Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/generators/sudoku.py @ 0:4f3585e2f14b draft default tip
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author | shellac |
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date | Mon, 22 Mar 2021 18:12:50 +0000 |
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1 """Generator for Sudoku graphs |
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2 |
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3 This module gives a generator for n-Sudoku graphs. It can be used to develop |
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4 algorithms for solving or generating Sudoku puzzles. |
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5 |
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6 A completed Sudoku grid is a 9x9 array of integers between 1 and 9, with no |
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7 number appearing twice in the same row, column, or 3x3 box. |
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8 |
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9 8 6 4 | 3 7 1 | 2 5 9 |
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10 3 2 5 | 8 4 9 | 7 6 1 |
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11 9 7 1 | 2 6 5 | 8 4 3 |
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12 ------+-------+------ |
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13 4 3 6 | 1 9 2 | 5 8 7 |
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14 1 9 8 | 6 5 7 | 4 3 2 |
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15 2 5 7 | 4 8 3 | 9 1 6 |
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16 ------+-------+------ |
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17 6 8 9 | 7 3 4 | 1 2 5 |
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18 7 1 3 | 5 2 8 | 6 9 4 |
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19 5 4 2 | 9 1 6 | 3 7 8 |
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20 |
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21 |
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22 The Sudoku graph is an undirected graph with 81 vertices, corresponding to |
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23 the cells of a Sudoku grid. It is a regular graph of degree 20. Two distinct |
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24 vertices are adjacent if and only if the corresponding cells belong to the |
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25 same row, column, or box. A completed Sudoku grid corresponds to a vertex |
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26 coloring of the Sudoku graph with nine colors. |
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27 |
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28 More generally, the n-Sudoku graph is a graph with n^4 vertices, corresponding |
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29 to the cells of an n^2 by n^2 grid. Two distinct vertices are adjacent if and |
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30 only if they belong to the same row, column, or n by n box. |
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31 |
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32 References |
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33 ---------- |
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34 .. [1] Herzberg, A. M., & Murty, M. R. (2007). Sudoku squares and chromatic |
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35 polynomials. Notices of the AMS, 54(6), 708-717. |
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36 .. [2] Sander, Torsten (2009), "Sudoku graphs are integral", |
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37 Electronic Journal of Combinatorics, 16 (1): Note 25, 7pp, MR 2529816 |
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38 .. [3] Wikipedia contributors. "Glossary of Sudoku." Wikipedia, The Free |
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39 Encyclopedia, 3 Dec. 2019. Web. 22 Dec. 2019. |
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40 """ |
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41 |
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42 import networkx as nx |
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43 from networkx.exception import NetworkXError |
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44 |
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45 __all__ = ["sudoku_graph"] |
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46 |
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47 |
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48 def sudoku_graph(n=3): |
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49 """Returns the n-Sudoku graph. The default value of n is 3. |
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50 |
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51 The n-Sudoku graph is a graph with n^4 vertices, corresponding to the |
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52 cells of an n^2 by n^2 grid. Two distinct vertices are adjacent if and |
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53 only if they belong to the same row, column, or n-by-n box. |
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54 |
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55 Parameters |
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56 ---------- |
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57 n: integer |
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58 The order of the Sudoku graph, equal to the square root of the |
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59 number of rows. The default is 3. |
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60 |
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61 Returns |
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62 ------- |
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63 NetworkX graph |
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64 The n-Sudoku graph Sud(n). |
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65 |
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66 Examples |
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67 -------- |
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68 >>> G = nx.sudoku_graph() |
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69 >>> G.number_of_nodes() |
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70 81 |
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71 >>> G.number_of_edges() |
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72 810 |
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73 >>> sorted(G.neighbors(42)) |
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74 [6, 15, 24, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 44, 51, 52, 53, 60, 69, 78] |
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75 >>> G = nx.sudoku_graph(2) |
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76 >>> G.number_of_nodes() |
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77 16 |
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78 >>> G.number_of_edges() |
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79 56 |
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80 |
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81 References |
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82 ---------- |
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83 .. [1] Herzberg, A. M., & Murty, M. R. (2007). Sudoku squares and chromatic |
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84 polynomials. Notices of the AMS, 54(6), 708-717. |
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85 .. [2] Sander, Torsten (2009), "Sudoku graphs are integral", |
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86 Electronic Journal of Combinatorics, 16 (1): Note 25, 7pp, MR 2529816 |
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87 .. [3] Wikipedia contributors. "Glossary of Sudoku." Wikipedia, The Free |
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88 Encyclopedia, 3 Dec. 2019. Web. 22 Dec. 2019. |
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89 """ |
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90 |
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91 if n < 0: |
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92 raise NetworkXError("The order must be greater than or equal to zero.") |
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93 |
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94 n2 = n * n |
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95 n3 = n2 * n |
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96 n4 = n3 * n |
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97 |
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98 # Construct an empty graph with n^4 nodes |
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99 G = nx.empty_graph(n4) |
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100 |
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101 # A Sudoku graph of order 0 or 1 has no edges |
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102 if n < 2: |
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103 return G |
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104 |
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105 # Add edges for cells in the same row |
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106 for row_no in range(0, n2): |
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107 row_start = row_no * n2 |
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108 for j in range(1, n2): |
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109 for i in range(j): |
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110 G.add_edge(row_start + i, row_start + j) |
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111 |
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112 # Add edges for cells in the same column |
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113 for col_no in range(0, n2): |
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114 for j in range(col_no, n4, n2): |
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115 for i in range(col_no, j, n2): |
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116 G.add_edge(i, j) |
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117 |
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118 # Add edges for cells in the same box |
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119 for band_no in range(n): |
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120 for stack_no in range(n): |
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121 box_start = n3 * band_no + n * stack_no |
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122 for j in range(1, n2): |
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123 for i in range(j): |
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124 u = box_start + (i % n) + n2 * (i // n) |
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125 v = box_start + (j % n) + n2 * (j // n) |
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126 G.add_edge(u, v) |
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127 |
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128 return G |