Rank system

[kyoyama-kazusa]

Summary

Implement a rank system that is just like XSudo.

Implemented APIs can be checked in this picture:

Now supports:

• Basic truth and link API
• Find permutations
• Find eliminations
• Find rank
• Find rank-0 sets

Test code

using System;
using Sudoku.Analytics.Ranking;
using Sudoku.Concepts;
using Sudoku.Concepts.Coordinates.Formatting;
using Sudoku.Concepts.Supersymmetry;

var grid = Grid.Parse(
    """
    ,------------------,--------------------,----------------,
    | 14    3      16  | 7      2     1468  | 9     5    68  |
    | 8     14569  259 | 13469  3469  13469 | 146   7    236 |
    | 1249  14679  279 | 5      3469  1368  | 1468  124  236 |
    :------------------+--------------------+----------------:
    | 5     1679   179 | 2369   8     369   | 1367  123  4   |
    | 24    468    268 | 2346   1     7     | 368   9    5   |
    | 1249  4789   3   | 2469   5     469   | 678   12   268 |
    :------------------+--------------------+----------------:
    | 6     59     59  | 8      7     2     | 34    34   1   |
    | 3     18     18  | 49     49    5     | 2     6    7   |
    | 7     2      4   | 136    36    136   | 5     8    9   |
    '------------------'--------------------'----------------'
    """,
    new PencilmarkGridFormatInfo()
);
var pattern = new RankPattern(
    grid,
    [
        Space.RowDigit(0, 0),
        Space.RowDigit(0, 3),
        Space.RowDigit(0, 7),
        Space.RowDigit(4, 7),
        Space.RowDigit(5, 6),
        Space.RowDigit(5, 7),
        Space.BlockDigit(3, 3),
        Space.RowColumn(65 / 9, 65 % 9)
    ],
    [
        Space.RowColumn(0 / 9, 0 % 9),
        Space.RowColumn(5 / 9, 5 % 9),
        Space.RowColumn(37 / 9, 37 % 9),
        Space.RowColumn(46 / 9, 46 % 9),
        Space.RowColumn(51 / 9, 51 % 9),
        Space.ColumnDigit(0, 3),
        Space.ColumnDigit(2, 0),
        Space.ColumnDigit(2, 7),
        Space.ColumnDigit(8, 7),
        Space.BlockDigit(5, 7)
    ]
);

Console.WriteLine(pattern.ToFullString());

Picture:

[kyoyama-kazusa]

Test example 2:

using System;
using Sudoku.Analytics.Ranking;
using Sudoku.Concepts;
using Sudoku.Concepts.Coordinates.Formatting;
using Sudoku.Concepts.Supersymmetry;

var grid = Grid.Parse(
    """
    ,---------------------,----------------------,-------------------,
    | 8     5     149     | 6     149      7     | 14      2    3    |
    | 149   1267  124679  | 1348  13589    458   | 14678   468  1467 |
    | 3     167   1467    | 2     148      48    | 14678   5    9    |
    :---------------------+----------------------+-------------------:
    | 7     126   12456   | 148   12468    9     | 14568   3    146  |
    | 1459  1236  1234569 | 1348  1234678  2468  | 156789  468  167  |
    | 19    8     139     | 5     137      46    | 179     46   2    |
    :---------------------+----------------------+-------------------:
    | 6     4     35      | 9     25       1     | 23      7    8    |
    | 15    137   1357    | 48    24568    24568 | 23      9    46   |
    | 2     9     8       | 7     46       3     | 46      1    5    |
    '---------------------'----------------------'-------------------'
    """,
    new PencilmarkGridFormatInfo()
);
var pattern = new RankPattern(
    grid,
    [
        Space.ColumnDigit(0, 3),
        Space.ColumnDigit(3, 3),
        Space.ColumnDigit(7, 3),
        Space.ColumnDigit(8, 3),
        Space.BlockDigit(3, 3)
    ],
    [
        Space.RowDigit(1, 3),
        Space.RowDigit(3, 3),
        Space.RowDigit(4, 3),
        Space.RowDigit(7, 3),
        Space.BlockDigit(5, 3)
    ]
);
Console.WriteLine(pattern.ToFullString());

Picture:

[kyoyama-kazusa]

This is a special case describing XSudo differs with my program on designation of rank.

TBH my program can eliminate r4c7(4) no matter whether the link 4b6 is needed or not; however, XSudo cannot eliminate if lacking 4b6. This is because XSudo uses link constraints to limit "cannot be true for cells in a link"; but in fact, we cannot fill a same digit into a same house, so all cases are ignored by my rank algorithm.

