是否有算法或方法可以获得数独游戏的初始状态数独游戏。最好是能否有不同程度的难度？
答案 0 :(得分：15)
基本上有两种方法。在这两个中你需要有2 solvers，一个类似于人的求解器，它使用可由人类和回溯求解器执行的策略。
使用第一种方法生成随机完整解决方案并迭代删除随机单元解决方案。回溯求解器将确保只存在一个解决方案，而人类解算器将确保它仍然可由人类解决，它也可用于衡量难题的难度。
第二种方法以相反的方式起作用。首先，您创建一个空板并随机放置17个单元解决方案（以一致的方式）。图17是已知用于生成具有独特解决方案的拼图的最低填充细胞计数。现在每个步骤中的算法检查，如果它已经有一个唯一的解决方案，如果没有，它会添加另一个（连续）填充的单元格。如果解决方案保证了解决方案的独特性，并且难题可由人类解决，并且难度低于某个限制，则算法终止。
答案 1 :(得分：4)
答案 2 :(得分：2)
您可能对此Sudoku generator感兴趣。
答案 3 :(得分：2)
我最近开源了我的Objective C Sudoku板生成器，如果你有兴趣...
http://jayfuerstenberg.com/devblog/open-source-code-for-developing-sudoku-for-iphone-and-os-x
它显然适用于iPhone和Mac，但逻辑可移植到您正在开发的任何平台上。
答案 4 :(得分：1)
我相信Devin正在寻找一个最初的数独配置，或者一个数独谜题（填充少于81个单元格），这应该保证存在一个或多个解决方案。随机N小区配置可能无法保证存在解决方案。
我想到的方法是首先获得一个完整的数独解决方案，使用它作为基础（将其命名为X） 通过在任何序列中应用任意数量的以下转换，X可以转换为大量其他有效的数独解，X1，X2，X3： 一个。回转 湾镜子翻转 C。将所有数字x与数字y交换。
然后，通过从基地中随机扣除细胞，可以使用这些基础中的每一个来生成数独谜题。
答案 5 :(得分：0)
以递归方式获取9x9数独元素。
using System;
using System.Collections.Generic;
using System.Drawing;
using System.Linq;
using System.Text;
using System.Windows.Forms;
namespace SP3.Sudoku
{
static class Program
{
[STAThread]
static void Main()
{
Application.EnableVisualStyles();
Application.SetCompatibleTextRenderingDefault(false);
Application.Run(new Sudoku());
}
}
public partial class Sudoku : Form
{
private System.Windows.Forms.Button btGenerate;
private System.Windows.Forms.Button btClear;
private System.ComponentModel.BackgroundWorker bw;
private System.Windows.Forms.Button btTestOk;
private delegate void setCellValue(int cellIndex, int cellValue);
public Sudoku()
{
InitializeComponent();
createControls();
}
public List<int> SudokuControlsValues
{
get
{
List<int> result = new List<int>(81);
for (int i = 0; i < 9; i++)
for (int j = 0; j < 9; j++)
result.Add((int)sudokuControlsValues[j + (i * 9)].Value);
return result;
}
set
{
List<int> result = value as List<int>;
for (int i = 0; i < result.Count; i++)
sudokuControlsValues[i].Value = result[i];
}
}
private void InitializeComponent()
{
this.btGenerate = new System.Windows.Forms.Button();
this.btClear = new System.Windows.Forms.Button();
this.bw = new System.ComponentModel.BackgroundWorker();
this.btTestOk = new System.Windows.Forms.Button();
this.SuspendLayout();
//
// btGenerate
//
this.btGenerate.Location = new System.Drawing.Point(534, 458);
this.btGenerate.Name = "btGenerate";
this.btGenerate.Size = new System.Drawing.Size(75, 23);
this.btGenerate.TabIndex = 1;
this.btGenerate.Text = "Generate";
this.btGenerate.UseVisualStyleBackColor = true;
