September 12 2022 2:47:52.920 PM combo_test(): FORTRAN90 version Test combo(). BACKTRACK_TEST BACKTRACK supervises a backtrack search. Here, we search for an arrangement of nonattacking queens on a chessboard. 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 BAL_SEQ_CHECK TEST BAL_SEQ_CHECK checks N and T(1:2*N). Check? N T(1:2*N) T 5 0 0 1 0 1 F 5 1 1 0 1 0 F 5 0 0 1 0 1 BAL_SEQ_ENUM_TEST BAL_SEQ_ENUM enumerates balanced sequences of N items. N # 0 1 1 1 2 2 3 5 4 14 5 42 6 132 7 429 8 1430 9 4862 10 16796 BAL_SEQ_RANK_TEST BAL_SEQ_RANK ranks a balanced sequence of N items. 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 BAL_SEQ_SUCCESSOR_TEST BAL_SEQ_SUCCESSOR lists balanced sequences of N items, one at a time. 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 BAL_SEQ_TO_TABLEAU_TEST BAL_SEQ_TO_TABLEAU converts a balanced sequence to a tableau; Balanced sequence: 0 0 1 1 0 0 1 1 Tableau: Col 1 2 3 4 Row 1: 1 2 5 6 2: 3 4 7 8 BAL_SEQ_UNRANK_TEST BAL_SEQ_UNRANK unranks a balanced sequence of N items. The element of rank 21 0 0 1 0 1 1 0 0 1 1 BELL_NUMBERS_TEST 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 CYCLE_CHECK TEST CYCLE_CHECK checks a permutation in cycle form. Permutation in cycle form: Number of cycles is 3 5 1 3 8 6 2 4 7 Check = F Permutation in cycle form: Number of cycles is 0 Check = F Permutation in cycle form: Number of cycles is 3 5 1 3 8 6 2 4 Check = F Permutation in cycle form: Number of cycles is 3 5 1 3 12 6 2 4 7 Check = F Permutation in cycle form: Number of cycles is 3 5 1 3 8 5 2 4 7 Check = F Permutation in cycle form: Number of cycles is 3 5 1 3 8 6 2 4 7 Check = T CYCLE_TO_PERM_TEST CYCLE_TO_PERM converts a permutation from cycle to array form; 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 DIST_ENUM_TEST DIST_ENUM enumerates distributions of N indistinguishable objects among M distinguishable slots: N: 0 1 2 3 4 5 M 0: 0 0 0 0 0 0 1: 1 1 1 1 1 1 2: 1 2 3 4 5 6 3: 1 3 6 10 15 21 4: 1 4 10 20 35 56 5: 1 5 15 35 70 126 6: 1 6 21 56 126 252 7: 1 7 28 84 210 462 8: 1 8 36 120 330 792 9: 1 9 45 165 495 1287 10: 1 10 55 220 715 2002 DIST_NEXT_TEST DIST_NEXT produces the next distribution of M indistinguishable objects among K distinguishable slots. 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 EDGE_CHECK TEST EDGE_CHECK checks a graph described by edges. Check? Nodes Edges EdgeList F -5 3 Edge list of graph: Col 1 2 3 Row 1: 1 2 3 2: 2 3 1 F 3 -1 Edge list of graph: (None) F 3 3 Edge list of graph: Col 1 2 3 Row 1: 1 2 3 2: 2 3 4 F 3 3 Edge list of graph: Col 1 2 3 Row 1: 1 2 3 2: 2 2 1 F 3 3 Edge list of graph: Col 1 2 3 Row 1: 1 2 2 2: 2 3 1 T 3 3 Edge list of graph: Col 1 2 3 Row 1: 1 2 3 2: 2 3 1 EDGE_DEGREE_TEST EDGE_DEGREE determines the degree of each node in a graph. The edge array: Col 1 2 3 4 5 Row 1: 1 2 2 3 4 2: 2 3 4 4 5 The degree vector: 1 1 2 3 3 2 4 3 5 1 EDGE_ENUM_TEST EDGE_ENUM enumerates the maximum number of edges possible in a graph of NODE_NUM nodes. NODE_NUM EDGE_NUM(max) 1 0 2 1 3 3 4 6 5 10 6 15 7 21 8 28 9 36 10 45 GRAY_CODE_CHECK TEST GRAY_CODE_CHECK checks N and T(1:N). Check? N T(1:N) 1 5 0 1 1 0 1 0 5 1 0 7 1 0 1 5 1 1 1 1 1 GRAY_CODE_ENUM_TEST GRAY_CODE_ENUM enumerates Gray codes N Enum(N) 0 1 1 2 2 4 3 8 4 16 5 32 6 64 7 128 8 256 9 512 10 1024 gray_code_random_test(): gray_code_random() returns a random Gray code of N digits. 