btj\dZddlZddlmZdgZejddd dZdS) aGenerator for Sudoku graphs This module gives a generator for n-Sudoku graphs. It can be used to develop algorithms for solving or generating Sudoku puzzles. A completed Sudoku grid is a 9x9 array of integers between 1 and 9, with no number appearing twice in the same row, column, or 3x3 box. +---------+---------+---------+ | | 8 6 4 | | 3 7 1 | | 2 5 9 | | | 3 2 5 | | 8 4 9 | | 7 6 1 | | | 9 7 1 | | 2 6 5 | | 8 4 3 | +---------+---------+---------+ | | 4 3 6 | | 1 9 2 | | 5 8 7 | | | 1 9 8 | | 6 5 7 | | 4 3 2 | | | 2 5 7 | | 4 8 3 | | 9 1 6 | +---------+---------+---------+ | | 6 8 9 | | 7 3 4 | | 1 2 5 | | | 7 1 3 | | 5 2 8 | | 6 9 4 | | | 5 4 2 | | 9 1 6 | | 3 7 8 | +---------+---------+---------+ The Sudoku graph is an undirected graph with 81 vertices, corresponding to the cells of a Sudoku grid. It is a regular graph of degree 20. Two distinct vertices are adjacent if and only if the corresponding cells belong to the same row, column, or box. A completed Sudoku grid corresponds to a vertex coloring of the Sudoku graph with nine colors. More generally, the n-Sudoku graph is a graph with n^4 vertices, corresponding to the cells of an n^2 by n^2 grid. Two distinct vertices are adjacent if and only if they belong to the same row, column, or n by n box. References ---------- .. [1] Herzberg, A. M., & Murty, M. R. (2007). Sudoku squares and chromatic polynomials. Notices of the AMS, 54(6), 708-717. .. [2] Sander, Torsten (2009), "Sudoku graphs are integral", Electronic Journal of Combinatorics, 16 (1): Note 25, 7pp, MR 2529816 .. [3] Wikipedia contributors. "Glossary of Sudoku." Wikipedia, The Free Encyclopedia, 3 Dec. 2019. Web. 22 Dec. 2019. N) NetworkXError sudoku_graphT)graphs returns_graphc|dkrtd||z}||z}||z}tj|}|dkr|St|D]H}||z}td|D]0}t|D]}|||z||z1It|D]@} t| ||D],}t| ||D]}|||-At|D]|} t|D]j} || z|| zz} td|D]L}t|D]:}| ||zz|||zzz} | ||zz|||zzz}|| |;Mk}|S)aReturns the n-Sudoku graph. The default value of n is 3. The n-Sudoku graph is a graph with n^4 vertices, corresponding to the cells of an n^2 by n^2 grid. Two distinct vertices are adjacent if and only if they belong to the same row, column, or n-by-n box. Parameters ---------- n: integer The order of the Sudoku graph, equal to the square root of the number of rows. The default is 3. Returns ------- NetworkX graph The n-Sudoku graph Sud(n). Examples -------- >>> G = nx.sudoku_graph() >>> G.number_of_nodes() 81 >>> G.number_of_edges() 810 >>> sorted(G.neighbors(42)) [6, 15, 24, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 44, 51, 52, 53, 60, 69, 78] >>> G = nx.sudoku_graph(2) >>> G.number_of_nodes() 16 >>> G.number_of_edges() 56 References ---------- .. [1] Herzberg, A. M., & Murty, M. R. (2007). Sudoku squares and chromatic polynomials. Notices of the AMS, 54(6), 708-717. .. [2] Sander, Torsten (2009), "Sudoku graphs are integral", Electronic Journal of Combinatorics, 16 (1): Note 25, 7pp, MR 2529816 .. [3] Wikipedia contributors. "Glossary of Sudoku." Wikipedia, The Free Encyclopedia, 3 Dec. 2019. Web. 22 Dec. 2019. rz0The order must be greater than or equal to zero.)rnx empty_graphrangeadd_edge)nn2n3n4Grow_no row_startjicol_noband_nostack_no box_startuvs X/var/www/html/CA-Chatbot/venv/lib/python3.11/site-packages/networkx/generators/sudoku.pyrr2s X 1uuNOOO QB aB aB rA 1uu))99RK q" 9 9A1XX 9 9 9q=)a-8888 9 9 ))!!vr2&& ! !A61b)) ! ! 1a     ! ! 88%%a % %HW q8|3I1b\\ % %q%%A!QU+bAFm;A!QU+bAFm;AJJq!$$$$% % % H)r)__doc__networkxr networkx.exceptionr__all__ _dispatchablerrrr&s{))V,,,,,,  T222P P P 32P P P r