   5   3
   6   2   7   1   3   5   8   4
   6   1   5   2   8   3   7   4
   5   8   4   1   7   2   6   3
   5   8   4   1   3   6   2   7
   5   7   4   1   3   8   6   2
   5   7   2   6   3   1   8   4
   5   7   2   6   3   1   4   8
   5   7   2   4   8   1   3   6
   5   7   1   4   2   8   6   3
   5   7   1   3   8   6   4   2
   5   3   8   4   7   1   6   2
   5   3   1   7   2   8   6   4
   5   3   1   6   8   2   4   7
   5   2   8   1   4   7   3   6
   5   2   6   1   7   4   8   3
   5   2   4   7   3   8   6   1
   5   2   4   6   8   3   1   7
   5   1   8   6   3   7   2   4
   5   1   8   4   2   7   3   6
   5   1   4   6   8   2   7   3
   4   8   5   3   1   7   2   6
   4   8   1   5   7   2   6   3
   4   8   1   3   6   2   7   5
   4   7   5   3   1   6   8   2
   4   7   5   2   6   1   3   8
   4   7   3   8   2   5   1   6
   4   7   1   8   5   2   6   3
   4   6   8   3   1   7   5   2
   4   6   8   2   7   1   3   5
   4   6   1   5   2   8   3   7
   4   2   8   6   1   3   5   7
   4   2   8   5   7   1   3   6
   4   2   7   5   1   8   6   3
   4   2   7   3   6   8   5   1
   4   2   7   3   6   8   1   5
   4   2   5   8   6   1   3   7
   4   1   5   8   6   3   7   2
   4   1   5   8   2   7   3   6
   3   8   4   7   1   6   2   5
   3   7   2   8   6   4   1   5
   3   7   2   8   5   1   4   6
   3   6   8   2   4   1   7   5
   3   6   8   1   5   7   2   4
   3   6   8   1   4   7   5   2
   3   6   4   2   8   5   7   1
   3   6   4   1   8   5   7   2
   3   6   2   7   5   1   8   4
   3   6   2   7   1   4   8   5
   3   6   2   5   8   1   7   4
   3   5   8   4   1   7   2   6
   3   5   7   1   4   2   8   6
   3   5   2   8   6   4   7   1
   3   5   2   8   1   7   4   6
   3   1   7   5   8   2   4   6
   2   8   6   1   3   5   7   4
   2   7   5   8   1   4   6   3
   2   7   3   6   8   5   1   4
   2   6   8   3   1   4   7   5
   2   6   1   7   4   8   3   5
   2   5   7   4   1   8   6   3
   2   5   7   1   3   8   6   4
   2   4   6   8   3   1   7   5
   1   7   5   8   2   4   6   3
   1   7   4   6   8   2   5   3
   1   6   8   3   7   4   2   5
   1   5   8   6   3   7   2   4
 
TEST33
  RGF_G_TABLE tabulates generalized restricted
  growth functions.
 
     1     1     1     1     1     1     1
     1     2     3     4     5     6
     2     5    10    17    26
     5    15    37    77
    15    52   151
    52   203
   203
 
TEST34
  Restricted growth functions:
 
  RGF_ENUM enumerates,
  RGF_RANK ranks,
  RGF_SUCCESSOR lists;
  RGF_UNRANK unranks.
 
  For M =        4
  the number of RGF's is       15
 
    0    1    1    1    1
    1    1    1    1    2
    2    1    1    2    1
    3    1    1    2    2
    4    1    1    2    3
    5    1    2    1    1
    6    1    2    1    2
    7    1    2    1    3
    8    1    2    2    1
    9    1    2    2    2
   10    1    2    2    3
   11    1    2    3    1
   12    1    2    3    2
   13    1    2    3    3
   14    1    2    3    4
 
  The element of rank        7
 
    1    2    1    3
 
  The rank of the element:
 
    1    2    1    3
 
  is computed as        7
 
TEST35
  RGF_TO_SETPART converts a balanced
  sequence to a restricted growth function;
  SETPART_TO_RGF converts a restricted growth
  function to a balanced sequence.
 
  "Random" restricted growth function:
 
 1 1 1 1 1 2 1 3
 
  Corresponding set partition
 
   1   2   3   4   5   7
   6
   8
 
Corresponding restricted growth function:
 
 1 1 1 1 1 2 1 3
 
TEST36
  Set partitions:
 
  SETPART_ENUM enumerates,
 
     1     1
     2     2
     3     5
     4    15
     5    52
     6   203
 
TEST37
  STIRLING_NUMBERS1 computes a table of Stirling
  numbers of the first kind.
 
    I S(I,0) S(I,1) S(I,2) S(I,3) S(I,4) S(I,5)
 
    0    1    0    0    0    0    0    0
    1    0    1    0    0    0    0    0
    2    0   -1    1    0    0    0    0
    3    0    2   -3    1    0    0    0
    4    0   -6   11   -6    1    0    0
    5    0   24  -50   35  -10    1    0
    6    0 -120  274 -225   85  -15    1
 
TEST38
  STIRLING_NUMBERS2 computes a table of Stirling
  numbers of the second kind.
 