this.btGenerate.Click += new System.EventHandler(this.btGenerate_Click);
//
// btClear
//
this.btClear.Location = new System.Drawing.Point(453, 458);
this.btClear.Name = "btClear";
this.btClear.Size = new System.Drawing.Size(75, 23);
this.btClear.TabIndex = 3;
this.btClear.Text = "Clear";
this.btClear.UseVisualStyleBackColor = true;
this.btClear.Click += new System.EventHandler(this.btClear_Click);
//
// bw
//
this.bw.WorkerReportsProgress = true;
this.bw.WorkerSupportsCancellation = true;
this.bw.DoWork += new System.ComponentModel.DoWorkEventHandler(this.bw_DoWork);
//
// btTestOk
//
this.btTestOk.Location = new System.Drawing.Point(372, 458);
this.btTestOk.Name = "btTestOk";
this.btTestOk.Size = new System.Drawing.Size(75, 23);
this.btTestOk.TabIndex = 4;
this.btTestOk.Text = "Test";
this.btTestOk.UseVisualStyleBackColor = true;
this.btTestOk.Click += new System.EventHandler(this.btTestOk_Click);
//
// Sudoku
//
this.AutoScaleDimensions = new System.Drawing.SizeF(6F, 13F);
this.AutoScaleMode = System.Windows.Forms.AutoScaleMode.Font;
this.BackColor = System.Drawing.SystemColors.ControlDark;
this.ClientSize = new System.Drawing.Size(624, 493);
this.Controls.Add(this.btTestOk);
this.Controls.Add(this.btClear);
this.Controls.Add(this.btGenerate);
this.FormBorderStyle = System.Windows.Forms.FormBorderStyle.FixedSingle;
this.MaximizeBox = false;
this.MinimizeBox = false;
this.Name = "Sudoku";
this.ShowIcon = false;
this.StartPosition = System.Windows.Forms.FormStartPosition.CenterScreen;
this.Text = "Sudoku generator";
this.ResumeLayout(false);
}
private void btGenerate_Click(object sender, System.EventArgs e)
{
bw.RunWorkerAsync();
}
private void btClear_Click(object sender, System.EventArgs e)
{
createControls();
}
private void createControls()
{
createControls(new Size(33, 10), new Size(3, 5), new Size(15, 30), new Size(15, 30), false, true);
}
private void clearControls()
{
if (sudokuControlsValues == null)
return;
foreach (NumericUpDown item in sudokuControlsValues)
{
if (item != null)
{
this.Controls.Remove(item);
item.Dispose();
}
}
sudokuControlsValues = null;
}
private void createControls(Size size, Size itemSeparation, Size startMargin, Size groupSeparation, bool AddRandomValue, bool addTest)
{
clearControls();
sudokuControlsValues = new List<NumericUpDown>(81);
int
grSeparationW = 0,
grSeparationH = 0;
for (int i = 0; i < 9; i++)
{
for (int j = 0; j < 9; j++)
{
NumericUpDown nud = new NumericUpDown();
// In order to debug easier save indexes values within the tag property and assing click event.
if (addTest)
{
nud.Tag = new int[2] { i, j };
nud.Click += nud_Click;
}
// Values
nud.Maximum = 9;
nud.Minimum = 0;
nud.TextAlign = HorizontalAlignment.Center;
nud.Size = size;
// Location
nud.Location = new Point(
(j * (nud.Width + itemSeparation.Width) + grSeparationW) + startMargin.Width,
(i * (nud.Height + itemSeparation.Height) + grSeparationH) + +startMargin.Height);
if (AddRandomValue)
nud.Value = (decimal)new Random(DateTime.Now.Millisecond).Next(1, 10);
Controls.Add(nud);
// Box separation
if (j % 3 == 2)
grSeparationW += groupSeparation.Width;
// Matrix reference
sudokuControlsValues.Add(nud);
}
grSeparationW = 0;
if (i % 3 == 2)
grSeparationH += groupSeparation.Height;
}
}
private void nud_Click(object sender, EventArgs e)
{
NumericUpDown ctr = sender as NumericUpDown;
Color backColr = Color.FromName(ctr.BackColor.Name);
Color fontColr = Color.FromName(ctr.ForeColor.Name);
ctr.BackColor = fontColr;
ctr.ForeColor = backColr;
int[] indexes = (int[])ctr.Tag;
// Get elements
List<int> elements = SudokuControlsValues;
List<int>
row = readRow(indexes[0], elements),
column = readColumn(indexes[1], elements),
square = readSquare(indexes[0], indexes[1], elements);
StringBuilder message = new StringBuilder();
message.AppendLine("VALUE => {0}\n");
message.AppendLine("ROW INDEX => {1}");
message.AppendLine("COLUMN INDEX => {2}");
message.AppendLine("ROW => {3}");
message.AppendLine("COLUMN => {4}");
message.AppendLine("SQUARE => {5}");
message.AppendLine("ROW TIMES => {6}");
message.AppendLine("COLUMN TIMES => {7}");
message.AppendLine("SQUARE TIMES => {8}");
MessageBox.Show(
string.Format(message.ToString(),
new object[]
{
ctr.Value,
indexes[0], // Row
indexes[1], // Column
string.Join(" ", row),
string.Join(" ", column),
string.Join(" ", square),
row.Count(n=>n==(int)ctr.Value),
column.Count(n=>n==(int)ctr.Value),
square.Count(n=>n==(int)ctr.Value),
}));
ctr.BackColor = backColr;
ctr.ForeColor = fontColr;
}
private List<int> readRow(int index, List<int> elements)
{
List<int> result = new List<int>();
for (int i = 9 * index; i < (9 * index) + 9; i++)
result.Add(elements[i]);
return result;
}
private List<int> readColumn(int index, List<int> elements)
{
List<int> result = new List<int>();
for (int i = index; i < elements.Count; i += 9)
result.Add(elements[i]);
return result;
}
private List<int> readSquare(int rowIndex, int columnIndex, List<int> elements)
{
List<int> r = new List<int>();
// int root = (int)(Math.Sqrt((double)elements.Count));
int root = 9;
rowIndex = rowIndex - rowIndex % 3;
columnIndex = columnIndex - columnIndex % 3;
for (int i = rowIndex; i < rowIndex + 3; i++)
for (int j = columnIndex; j < columnIndex + 3; j++)
r.Add(elements[(i * root) + j]);
return r;
}
private void bw_DoWork(object sender, System.ComponentModel.DoWorkEventArgs e)
{
List<int> data = new List<int>();
List<int> remainingNums = new List<int>();
for (int i = 0; i < 9; i++)
for (int j = 1; j < 10; j++)
{
remainingNums.Add(j);
data.Add(0);
}
populateRecursive(data, 0, remainingNums, e);
}
private bool populateRecursive(List<int> data, int cellIdx, List<int> remainingNums, System.ComponentModel.DoWorkEventArgs e)
{
if (remainingNums.Count < 1)
return true;
List<int> options = calcNumberOptions(data, cellIdx, remainingNums);
options = shuffle(options);
for (int i = 0; i < options.Count; i++)
{
int num = options[i];
remainingNums.Remove(options[i]);
data[cellIdx] = num;
setCell(cellIdx, num);
if (populateRecursive(data, cellIdx + 1, remainingNums, e))
return true;
data[cellIdx] = 0;
remainingNums.Add(num);
}
return false;
}
private void setCell(int cellIdx, int value)
