数独游戏局的建立算法 (Sudoku Generating Algorithm Using Backtracking)

用了一点简单的回溯就可以建立一个数独Grid了, 算法并不复杂, 效率也很不错哦.

求解一个数独其实也可以用回溯搞定.

using System;

using System.Collections.Generic;

using System.Text;

namespace Adrian.Sudoku

{

public class SudokuDataGenerator

{

public static SudokuData New()

{

SudokuData dt = new SudokuData();

Random ran = new Random();

// data stores in "grid:int[,]"

int[,] grid = dt.Data;

// stores data for backtracking

List<int>[,] used = new List<int>[9, 9];

int i = 0;

int j = 0;

for (i = 0; i < 9; i++)

{

for (j = 0; j < 9; j++)

{

used[i, j] = new List<int>();

}

}

for (i = 0; i < 9; i++)

{

for (j = 0; j < 9; j++)

{

bool ok = false;

// used numbers of current cell

List<int> curUsed = used[i, j];

while (!ok && curUsed.Count < 9)

{

int posValue = ran.Next(1, 10);

// find an unused number

while (curUsed.Contains(posValue))

{

posValue = ran.Next(1, 10);

}

// satisfy the constraint?

ok = Check(grid, i, j, posValue);

if (ok)

{

grid[i, j] = posValue;

}

curUsed.Add(posValue);

}

// used up 1~9

if (!ok)

{

// backtracking

// go back to the last cell and try the rest numbers

curUsed.Clear();

if (j > 0)

{

j -= 2;

grid[i, j + 1] = 0;

}

else

{

i--;

j = 7;

grid[i, 8] = 0;

}

}

}

}

return dt;

}

private static bool Check(int[,] grid, int row, int col, int possibleValue)

{

int i = 0;

int j = 0;

// check column

for (i = 0; i < 9; i++)

{

if (grid[row, i] == possibleValue)

{

return false;

}

}

// check row

for (j = 0; j < 9; j++)

{

if (grid[j, col] == possibleValue)

{

return false;

}

}

// check 3*3 child grid

int rowStart = (row - row % 3);

int colStart = (col - col % 3);

for (i = rowStart; i < rowStart + 3; i++)

{

for (j = colStart; j < colStart + 3; j++)

{

if (grid[i, j] == possibleValue)

{

return false;

}

}

}

return true;

}

}

}

参考：

Sudoku Generator

A Sudoku Solver in C

Sudoku-Help Difficulty (SHD) Rating

Minimum Sudoku