    I S(I,0) S(I,1) S(I,2) S(I,3) S(I,4) S(I,5)
 
    0    1    0    0    0    0    0    0
    1    0    1    0    0    0    0    0
    2    0    1    1    0    0    0    0
    3    0    1    3    1    0    0    0
    4    0    1    7    6    1    0    0
    5    0    1   15   25   10    1    0
    6    0    1   31   90   65   15    1
 
TEST39
  All subsets of a set,
  using the colexicographic ordering:
 
  SUBSET_COLEX_RANK ranks,
  SUBSET_COLEX_SUCCESSOR lists,
  SUBSET_COLEX_UNRANK unranks.
  SUBSET_ENUM enumerates.
 
  For N =        5
  the number of subsets is       32
 
    0    0    0    0    0    0
    1    1    0    0    0    0
    2    0    1    0    0    0
    3    1    1    0    0    0
    4    0    0    1    0    0
    5    1    0    1    0    0
    6    0    1    1    0    0
    7    1    1    1    0    0
    8    0    0    0    1    0
    9    1    0    0    1    0
   10    0    1    0    1    0
   11    1    1    0    1    0
   12    0    0    1    1    0
   13    1    0    1    1    0
   14    0    1    1    1    0
   15    1    1    1    1    0
   16    0    0    0    0    1
   17    1    0    0    0    1
   18    0    1    0    0    1
   19    1    1    0    0    1
   20    0    0    1    0    1
   21    1    0    1    0    1
   22    0    1    1    0    1
   23    1    1    1    0    1
   24    0    0    0    1    1
   25    1    0    0    1    1
   26    0    1    0    1    1
   27    1    1    0    1    1
   28    0    0    1    1    1
   29    1    0    1    1    1
   30    0    1    1    1    1
   31    1    1    1    1    1
 
  The element of rank       10
 
    0    1    0    1    0
 
  The rank of the element:
 
    0    1    0    1    0
 
  is computed as       10
 
TEST40
  All subsets of a set,
  using the lexicographic ordering:
 
  SUBSET_ENUM enumerates,
  SUBSET_LEX_RANK ranks,
  SUBSET_LEX_SUCCESSOR lists,
  SUBSET_LEX_UNRANK unranks.
 
  For N =        5
  the number of subsets is       32
 
    0    0    0    0    0    0
    1    0    0    0    0    1
    2    0    0    0    1    0
    3    0    0    0    1    1
    4    0    0    1    0    0
    5    0    0    1    0    1
    6    0    0    1    1    0
    7    0    0    1    1    1
    8    0    1    0    0    0
    9    0    1    0    0    1
   10    0    1    0    1    0
   11    0    1    0    1    1
   12    0    1    1    0    0
   13    0    1    1    0    1
   14    0    1    1    1    0
   15    0    1    1    1    1
   16    1    0    0    0    0
   17    1    0    0    0    1
   18    1    0    0    1    0
   19    1    0    0    1    1
   20    1    0    1    0    0
   21    1    0    1    0    1
   22    1    0    1    1    0
   23    1    0    1    1    1
   24    1    1    0    0    0
   25    1    1    0    0    1
   26    1    1    0    1    0
   27    1    1    0    1    1
   28    1    1    1    0    0
   29    1    1    1    0    1
   30    1    1    1    1    0
   31    1    1    1    1    1
 
  The element of rank       10
 
    0    1    0    1    0
 
  The rank of the element:
 
    0    1    0    1    0
 
  is computed as       10
 
TEST41
  SUBSETSUM_SWAP seeks a solution of the subset
  sum problem using pair swapping.
 
  The desired sum is   17
 
    A(I), INDEX(I)
 
     30    0
     12    1
     11    0
      8    0
      8    0
      7    0
      3    1
 
  The achieved sum is       15
 
TEST42
  Trees:
 
  TREE_ENUM enumerates,
  TREE_RANK ranks,
  TREE_SUCCESSOR lists,
  TREE_UNRANK unranks.
 
  For N =        4
  the number of trees is       16
 
    0      4    3    2
           1    1    1
    1      4    3    2
           1    2    1
    2      4    2    3
           1    3    1
    3      3    2    4
           1    4    1
    4      4    3    2
           2    1    1
    5      4    3    2
           2    2    1
    6      4    2    3
           2    3    1
    7      3    2    4
           2    4    1
    8      4    3    2
           3    1    1
    9      4    3    2
           3    2    1
   10      4    2    3
           3    3    1
   11      2    3    4
           3    4    1
   12      3    4    2
           4    1    1
   13      3    4    2
           4    2    1
   14      2    4    3
           4    3    1
   15      3    2    4
           4    4    1
 
  The element of rank        8
 
      4    3    2
      3    1    1
 
  The rank of the element:
 
      4    3    2
      3    1    1
 
  is computed as        8
 
COMBO_PRB
  Normal end of execution.
 
 9 December  2013  10:50:29.658 AM