@algorithm.ts/sudoku

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This library is used to solve Sudoku problems and generate Sudoku problems with unique solution.

The Sudoku problem is described as a square matrix of size (a*a) * (a*a), and the value of a position in the square matrix is an integer between [-1, a*a). Among them, -1 means no value is filled in this position yet. A classic Sudoku problem needs to satisfy the following constraints:

1. Each position in the square matrix needs to be filled with an integer between [0, a*a)
2. There are no repeated numbers in each row of the square matrix
3. There are no repeated numbers in each column of the square matrix
4. The square matrix can be divided into aa sub-squares of size aa, and there are no repeated numbers in each column of the sub-squares A typescript implementation of the sudoku algorithm.

sudoku is a shuffle algorithm, which can complete the shuffle in $O(N)$ time complexity on the basis of only using a constant level of extra space.

If you are curious about this algorithm, you can visit [here][sudoku] for more details.

Install

• npm

  npm install --save @algorithm.ts/sudoku
  

• pnpm

  pnpm add @algorithm.ts/sudoku
  

Usage

• SudokuSolver: Solve a Sudoku puzzle.

• SudokuCreator: Create a Sudoku data (puzzle and solution) with only unique solution.

• Utility functions

  Function	Description
  createSudokuBoardData	Create a sudoku board (one-dimensional array).
  fillSudokuBoardData	Fill the sudoku board with the given value.
  copySudokuBoardData	Copy sudoku board from src to dst.
  verifySolution	Check if the solution of the given Sudoku game is valid.
  toMatrixStyleBoardData	Convert the one-dimensional array to two-dimensional array.
  createMatrixCodeMap
  createMatrixCoordinateMap

Examples

Solve a sudoku puzzle

• Solve a 16x16 sudoku puzzle

  import type { ISudokuBoardData } from '@algorithm.ts/sudoku'
  import { SudokuSolver, createSudokuBoardData } from '@algorithm.ts/sudoku'
  
  // 4 x 4 = 16
  const solver = new SudokuSolver({ childMatrixSize: 4 })
  
  const puzzle: ISudokuBoardData =  [
     2,  3, 14, -1,  8,  6, -1, -1, -1, 13, -1, -1, -1, 10, 12, -1,
     0, -1, -1, -1, -1, -1,  1,  9, -1, -1,  4, -1,  8, -1, -1,  2,
    -1, -1, -1,  6,  7, -1,  2, -1, -1, -1, 10,  1, -1,  0, -1, 15,
    -1,  8, -1, -1, -1, -1, 12, -1, -1,  5,  0,  7,  4, -1,  1,  6,
     7,  1, -1,  3, -1,  4, 10, 14, -1, -1, -1, -1,  2, -1, 15,  9,
    14, 12, -1, -1,  2,  3, -1, -1,  1, -1,  7, -1, -1,  6, 13, -1,
    10,  2,  5, -1, -1,  0,  7, -1,  3, -1, -1,  8, 11,  1, -1,  4,
    -1, 13,  6, -1, -1, -1, -1,  1, -1, -1, 14,  2, -1,  3,  7, -1,
    -1, -1, -1,  2,  1, -1, -1, -1, -1, -1,  8,  9, 14,  7, -1, -1,
     8,  9, 10, -1,  3, -1, -1,  2,  6, -1, 11, -1, -1, -1,  5,  0,
     1, -1,  3,  5, -1, -1, -1, -1,  4,  0, -1, -1, -1, 11, -1, 12,
     6, -1, -1,  4,  5, -1, 15, 11, 14, -1,  1, -1, 13,  9,  8, -1,
    -1,  6, -1, -1, -1,  2, -1, 12, -1, -1, -1, 14,  9, -1,  0, 13,
    -1, -1,  0,  7, -1,  9, 13,  8, -1, -1,  3, -1, -1,  2,  6, 14,
    -1, -1, -1,  8, -1, 11, -1, -1, -1, 12, -1, -1, 15,  5,  3,  1,
     3, -1, -1, -1, -1, -1, -1, -1,  9, 15,  2,  0, -1,  8, -1, 11
  ]
  
  solver.solve(puzzle, null)  // => true
  
  const solution: ISudokuBoardData = createSudokuBoardData(16)
  solver.solve(puzzle, solution)  // => true
  
  solution
  /** ===>
   * [
   *    2,  3, 14,  1,  8,  6,  0,  4, 11, 13,  9, 15,  5, 10, 12,  7,
   *    0,  5,  7, 10, 14, 15,  1,  9, 12,  3,  4,  6,  8, 13, 11,  2,
   *   12, 11,  4,  6,  7,  5,  2, 13,  8, 14, 10,  1,  3,  0,  9, 15,
   *   15,  8,  9, 13, 11, 10, 12,  3,  2,  5,  0,  7,  4, 14,  1,  6,
   *    7,  1,  8,  3,  6,  4, 10, 14,  0, 11, 13,  5,  2, 12, 15,  9,
   *   14, 12, 15, 11,  2,  3,  9,  5,  1,  4,  7, 10,  0,  6, 13,  8,
   *   10,  2,  5,  9, 13,  0,  7, 15,  3,  6, 12,  8, 11,  1, 14,  4,
   *    4, 13,  6,  0, 12,  8, 11,  1, 15,  9, 14,  2, 10,  3,  7,  5,
   *   13, 15, 11,  2,  1, 12,  6,  0,  5, 10,  8,  9, 14,  7,  4,  3,
   *    8,  9, 10, 14,  3, 13,  4,  2,  6,  7, 11, 12,  1, 15,  5,  0,
   *    1,  7,  3,  5,  9, 14,  8, 10,  4,  0, 15, 13,  6, 11,  2, 12,
   *    6,  0, 12,  4,  5,  7, 15, 11, 14,  2,  1,  3, 13,  9,  8, 10,
   *   11,  6,  1, 15, 10,  2,  3, 12,  7,  8,  5, 14,  9,  4,  0, 13,
   *    5,  4,  0,  7, 15,  9, 13,  8, 10,  1,  3, 11, 12,  2,  6, 14,
   *    9, 10,  2,  8,  0, 11, 14,  7, 13, 12,  6,  4, 15,  5,  3,  1,
   *    3, 14, 13, 12,  4,  1,  5,  6,  9, 15,  2,  0,  7,  8, 10, 11
   * ]
   */
  

Create a sudoku game data

• Create a 9x9 sudoku puzzle

  import { SudokuCreator } from '@algorithm.ts/sudoku'
  
  // 3 x 3 = 9
  const creator = new SudokuCreator({ childMatrixSize: 3 })
  

  • Create a easy puzzle.

    creator.createSudoku()
    // or
    creator.createSudoku(0.2)
    

    The result is a js object similar to the one shown below:

    {
      "puzzle": [
         8, -1, 6,  1,  0,  2,  3,  5, -1,
         0, -1, 5, -1,  4, -1,  8,  1,  7,
         4,  3, 1,  8, -1, -1,  2,  6,  0,
        -1,  0, 7,  4, -1,  1,  5,  8,  2,
         2,  1, 4,  5,  3, -1, -1,  7,  6,
         5,  6, 8,  0,  2,  7,  4,  3,  1,
         1,  4, 3,  2, -1,  6,  7,  0,  8,
         6,  5, 0,  7,  8,  4,  1,  2,  3,
        -1, -1, 2,  3, -1, -1,  6,  4,  5
      ],
      "solution": [
        8, 7, 6, 1, 0, 2, 3, 5, 4,
        0, 2, 5, 6, 4, 3, 8, 1, 7,
        4, 3, 1, 8, 7, 5, 2, 6, 0,
        3, 0, 7, 4, 6, 1, 5, 8, 2,
        2, 1, 4, 5, 3, 8, 0, 7, 6,
        5, 6, 8, 0, 2, 7, 4, 3, 1,
        1, 4, 3, 2, 5, 6, 7, 0, 8,
        6, 5, 0, 7, 8, 4, 1, 2, 3,
        7, 8, 2, 3, 1, 0, 6, 4, 5
      ]
    }
    

  • Create a hard puzzle.

    creator.createSudoku(1.0)
    

    The result is a js object similar to the one shown below:

    {
      "puzzle": [
        -1, -1, -1, -1, -1,  8, -1, -1,  4,
        -1, -1, -1,  3, -1, -1,  5,  8, -1,
        -1, -1, -1,  6,  4, -1,  0, -1, -1,
        -1, -1, -1, -1,  2, -1,  6, -1, -1,
        -1,  0, -1, -1, -1, -1,  7,  3,  5,
        -1,  7, -1, -1,  3, -1, -1, -1, -1,
         3, -1, -1, -1, -1,  2, -1, -1,  0,
        -1, -1, -1,  8,  6,  5, -1, -1, -1,
         2, -1,  4, -1, -1, -1, -1, -1, -1
      ],
      "solution": [
        0, 6, 1, 2, 5, 8, 3, 7, 4,
        4, 2, 7, 3, 0, 1, 5, 8, 6,
        8, 3, 5, 6, 4, 7, 0, 2, 1,
        5, 4, 3, 7, 2, 0, 6, 1, 8,
        6, 0, 2, 1, 8, 4, 7, 3, 5,
        1, 7, 8, 5, 3, 6, 4, 0, 2,
        3, 8, 6, 4, 7, 2, 1, 5, 0,
        7, 1, 0, 8, 6, 5, 2, 4, 3,
        2, 5, 4, 0, 1, 3, 8, 6, 7
      ]
    }
    