For all valid cases (ignoring satisfiability on links), r4c7(4) can be eliminated in my algorithm.

---

Translation (翻译)

这是一个特殊情况，我和 XSudo 会在这个题上有不同的表现。

说实话我这可以直接删 r4c7(4) 不论有没有 4b6 这个弱区域；但是 XSudo 不行。他需要依赖 4b6 来表示同一个宫的 4 不能同真。但是我在设计算法上就已经过滤了这种情况，毕竟实际填数逻辑上压根就不允许同一个宫填两个相同的数字，所以我会把这些算作非法情况给忽略掉。

然后再看所有合法操作（忽略掉了弱区域的验证后），r4c7(4) 在我这里就是可以删数的。

[kyoyama-kazusa]

Test example 3:

using System;
using Sudoku.Analytics.Ranking;
using Sudoku.Concepts;
using Sudoku.Concepts.Coordinates.Formatting;
using Sudoku.Concepts.Supersymmetry;

var grid = Grid.Parse(
    """
    ,-----------------,-------------------,----------------,
    | 247   2457  3   | 256   258    9    | 268   456  1   |
    | 6     25    9   | 4     12358  1358 | 2378  35   37  |
    | 124   8     145 | 256   7      356  | 236   9    34  |
    :-----------------+-------------------+----------------:
    | 1237  2367  167 | 8     1235   1357 | 9     34   347 |
    | 1347  9     147 | 17    6      137  | 5     2    8   |
    | 5     237   8   | 279   239    4    | 37    1    6   |
    :-----------------+-------------------+----------------:
    | 49    456   456 | 3     4589   568  | 1     7    2   |
    | 379   367   2   | 1679  19     167  | 4     8    5   |
    | 8     1     457 | 57    45     2    | 36    36   9   |
    '-----------------'-------------------'----------------'
    """,
    new PencilmarkGridFormatInfo()
);
var pattern = new RankPattern(
    grid,
    [
        Space.RowDigit(4, 2),
        Space.BlockDigit(1, 2),
        Space.BlockDigit(5, 6),
        Space.RowColumn(1, 1),
        Space.RowColumn(1, 7),
        Space.RowColumn(1, 8),
        Space.RowColumn(5, 1),
    ],
    [
        Space.RowDigit(1, 2),
        Space.RowDigit(1, 4),
        Space.RowDigit(5, 6),
        Space.ColumnDigit(1, 1),
        Space.ColumnDigit(5, 2),
        Space.ColumnDigit(8, 6),
        Space.BlockDigit(3, 2)
    ]
);

Console.WriteLine(pattern.ToFullString());

Picture:

[kyoyama-kazusa]

Test example 4:

using System;
using Sudoku.Analytics.Ranking;
using Sudoku.Concepts;
using Sudoku.Concepts.Coordinates.Formatting;
using Sudoku.Concepts.Supersymmetry;

var grid = Grid.Parse(
    """
    ,----------------------,----------------------,-----------------------,
    | 8       1246   24569 | 2347   12357   1234  | 13569  4579   1345679 |
    | 12459   124    3     | 6      12578   1248  | 1589   45789  14579   |
    | 1456    7      456   | 348    9       1348  | 2      458    13456   |
    :----------------------+----------------------+-----------------------:
    | 123469  5      2469  | 2389   2368    7     | 1689   2489   12469   |
    | 12369   12368  269   | 2389   4       5     | 7      289    1269    |
    | 24679   2468   24679 | 1      268     2689  | 5689   3      24569   |
    :----------------------+----------------------+-----------------------:
    | 23457   234    1     | 23479  237     2349  | 359    6      8       |
    | 23467   2346   8     | 5      2367    23469 | 39     1      2379    |
    | 23567   9      2567  | 2378   123678  12368 | 4      257    2357    |
    '----------------------'----------------------'-----------------------'
    """,
    new PencilmarkGridFormatInfo()
);
var pattern = new RankPattern(
    grid,
    [
        Space.RowColumn(0, 1),
        Space.RowColumn(1, 1),
        Space.RowColumn(5, 1),
        Space.RowColumn(6, 1),
        Space.RowColumn(7, 1),
        Space.RowColumn(0, 4),
        Space.RowColumn(1, 4),
        Space.RowColumn(5, 4),
        Space.RowColumn(6, 4),
        Space.RowColumn(7, 4),
        Space.RowColumn(0, 5),
        Space.RowColumn(1, 5),
        Space.RowColumn(5, 5),
        Space.RowColumn(6, 5),
        Space.RowColumn(7, 5),
        Space.RowColumn(0, 6),
        Space.RowColumn(1, 6),
        Space.RowColumn(5, 6),
        Space.RowColumn(6, 6),
        Space.RowColumn(7, 6),
    ],
    [
        Space.RowDigit(0, 0),
        Space.RowDigit(1, 0),
        Space.RowDigit(0, 2),
        Space.RowDigit(6, 2),
        Space.RowDigit(7, 2),
        Space.RowDigit(0, 5),
        Space.RowDigit(5, 5),
        Space.RowDigit(7, 5),
        Space.RowDigit(1, 7),
        Space.RowDigit(5, 7),
        Space.ColumnDigit(1, 1),
        Space.ColumnDigit(4, 1),
        Space.ColumnDigit(5, 1),
        Space.ColumnDigit(1, 3),
        Space.ColumnDigit(5, 3),
        Space.ColumnDigit(4, 4),
        Space.ColumnDigit(6, 4),
        Space.ColumnDigit(4, 6),
        Space.ColumnDigit(5, 8),
        Space.ColumnDigit(6, 8)
    ]
);