{
NumericUpDown nud = sudokuControlsValues[cellIdx] as NumericUpDown;
if (nud.InvokeRequired)
{
setCellValue d = new setCellValue(setCell);
this.Invoke(d, new object[] { cellIdx, value });
}
else
nud.Value = value;
}
private List<int> shuffle(List<int> elements)
{
if (elements.Count < 1)
return elements;
List<int> bse = new List<int>(elements);
List<int> res = new List<int>();
int indexTaken = -1;
do
{
indexTaken = new Random((int)DateTime.Now.Ticks).Next(bse.Count);
res.Add(bse[indexTaken]);
bse.RemoveAt(indexTaken);
}
while (bse.Count > 0);
return res;
}
private List<int> cellIndexToCellParIndex(int cellIndex)
{
int
rowIndex = (int)Math.Floor(cellIndex / 9f),
colIndex = cellIndex - rowIndex * 9;
return new List<int> { rowIndex, colIndex };
}
private List<int> calcNumberOptions(List<int> data, int cellIndex, List<int> remainingNums)
{
List<int> result = new List<int> { 1, 2, 3, 4, 5, 6, 7, 8, 9 };
List<int> cellParIndex = cellIndexToCellParIndex(cellIndex);
int
rowIndex = cellParIndex[0],
colIndex = cellParIndex[1];
List<int> readAllElements = new List<int>();
readAllElements.AddRange(readRow(rowIndex, data));
readAllElements.AddRange(readColumn(colIndex, data));
readAllElements.AddRange(readSquare(rowIndex, colIndex, data));
readAllElements = readAllElements.Distinct().ToList();
readAllElements.ForEach(n => result.Remove(n));
return result;
}
private List<NumericUpDown> sudokuControlsValues = new List<NumericUpDown>(81);
private void btTestOk_Click(object sender, EventArgs e)
{
List<int> elements = SudokuControlsValues;
string result = "OK!";
for (int i = 0; i < elements.Count; i++)
{
List<int> cellIndexPar = cellIndexToCellParIndex(i);
int
currentElement = elements[i],
rowIndex = cellIndexPar[0],
cellIndex = cellIndexPar[1];
List<int>
row = readRow(rowIndex, elements),
col = readColumn(cellIndex, elements),
sqr = readSquare(rowIndex, cellIndex, elements);
if (row.Count(n => n == currentElement) > 1 ||
col.Count(n => n == currentElement) > 1 ||
sqr.Count(n => n == currentElement) > 1)
{
result = "KO...";
break;
}
}
MessageBox.Show(result);
}
}
}
答案 6 :(得分：0)
在Scala中有一些乐趣。您可以删除更多单元格以使其更加困难.Scala
import scala.collection.mutable.Set
import scala.util.Random
object SudokuApp extends App {
def printout(header: String, p: Array[Array[Int]]) {
println(s"--- $header ---")
p.map { row => row.map(print); println("") }
}
// create a possible solution
val puzzle = new Sudoku(Array.fill(9, 9)(0)).a
// create a puzzle by remove a number of cells
remove(puzzle, 60);
printout("puzzle", puzzle)
// solve the puzzle
printout("solution", new Sudoku(puzzle).a)
def remove(a: Array[Array[Int]], count: Int) {
val rs = Random.shuffle(List.range(0, 81))
for (i <- 0 until count)
a(rs(i) / 9)(rs(i) % 9) = 0
}
}
class Sudoku(val a: Array[Array[Int]]) {
val r = Array.fill(9)(Set[Int]())
val c = Array.fill(9)(Set[Int]())
val z = Array.fill(3, 3)(Set[Int]())
for (x <- 0 to 8; y <- 0 to 8)
if (a(x)(y) != 0)
setExist(a(x)(y), x, y)
def setExist(v: Int, x: Int, y: Int) {
r(x) += v
c(y) += v
z(x / 3)(y / 3) += v
}
def fill(x: Int, y: Int): Boolean = {
if (a(x)(y) == 0) {
val candidates = Set() ++ (1 to 9) -- r(x) -- c(y) -- z(x / 3)(y / 3)
def current(): Boolean = {
if (candidates.isEmpty)
false
else {
val v = Random.shuffle(candidates.toList).iterator.next
candidates -= v
a(x)(y) = v
setExist(v, x, y)
val good = if (y < 8) fill(x, y + 1) else if (x < 8) fill(x + 1, 0) else true
if (good)
true
else {
a(x)(y) = 0
r(x) -= v
c(y) -= v
z(x / 3)(y / 3) -= v
current
}
}
}
current
}
else if (y < 8) fill(x, y + 1) else if (x < 8) fill(x + 1, 0) else true
}
fill(0, 0)
}