0 0 0 1 0 1 0 0 0 0 1 0 1 0 1 0 1 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 1 0 0 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 1 1 0 1 GRAY_CODE_RANK_TEST GRAY_CODE_RANK ranks Gray codes. Element to be ranked: 1 1 2 1 3 0 4 0 5 0 Computed rank: 16 GRAY_CODE_SUCCESSOR_TEST GRAY_CODE_SUCCESSOR lists Gray codes one by one. 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 GRAY_CODE_UNRANK_TEST GRAY_CODE_UNRANK unranks a Gray code. The element of rank 16 1 1 0 0 0 I4_CHOOSE_TEST 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 I4_FACTORIAL_TEST: 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 I4_FALL_TEST: I4_FALL evaluates the falling factorial function: M N Exact I4_FALL(M,N) 5 0 1 1 5 1 5 5 5 2 20 20 5 3 60 60 5 4 120 120 5 5 120 120 5 6 0 0 50 0 1 1 10 1 10 10 4000 1 4000 4000 10 2 90 90 18 3 4896 4896 4 4 24 24 98 3 912576 912576 1 7 0 0 I4VEC_BACKTRACK_TEST I4VEC_BACKTRACK uses backtracking, seeking a vector X of N values which satisfies some condition. In this demonstration, we have 8 integers W(I). We seek all subsets that sum to 53. X(I) is 0 or 1 if the entry is skipped or used. 1 53: 15 22 16 2 53: 15 14 16 8 3 53: 22 14 9 8 Done! I4VEC_DOT_PRODUCT_TEST I4VEC_DOT_PRODUCT computes the dot product of two I4VECs. The vector A: 1 1 2 0 3 8 4 10 5 2 The vector B: 1 10 2 4 3 5 4 5 5 8 The dot product is 116 I4VEC_PART1_TEST: I4VEC_PART1 partitions an integer N into NPART parts. Partition N = 17 into NPART = 5 parts: The partition: 1 13 2 1 3 1 4 1 5 1 I4VEC_PART2_TEST: I4VEC_PART2 partitions an integer N into NPART parts. Partition N = 17 into NPART = 5 parts: The partition: 1 4 2 4 3 3 4 3 5 3 I4VEC_SEARCH_BINARY_A_TEST I4VEC_SEARCH_BINARY_A searches a ascending sorted vector. Ascending sorted array: 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 I4VEC_SEARCH_BINARY_D_TEST I4VEC_SEARCH_BINARY_D searches a descending sorted vector. Descending sorted array: 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 I4VEC_SORT_INSERT_A_TEST I4VEC_SORT_INSERT_A ascending sorts an I4VEC; 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 I4VEC_SORT_INSERT_D_TEST I4VEC_SORT_INSERT_D descending sorts an I4VEC. 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 I4VEC_UNIFORM_AB_TEST I4VEC_UNIFORM_AB computes pseudorandom values in an interval [A,B]. The lower endpoint A = -100 The upper endpoint B = 200 The random vector: 1 92 2 118 3 -85 4 132 5 -60 6 145 7 -69 8 31 9 -80 10 -52 11 177 12 -50 13 45 14 -31 15 -31 16 17 17 150 18 -62 19 -1 20 45 KNAPSACK_01_TEST 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 KNAPSACK_RATIONAL_TEST 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 KNAPSACK_REORDER_TEST KNAPSACK_REORDER reorders the knapsack data. 