Console.WriteLine(pattern.ToFullString());

Picture:

[kyoyama-kazusa]

Test example 5:

using System;
using Sudoku.Analytics.Ranking;
using Sudoku.Concepts;
using Sudoku.Concepts.Coordinates.Formatting;
using Sudoku.Concepts.Supersymmetry;

var grid = Grid.Parse(
    """
    ,--------------------,--------------------,---------------,
    | 9     46     146   | 3     2       8    | 7    5    16  |
    | 1258  2568   156   | 7     169     19   | 89   4    3   |
    | 3     678    167   | 469   1469    5    | 2    89   16  |
    :--------------------+--------------------+---------------:
    | 124   3      14569 | 4569  4569    127  | 49   27   8   |
    | 245   24569  8     | 4569  34569   237  | 1    39   257 |
    | 7     2459   1459  | 4589  134589  1239 | 349  6    25  |
    :--------------------+--------------------+---------------:
    | 58    79     2     | 1     3589    39   | 6    378  4   |
    | 6     1      79    | 589   3589    4    | 358  237  27  |
    | 458   458    3     | 2     7       6    | 58   1    9   |
    '--------------------'--------------------'---------------'
    """,
    new PencilmarkGridFormatInfo()
);
var pattern = new RankPattern(
    grid,
    [
        Space.RowDigit(1, 8),
        Space.RowDigit(2, 8),
        Space.ColumnDigit(1, 8),
        Space.ColumnDigit(2, 8),
        Space.BlockDigit(5, 8),
        Space.BlockDigit(7, 8),
    ],
    [
        Space.RowDigit(3, 8),
        Space.RowDigit(4, 8),
        Space.RowDigit(5, 8),
        Space.RowDigit(6, 8),
        Space.RowDigit(7, 8),
        Space.ColumnDigit(3, 8),
        Space.ColumnDigit(4, 8),
        Space.ColumnDigit(5, 8),
        Space.ColumnDigit(6, 8),
        Space.ColumnDigit(7, 8),
    ]
);

Console.WriteLine(pattern.ToFullString());

Picture:

[kyoyama-kazusa]

Test example 6:

using System;
using Sudoku.Analytics.Ranking;
using Sudoku.Concepts;
using Sudoku.Concepts.Coordinates.Formatting;
using Sudoku.Concepts.Supersymmetry;

var grid = Grid.Parse(
    """
    ,---------------------,------------------------,---------------------,
    | 1278    4      1278 | 123789  6       1379   | 23589  235789  378  |
    | 2678    5      2678 | 234789  2347    3479   | 1      236789  3678 |
    | 3       1678   9    | 1278    127     5      | 268    2678    4    |
    :---------------------+------------------------+---------------------:
    | 124568  168    1268 | 12345   9       134    | 7      123468  1368 |
    | 124578  178    1278 | 6       123457  1347   | 23489  123489  138  |
    | 12467   9      3    | 1247    1247    8      | 246    1246    5    |
    :---------------------+------------------------+---------------------:
    | 167     2      167  | 134579  8       134679 | 3456   134567  1367 |
    | 1678    13678  5    | 1347    1347    2      | 3468   134678  9    |
    | 9       13678  4    | 1357    1357    1367   | 3568   135678  2    |
    '---------------------'------------------------'---------------------'
    """,
    new PencilmarkGridFormatInfo()
);
var pattern = new RankPattern(
    grid,
    SpaceSet.Parse("167r3 1c269 6c29 7c269 7n13"),
    SpaceSet.Parse("1r457 6r47 7r57 3n2 9n6 1b27 6b37 7b237")
);

Console.WriteLine(pattern.ToFullString());

Picture: