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".

Usage

1. Prepare a std::vector<int> 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	1	2	3	4	5	6	7	8
Pinzu	9	10	11	12	13	14	15	16	17
Souzu	18	19	20	21	22	23	24	25	26
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::vector<int> 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 tile groups and a pair):

int Calsht::calc_lh(int* hand, int m)

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

• Seven Pairs:

int Calsht::calc_sp(int* hand)

• Thirteen Orphans:

int Calsht::calc_to(int* hand)

• Normal Form:

std::tuple<int,int> Calsht::operator()(const std::vector<int>& hand, int m, int mode)

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.

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

#include <iostream>
#include <vector>
#include "calsht.hpp"

int main()
{
  Calsht calsht;

  // Set the location of shanten tables
  calsht.initialize(".");

  std::vector<int> 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
  };

  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.

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++17 or higher.

Execute

$ ./sample [number of tiles (e.g. 14)] [number of rounds (e.g. 100000000)]
=========================RESULT=========================
-1  315         0.000315
0   69900       0.0699
1   2333875     2.33387
2   19496567    19.4966
3   43932086    43.9321
4   28515676    28.5157
5   5496180     5.49618
6   155401      0.155401
Number of Tiles         14
Total                   100000000
Time (msec.)            99710
Expected Value          3.15599

Three Player Mahjong mode

Enable THREE_PLAYER.

Example:

$ cmake .. -DCMAKE_BUILD_TYPE=Release -DTHREE_PLAYER=on

Building tables (Unneeded)

Build tables of parameters required for calculating Shanten number. Make "index_h.txt" and "index_s.txt".

$ ./mkind1

License

GNU General Public License v3.0.