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 KSUBSET_COLEX_CHECK TEST KSUBSET_COLEX_CHECK checks a K subset of an N set. Subset: (empty vector) N = 5, K = -1 Check = F Subset: 5 3 2 N = 0, K = 3 Check = F Subset: 5 2 3 N = 5, K = 3 Check = F Subset: 7 3 2 N = 5, K = 3 Check = F Subset: 5 3 2 N = 5, K = 3 Check = T Subset: (empty vector) N = 5, K = 0 Check = T Subset: (empty vector) N = 0, K = 0 Check = T KSUBSET_COLEX_RANK_TEST KSUBSET_COLEX_RANK ranks K-subsets of an N set, using the colexicographic ordering. The element to be ranked: 5 3 1 The rank is computed as 5 KSUBSET_COLEX_SUCCESSOR_TEST: KSUBSET_COLEX_SUCCESSOR lists K-subsets of an N set, using the colexicographic ordering. 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 KSUBSET_COLEX_UNRANK_TEST KSUBSET_COLEX_UNRANK unranks K-subsets of an N set using the colexicographic ordering. The element of rank 5: 5 3 1 KSUBSET_ENUM_TEST KSUBSET_ENUM enumerates K subsets of an N set. K: 0 1 2 3 4 5 N 0: 1 1: 1 1 2: 1 2 1 3: 1 3 3 1 4: 1 4 6 4 1 5: 1 5 10 10 5 1 6: 1 6 15 20 15 6 7: 1 7 21 35 35 21 8: 1 8 28 56 70 56 9: 1 9 36 84 126 126 10: 1 10 45 120 210 252 KSUBSET_LEX_CHECK TEST KSUBSET_LEX_CHECK checks a K subset of an N set. Subset: (empty vector) N = 5, K = -1 Check = F Subset: 2 3 5 N = 0, K = 3 Check = F Subset: 3 2 5 N = 5, K = 3 Check = F Subset: 2 3 7 N = 5, K = 3 Check = F Subset: 2 3 5 N = 5, K = 3 Check = T Subset: (empty vector) N = 5, K = 0 Check = T Subset: (empty vector) N = 0, K = 0 Check = T KSUBSET_LEX_RANK KSUBSET_LEX_RANK ranks K-subsets of an N set, using the lexicographic ordering. The rank of the element: 1 4 5 is computed as 5 KSUBSET_LEX_SUCCESSOR_TEST KSUBSET_LEX_SUCCESSOR lists K-subsets of an N set, using the lexicographic ordering. 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 KSUBSET_LEX_UNRANK_TEST KSUBSET_LEX_UNRANK unranks K-subsets of an N set using the lexicographic ordering. The element of rank 5 1 4 5 KSUBSET_REVDOOR_RANK_TEST KSUBSET_REVDOOR_RANK ranks K-subsets of an N set, using the revolving door ordering. The rank of the element: 2 4 5 is computed as 5 KSUBSET_REVDOOR_SUCCESSOR_TEST KSUBSET_REVDOOR_SUCCESSOR lists K-subsets of an N set, using the revolving door ordering. 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 KSUBSET_REVDOOR_UNRANK_TEST KSUBSET_REVDOOR_UNRANK unranks K-subsets of an N set, using the revolving door ordering. The element of rank 5 2 4 5 MARRIAGE_TEST 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 . + . . . MOUNTAIN_TEST 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 NPART_ENUM_TEST NPART_ENUM enumerates partitions of N into PART_NUM parts. PART_NUM: 1 2 3 4 5 6 N 0: 1: 1 2: 1 1 3: 1 1 1 4: 1 2 1 1 5: 1 2 2 1 1 6: 1 3 3 2 1 1 7: 1 3 4 3 2 1 8: 1 4 5 5 3 2 9: 1 4 7 6 5 3 10: 1 5 8 9 7 5 NPART_RSF_LEX_RANDOM_TEST NPART_RSF_LEX_RANDOM produces random examples. of partitions of N with NPART parts in reverse standard form. 1 4 7 2 5 5 1 2 9 4 4 4 1 3 8 1 4 7 1 3 8 4 4 4 2 4 6 2 5 5 NPART_RSF_LEX_RANK_TEST NPART_RSF_LEX_RANK ranks partitions of N with NPART parts in reverse standard form. The rank of the element: 1 5 6 is computed as 4 NPART_RSF_LEX_SUCCESSOR_TEST NPART_RSF_LEX_SUCCESSOR lists partitions of N with NPART parts in reverse standard form. 