• Create a 16x16 sudoku puzzle

  import { SudokuCreator } from '@algorithm.ts/sudoku'
  
  // 4 x 4 = 16
  const creator = new SudokuCreator({ childMatrixSize: 4 })
  creator.createSudoku(0.8)
  

  The result is a js object similar to the one shown below:

  {
    "puzzle": [
      -1, -1, -1, 12, -1,  5, -1,  9, -1, -1,  6, -1, -1,  1, -1, 14,
      -1,  2,  4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 15, -1,
      -1, -1,  8, -1, 12, 13,  4,  7,  2, -1, -1, -1, -1, -1, -1, -1,
       7, -1, -1, -1, -1, -1, -1, 14, -1, -1, -1, 12, -1, -1, -1, -1,
       4, -1, 15, -1,  6, -1, -1, -1, -1, -1, 11, -1,  3, -1, -1, -1,
      -1,  8, 10, 14, -1, -1, -1, -1,  5, 13, -1, -1, -1,  9, -1, -1,
      -1, -1,  6, 11,  3, 14, -1, -1,  0,  2, -1,  4, -1, -1, -1, 15,
      -1,  5, 13, -1, -1,  7, -1, -1,  9, -1, -1,  3,  2, -1, 10, -1,
      -1, -1, -1, -1, -1, -1, 14, -1,  6,  9, -1, -1, 10,  8, -1, -1,
      -1, -1, 14,  0,  7,  3, -1,  2, -1, 10, -1, -1, 15, 13, -1,  9,
      -1,  9,  7, -1, -1, -1, -1, 12, -1, 15, -1,  1, -1, -1,  0, -1,
      11, -1,  3, -1, -1,  0, -1, 15, 14,  5, -1, -1, -1,  2, 12,  6,
      -1, -1,  0, 13, -1, -1, -1,  5, -1, 11,  9, -1,  4, -1,  6,  3,
      -1, -1,  2, -1, -1, -1, 10, -1, 15,  6, -1, -1, 14, -1, -1, -1,
      -1, -1, -1, -1, 15, 12, -1, -1, -1,  4,  7, -1, -1, -1,  9, -1,
       6, -1, -1, -1, -1, -1,  8, -1, -1, -1,  5, -1, -1,  0, -1, -1
    ],
    "solution": [
      10,  3, 11, 12,  8,  5,  2,  9,  4,  7,  6, 15,  0,  1, 13, 14,
      13,  2,  4,  9,  1,  6,  3,  0, 11,  8, 14,  5, 12,  7, 15, 10,
       0, 14,  8, 15, 12, 13,  4,  7,  2,  1, 10,  9,  6,  3, 11,  5,
       7,  6,  1,  5, 11, 10, 15, 14, 13,  0,  3, 12,  9,  4,  8,  2,
       4,  0, 15,  2,  6,  9,  1, 13,  7, 12, 11, 10,  3,  5, 14,  8,
       3,  8, 10, 14,  2, 15, 12,  4,  5, 13,  1,  6, 11,  9,  7,  0,
       9,  7,  6, 11,  3, 14,  5, 10,  0,  2,  8,  4, 13, 12,  1, 15,
      12,  5, 13,  1,  0,  7, 11,  8,  9, 14, 15,  3,  2,  6, 10,  4,
      15, 13, 12,  4,  5, 11, 14,  1,  6,  9,  2,  0, 10,  8,  3,  7,
       5,  1, 14,  0,  7,  3,  6,  2,  8, 10, 12, 11, 15, 13,  4,  9,
       2,  9,  7,  6, 10,  8, 13, 12,  3, 15,  4,  1,  5, 14,  0, 11,
      11, 10,  3,  8,  4,  0,  9, 15, 14,  5, 13,  7,  1,  2, 12,  6,
       1, 12,  0, 13, 14,  2,  7,  5, 10, 11,  9,  8,  4, 15,  6,  3,
       8,  4,  2,  7,  9,  1, 10,  3, 15,  6,  0, 13, 14, 11,  5, 12,
      14, 11,  5,  3, 15, 12,  0,  6,  1,  4,  7,  2,  8, 10,  9, 13,
       6, 15,  9, 10, 13,  4,  8, 11, 12,  3,  5, 14,  7,  0,  2,  1
    ]
  }
  

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