Shanten Number

The algorithm used in this program has been proven to be able to calculate the shanten number accurately.

Read this in Japanese (日本語).

What is Shanten number in mahjong?

Shanten number is the minimul number of tile exchanges for "tempai".

Build

Debug mode

$ mkdir build
$ cd build
$ cmake .. -DCMAKE_BUILD_TYPE=Debug
$ make

Release mode

$ mkdir build
$ cd build
$ cmake .. -DCMAKE_BUILD_TYPE=Release
$ make

Note

It requires a compiler compatiable with C++20 or higher.

Compile options

-DENABLE_NYANTEN

It enables the table search algorithm to use the minimal perfect hash function used in Cryolite's nyanten¹². Enabling this option can reduce the size of tables. However, the number of tiles in a hand that can be calculated shanten number is limited to 14 or less.

-DFIX_RANDOM_SEED

It fixes the random seed used in the sample program.

Building tables

Build tables of parameters required for calculating shanten number. Create files index_h.bin and index_s.bin.

$ ./mkind

Tip

Intel Threading Building Blocks (TBB) is optional and, if available, will be automatically linked to enable parallel builds.

Usage

1. Prepare a std::array<int, 34> array representing a hand.

   • The n th element stores the number of n th tiles.

   	1	2	3	4	5	6	7	8	9
   Manzu	0 (1m)	1 (2m)	2 (3m)	3 (4m)	4 (5m)	5 (6m)	6 (7m)	7 (8m)	8 (9m)
   Pinzu	9 (1p)	10 (2p)	11 (3p)	12 (4p)	13 (5p)	14 (6p)	15 (7p)	16 (8p)	17 (9p)
   Souzu	18 (1s)	19 (2s)	20 (3s)	21 (4s)	22 (5s)	23 (6s)	24 (7s)	25 (8s)	26 (9s)
   Jihai	27 (East)	28 (South)	29 (West)	30 (North)	31 (White)	32 (Green)	33 (Red)

   • For example, if you have manzu tiles (1, 2, 3), pinzu tiles (2, 4, 5, 7, 7, 9), and jihai tiles (East, West, White, White, White), define the following array.

   std::array<int, 34> hand = {
       1, 1, 1, 0, 0, 0, 0, 0, 0, // Manzu
       0, 1, 0, 1, 1, 0, 2, 0, 1, // Pinzu
       0, 0, 0, 0, 0, 0, 0, 0, 0, // Souzu
       1, 0, 1, 0, 3, 0, 0        // Jihai
   };

2. Calculate the shanten number. Each method returns a value of shanten number + 1.

   • General Form (m melds and a pair):

   int Calsht::calc_lh(const std::array<int, 34>& t, int m, bool three_player = false) const

   • Seven Pairs:

   int Calsht::calc_sp(const std::array<int, 34>& t, bool three_player = false) const

   • Thirteen Orphans:

   int Calsht::calc_to(const std::array<int, 34>& t) const

   • Normal Form:

   std::tuple<int, int> Calsht::operator()(const std::array<int, 34>& t,
                                           int m,
                                           int mode,
                                           bool check_hand = false,
                                           bool three_player = false) const

Note

Normally, substitute the value obtained by dividing the number of tiles by 3 into m.

Note

mode specifies for which winning pattern calculate shanten number. When the pattern is "General Form", mode is 1, > when "Seven Pairs": 2, "Thirteen Orphans": 4. When calculating the shanten number for multiple winning patterns, specify the logical sum of them.

Note

This method returns a tuple of the minimum shunten number and its winnig pattern. The winning pattern is represented in the same way as mode.

Note

If you set check_hand to true, the hand will be validated. If you set three_player to true, it will calculate the number of shanten in three-player mahjong.

For example, calculate the shanten number of the hand defined above. The source code is as follows:

#include "calsht.hpp"
#include <array>
#include <filesystem>
#include <iostream>

int main()
{
  // Set the location of shanten tables
  Calsht calsht(std::filesystem::current_path());

  std::array<int, 34> hand = {
      1, 1, 1, 0, 0, 0, 0, 0, 0, // manzu
      0, 1, 0, 1, 1, 0, 2, 0, 1, // pinzu
      0, 0, 0, 0, 0, 0, 0, 0, 0, // souzu
      1, 0, 1, 0, 3, 0, 0        // jihai
  };

  const auto [sht, mode] = calsht(hand, 4, 7);

  std::cout << sht << std::endl;
  std::cout << mode << std::endl;

  return 0;
}

Output:

3
1

Sample Program

• Randomly genearte hands and calculate the appearance rate per shanten number and the expected value of shanten number.

$ ./sample 14 100000000 0
  -1         278    0.000278
   0       69553    0.069553
   1     2334287    2.334287
   2    19502040   19.502040
   3    43925782   43.925782
   4    28516861   28.516861
   5     5496101    5.496101
   6      155098    0.155098
Number of Tiles         14
Number of Hands         100000000
Expected Value          3.155940

License

GNU Lesser General Public License v3.0.

Footnotes

1. https://github.com/Cryolite/nyanten ↩

2. https://www.slideshare.net/slideshow/a-fast-and-space-efficient-algorithm-for-calculating-deficient-numbers-a-k-a-shanten-numbers-pptx/269706666 ↩