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 NPART_RSF_LEX_UNRANK_TEST NPART_RSF_LEX_UNRANK unranks partitions of N with NPART parts in reverse standard form. The element of rank 4 1 5 6 NPART_SF_LEX_SUCCESSOR_TEST NPART_SF_LEX_SUCCESSOR lists partitions of N with NPART parts in standard form. 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 NPART_TABLE_TEST NPART_TABLE tabulates partitions of N with NPART parts; I P(I,0) P(I,1) P(I,2) P(I,3) P(I,4) P(I,5) 0 1 0 0 0 0 11 1 0 1 0 0 0 0 2 0 1 1 0 0 0 3 0 1 1 1 0 0 4 0 1 2 1 1 0 5 0 1 2 2 1 1 6 0 1 3 3 2 1 7 0 1 3 4 3 2 8 0 1 4 5 5 3 9 0 1 4 7 6 5 10 0 1 5 8 9 7 PART_ENUM_TEST PART_ENUM enumerates partitions of N. N # 0 1 1 1 2 2 3 3 4 5 5 8 6 11 7 15 8 22 9 30 10 42 PART_RSF_CHECK TEST PART_RSF_CHECK checks a reverse standard form partition. Partition in RSF form. Partition of N = 0 Number of parts NPART = 4 1 4 4 6 Check = F Partition in RSF form. Partition of N = 15 Number of parts NPART = 0 (empty vector) Check = F Partition in RSF form. Partition of N = 15 Number of parts NPART = 4 -9 4 4 16 Check = F Partition in RSF form. Partition of N = 15 Number of parts NPART = 4 6 4 4 1 Check = F Partition in RSF form. Partition of N = 15 Number of parts NPART = 4 1 4 5 6 Check = F Partition in RSF form. Partition of N = 15 Number of parts NPART = 4 1 4 4 6 Check = T PART_SF_CHECK TEST PART_SF_CHECK checks a standard form partition. Partition in RSF form. Partition of N = 0 Number of parts NPART = 4 6 4 4 1 Check = F Partition in RSF form. Partition of N = 15 Number of parts NPART = 0 (empty vector) Check = F Partition in RSF form. Partition of N = 15 Number of parts NPART = 4 16 4 4 -9 Check = F Partition in RSF form. Partition of N = 15 Number of parts NPART = 4 1 4 4 6 Check = F Partition in RSF form. Partition of N = 15 Number of parts NPART = 4 6 5 4 1 Check = F Partition in RSF form. Partition of N = 15 Number of parts NPART = 4 6 4 4 1 Check = T PART_SF_CONJUGATE_TEST 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 PART_SF_MAJORIZE_TEST 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 PART_SUCCESSOR_TEST PART_SUCCESSOR produces partitions of N. 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 PART_TABLE_TEST PART_TABLE tabulates partitions of N. 0 1 1 1 2 2 3 3 4 5 5 7 6 11 7 15 8 22 9 30 10 42 PARTN_ENUM_TEST PARTN_ENUM enumerates partitions of N with maximum part NMAX. NMAX: 1 2 3 4 5 6 N 0: 1: 1 2: 1 1 3: 1 1 1 4: 1 2 1 1 5: 1 2 2 1 1 6: 1 3 3 2 1 1 7: 1 3 4 3 2 1 8: 1 4 5 5 3 2 9: 1 4 7 6 5 3 10: 1 5 8 9 7 5 PARTN_SF_CHECK TEST PARTN_SF_CHECK checks a standard form partition of N with largest entry NMAX. Partition in SF form. Partition of N = 0 Maximum entry NMAX = 6 Number of parts NPART = 4 6 4 4 1 Check = F Partition in SF form. Partition of N = 15 Maximum entry NMAX = 6 Number of parts NPART = 0 (empty vector) Check = F Partition in SF form. Partition of N = 15 Maximum entry NMAX = 6 Number of parts NPART = 4 6 6 6 -3 Check = F Partition in SF form. Partition of N = 15 Maximum entry NMAX = 6 Number of parts NPART = 4 8 4 2 1 Check = F Partition in SF form. Partition of N = 15 Maximum entry NMAX = 6 Number of parts NPART = 4 1 4 4 6 Check = F Partition in SF form. Partition of N = 15 Maximum entry NMAX = 6 Number of parts NPART = 4 6 5 4 1 Check = F Partition in SF form. Partition of N = 15 Maximum entry NMAX = 6 Number of parts NPART = 4 6 4 4 1 Check = T PARTN_SUCCESSOR_TEST PARTN_SUCCESSOR lists partitions of N with maximum element NMAX: 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 PARTITION_GREEDY_TEST 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 PERM_CHECK TEST PERM_CHECK checks a permutation. Permutation: 5 1 8 3 4 Check = F Permutation: 5 1 4 3 4 Check = F Permutation: 5 1 2 3 4 Check = T PERM_ENUM_TEST PERM_ENUM enumerates permutations of N items. N # 0 1 1 1 2 2 3 6 4 24 5 120 6 720 7 5040 8 40320 9 362880 10 3628800 PERM_INV_TEST PERM_INV inverts a permutation of the integers: 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 PERM_LEX_RANK_TEST PERM_LEX_RANK ranks permutations of the integers, using the lexicographic ordering. The element: 1 2 3 4 3 1 2 4 The rank is computed as 12 PERM_LEX_SUCCESSOR_TEST PERM_LEX_SUCCESSOR lists permutations of the integers, using the lexicographic ordering. 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 PERM_LEX_UNRANK_TEST PERM_LEX_UNRANK unranks permutations of the integers, using the lexicographic ordering. The element of rank 12: 1 2 3 4 3 1 2 4 PERM_MUL_TEST PERM_MUL multiplies two permutations. The permutation P: 1 2 3 4 3 1 2 4 The permutation Q: 1 2 3 4 2 3 1 4 The product R = P * Q is 1 2 3 4 1 2 3 4 PERM_PARITY_TEST PERM_PARITY computes the parity of a permutation. The permutation P: 1 2 3 4 5 2 1 3 4 5 The parity is 1 The permutation P: 1 2 3 4 5 4 1 2 5 3 The parity is 0 The permutation P: 1 2 3 4 5 2 1 3 4 5 The parity is 1 The permutation P: 1 2 3 4 5 4 5 3 1 2 The parity is 0 The permutation P: 1 2 3 4 5 5 1 3 4 2 The parity is 0 PERM_PRINT_TEST PERM_PRINT prints a permutation of (1,...,N). The 1-based permutation: 1 2 3 4 5 6 7 7 2 4 1 5 3 6 PERM_RANDOM_TEST PERM_RANDOM produces a random permutation of (1,...,N); For this test, N = 5 1 3 2 5 4 5 1 2 3 4 5 3 2 1 4 4 5 2 3 1 4 1 3 5 2 PERM_TJ_RANK_TEST PERM_TJ_RANK ranks permutations of the integers using the Trotter-Johnson ordering. The element to be ranked: 1 2 3 4 4 3 2 1 The rank is computed as 12 PERM_TJ_SUCCESSOR_TEST PERM_TJ_SUCCESSOR lists permutations of the integers using the Trotter-Johnson ordering. 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 PERM_TJ_UNRANK_TEST PERM_TJ_UNRANK unranks permutations of the integers using the Trotter-Johnson ordering: The element of rank 12: 1 2 3 4 4 3 2 1 PERM_TO_CYCLE 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 PRUEFER_CHECK TEST PRUEFER_CHECK checks a Pruefer code. Check? N T(1:2*N) F 2 (empty vector) T 3 1 F 4 5 2 T 5 5 1 3 PRUEFER_ENUM_TEST PRUEFER_ENUM enumerates trees on N nodes, using the Pruefer code N # 0 0 1 0 2 1 3 3 4 16 5 125 6 1296 7 16807 8 262144 9 4782969 10 100000000 pruefer_random_test(): pruefer_random() returns a random Pruefer code on N-2 digits. 7 1 3 8 1 3 1 4 1 4 6 1 6 6 7 7 5 5 3 1 2 5 2 6 3 4 7 8 3 8 3 6 3 6 4 4 5 4 5 6 2 3 5 4 5 7 6 5 5 1 1 4 5 2 2 1 5 6 7 5 PRUEFER_RANK_TEST PRUEFER_RANK ranks Pruefer codes. The rank of the element: 3 1 is computed as 8 PRUEFER_SUCCESSOR_TEST PRUEFER_SUCCESSOR lists Pruefer codes. 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 PRUEFER_TO_TREE_TEST PRUEFER_TO_TREE converts a Pruefer code to a tree; Random Pruefer code of rank 31 2 2 2 Edge list for the corresponding tree: 1 5 2 2 4 2 3 3 2 4 2 1 Corresponding Pruefer code: 2 2 2 Random Pruefer code of rank 25 2 1 1 Edge list for the corresponding tree: 1 5 2 2 4 1 3 3 1 4 2 1 Corresponding Pruefer code: 2 1 1 Random Pruefer code of rank 90 4 4 1 Edge list for the corresponding tree: 1 5 4 2 3 4 3 4 1 4 2 1 Corresponding Pruefer code: 4 4 1 Random Pruefer code of rank 85 4 3 1 Edge list for the corresponding tree: 1 5 4 2 4 3 3 3 1 4 2 1 Corresponding Pruefer code: 4 3 1 Random Pruefer code of rank 104 5 1 5 Edge list for the corresponding tree: 1 4 5 2 3 1 3 2 5 4 5 1 Corresponding Pruefer code: 5 1 5 PRUEFER_UNRANK_TEST PRUEFER_UNRANK unranks Pruefer codes. The element of rank 8 3 1 QUEENS_TEST QUEENS produces nonattacking queens on a chessboard using 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 R8_CHOOSE_TEST R8_CHOOSE evaluates C(N,K). N K CNK 0 0 1.00000 1 0 1.00000 1 1 1.00000 2 0 1.00000 2 1 2.00000 2 2 1.00000 3 0 1.00000 3 1 3.00000 3 2 3.00000 3 3 1.00000 4 0 1.00000 4 1 4.00000 4 2 6.00000 4 3 4.00000 4 4 1.00000 5 0 1.00000 5 1 5.00000 5 2 10.0000 5 3 10.0000 5 4 5.00000 5 5 1.00000 R8_GAMMA_LOG_TEST: R8_GAMMA_LOG computes the Log(Gamma()) function. X GAMMA_LOG(X) R8_GAMMA_LOG(X) 0.200000 1.524063822430784 1.524063822430784 0.400000 0.7966778177017837 0.7966778177017837 0.600000 0.3982338580692348 0.3982338580692349 0.800000 0.1520596783998375 0.1520596783998376 1.000000 0.000000000000000 0.000000000000000 1.100000 -0.4987244125983972E-01 -0.4987244125983976E-01 1.200000 -0.8537409000331583E-01 -0.8537409000331585E-01 1.300000 -0.1081748095078604 -0.1081748095078605 1.400000 -0.1196129141723712 -0.1196129141723713 1.500000 -0.1207822376352452 -0.1207822376352453 1.600000 -0.1125917656967557 -0.1125917656967558 1.700000 -0.9580769740706586E-01 -0.9580769740706586E-01 1.800000 -0.7108387291437215E-01 -0.7108387291437215E-01 1.900000 -0.3898427592308333E-01 -0.3898427592308337E-01 2.000000 0.000000000000000 0.000000000000000 3.000000 0.6931471805599453 0.6931471805599454 4.000000 1.791759469228055 1.791759469228055 10.000000 12.80182748008147 12.80182748008147 20.000000 39.33988418719949 39.33988418719949 30.000000 71.25703896716801 71.25703896716800 R8VEC_BACKTRACK_TEST R8VEC_BACKTRACK uses backtracking, seeking a vector X of N values which satisfies some condition. In this demonstration, we have 8 integers W(I). We seek all subsets that sum to 53. X(I) is 0 or 1 if the entry is skipped or used. 1 53.00: 15.00 22.00 16.00 2 53.00: 15.00 14.00 16.00 8.00 3 53.00: 22.00 14.00 9.00 8.00 Done! RGF_CHECK TEST RGF_CHECK checks a restricted growth function. RGF: (empty vector) Check = F RGF: 0 1 2 3 4 5 6 Check = F RGF: 1 3 5 8 9 10 12 Check = F RGF: 1 2 3 1 4 5 4 Check = T RGF_ENUM_TEST RGF_ENUM enumerates restricted growth functions. N # 0 1 1 1 2 2 3 5 4 15 5 52 6 203 7 877 8 4140 9 21147 10 115975 RGF_G_TABLE_TEST 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 RGF_RANK_TEST RGF_RANK ranks restricted growth functions. The rank of the element: 1 2 1 3 is computed as 7 RGF_SUCCESSOR_TEST RGF_SUCCESSOR lists restricted growth functions. 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 RGF_TO_SETPART_TEST RGF_TO_SETPART converts a balanced sequence to a restricted growth function; Restricted growth function: 1 1 1 1 1 2 1 3 Corresponding set partition 1 2 3 4 5 7 6 8 RGF_UNRANK_TEST RGF_UNRANK unranks restricted growth functions. The element of rank 7 1 2 1 3 SETPART_CHECK TEST SETPART_CHECK checks a set partition. The set partition M = 0 NSUB = 3 3 6 1 4 7 2 5 8 Check = F The set partition M = 8 NSUB = 0 Check = F The set partition M = 8 NSUB = 3 3 6 1 4 7 2 5 8 Check = F The set partition M = 8 NSUB = 3 3 6 1 4 9 2 5 8 Check = F The set partition M = 8 NSUB = 3 3 6 1 4 6 2 5 8 Check = F The set partition M = 8 NSUB = 3 3 6 1 4 7 2 5 8 Check = T SETPART_ENUM SETPART_ENUM enumerates set partitions. 1 1 2 2 3 5 4 15 5 52 6 203 SETPART_TO_RGF_TEST SETPART_TO_RGF converts a restricted growth function to a balanced sequence. The set partition 1 2 3 4 5 7 6 8 Corresponding restricted growth function: 1 1 1 1 1 2 1 3 STIRLING_NUMBERS1_TEST 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 STIRLING_NUMBERS2_TEST 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 \n SUBSET_CHECK TEST SUBSET_CHECK checks a subset. Subset: (empty vector) Check = F Subset: 1 2 0 Check = F Subset: 1 0 0 1 0 Check = T SUBSET_COLEX_RANK_TEST SUBSET_COLEX_RANK ranks all subsets of a set, using the colexicographic ordering. The rank of the element: 0 1 0 1 0 is computed as 10 SUBSET_COLEX_SUCCESSOR_TEST SUBSET_COLEX_SUCCESSOR lists all subsets of a set, using the colexicographic ordering. 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 SUBSET_COLEX_UNRANK_TEST SUBSET_COLEX_UNRANK unranks all subsets of a set, using the colexicographic ordering. The element of rank 10 0 1 0 1 0 SUBSET_COMPLEMENT_TEST SUBSET_COMPLEMENT returns the complement of a subset. Subset S1: 1 0 0 0 1 S2 = complement of S1: 0 1 1 1 0 SUBSET_DISTANCE_TEST SUBSET_DISTANCE computes the distance between subsets. Subset S1: 0 0 1 1 0 Subset S2: 0 0 1 0 1 Distance = 5 SUBSET_ENUM_TEST SUBSET_ENUM enumerates subsets of a set of N items. N # 0 1 1 2 2 4 3 8 4 16 5 32 6 64 7 128 8 256 9 512 10 1024 SUBSET_INTERSECT_TEST SUBSET_INTERSECT computes the intersection of subsets. Subset S1: 1 1 0 0 1 1 1 Subset S2: 0 0 0 1 1 0 1 Intersect: 0 0 0 0 1 0 1 SUBSET_LEX_RANK_TEST SUBSET_LEX_RANK ranks all subsets of a set, using the lexicographic ordering. The rank of the element: 0 1 0 1 0 is computed as 10 SUBSET_LEX_SUCCESSOR_TEST SUBSET_LEX_SUCCESSOR lists all subsets of a set, using the lexicographic ordering. 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 SUBSET_LEX_UNRANK_TEST SUBSET_LEX_UNRANK unranks all subsets of a set, using the lexicographic ordering. The element of rank 10 0 1 0 1 0 SUBSET_RANDOM_TEST SUBSET_RANDOM returns a random subset. 1 1 0 0 1 1 1 0 1 1 1 1 1 1 0 0 1 1 0 0 0 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 1 1 0 1 1 1 1 0 1 0 1 1 0 SUBSET_UNION_TEST SUBSET_UNION computes the union of subsets. Subset S1: 1 1 0 1 0 0 0 Subset S2: 1 1 1 1 0 1 1 Union: 1 1 1 1 0 1 1 SUBSET_WEIGHT_TEST SUBSET_WEIGHT returns the weight of a subset. Subset S: 0 1 1 1 0 Subset weight is 3 SUBSET_XOR_TEST SUBSET_XOR computes the exclusive OR of subsets. Subset S1: 0 1 1 1 0 1 0 Subset S2: 1 1 0 0 1 1 1 XOR: 1 0 1 1 1 0 1 SUBSETSUM_SWAP_TEST 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 TABLEAU_CHECK TEST TABLEAU_CHECK checks a 2xN tableau. Check? Check = F Tableau: (None) Check = F Tableau: Col 1 2 3 4 Row 1: 1 2 3 4 2: 2 4 7 9 Check = F Tableau: Col 1 2 3 4 Row 1: 1 3 5 3 2: 2 4 5 3 Check = F Tableau: Col 1 2 3 4 Row 1: 1 3 4 5 2: 2 4 5 3 Check = T Tableau: Col 1 2 3 4 Row 1: 1 3 6 7 2: 3 4 7 8 TABLEAU_ENUM_TEST TABLEAU_ENUM enumerates tableaus on N nodes. N # 0 1 1 1 2 2 3 5 4 14 5 42 6 132 7 429 8 1430 9 4862 10 16796 TABLEAU_TO_BAL_SEQ_TEST TABLEAU_TO_BAL_SEQ converts a tableau to a balanced sequence. Tableau: Col 1 2 3 4 Row 1: 1 2 5 6 2: 3 4 7 8 Balanced sequence: 0 0 1 1 0 0 1 1 TREE_CHECK TEST TREE_CHECK checks a tree. Check? Check = F Tree: (None) Check = T Tree: Col 1 2 Row 1: 1 2 2: 2 3 Check = F Tree: Col 1 2 3 4 Row 1: -1 3 4 5 2: -2 4 5 3 Check = T Tree: Col 1 2 3 4 5 Row 1: 1 2 3 4 5 2: 3 3 4 5 6 tree_enum_test(): tree_enum() enumerates trees on N nodes. N # 0 0 1 1 2 1 3 3 4 16 5 125 6 1296 7 16807 8 262144 9 4782969 10 100000000 tree_random_test(): tree_random() randomly selects a tree on N nodes. A random tree: 4 5 3 6 2 5 1 6 1 1 A random tree: 6 3 2 4 5 1 2 4 5 1 A random tree: 4 2 3 6 5 6 3 6 5 1 A random tree: 6 3 2 4 5 1 5 4 5 1 A random tree: 6 4 3 2 5 4 2 2 5 1 A random tree: 6 3 2 4 5 1 2 4 5 1 A random tree: 6 3 4 5 2 3 4 5 2 1 A random tree: 5 4 2 6 3 3 1 6 3 1 A random tree: 3 4 6 5 2 4 6 5 1 1 A random tree: 6 5 3 4 2 4 3 4 2 1 TREE_RANK_TEST TREE_RANK ranks trees. The rank of the element: 4 3 2 3 1 1 is computed as 8 TREE_SUCCESSOR_TEST TREE_SUCCESOR lists trees. 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 TREE_TO_PRUEFER_TEST TREE_TO_PRUEFER converts a tree to a Pruefer code. Random Pruefer code of rank 98 4 5 4 Edge list for the corresponding tree: 1 3 4 2 2 5 3 5 4 4 4 1 Corresponding Pruefer code: 4 5 4 Random Pruefer code of rank 83 4 2 4 Edge list for the corresponding tree: 1 5 4 2 3 2 3 2 4 4 4 1 Corresponding Pruefer code: 4 2 4 Random Pruefer code of rank 122 5 5 3 Edge list for the corresponding tree: 1 4 5 2 2 5 3 5 3 4 3 1 Corresponding Pruefer code: 5 5 3 Random Pruefer code of rank 11 1 3 2 Edge list for the corresponding tree: 1 5 1 2 4 3 3 3 2 4 2 1 Corresponding Pruefer code: 1 3 2 Random Pruefer code of rank 11 1 3 2 Edge list for the corresponding tree: 1 5 1 2 4 3 3 3 2 4 2 1 Corresponding Pruefer code: 1 3 2 tree_unrank_test(): tree_unrank() unranks trees. The element of rank 8 4 3 2 3 1 1 combo_test(): Normal end of execution. September 12 2022 2:47:52.922 PM