feat: sudoku solver 2D using recursive backtracking

This commit is contained in:
NIHART, Jeremi 2024-09-08 17:59:59 +02:00
commit fb1d6d3f57
17 changed files with 1147 additions and 0 deletions

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# Sudoku Solver Algorithms
This repository contains a collection of algorithms to solve Sudoku puzzles. The algorithms are implemented in C# and are base on existing methods and new ideas.

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namespace EndMove.Sudoku.Solver.Core.Algorithms;
public class BackTrackingSolver : SolverBase
{
public BackTrackingSolver(Action<int[,]> displayBoard) : base(displayBoard) { }
public override (bool, int[,]) Solve(int[,] board)
{
int row = -1, col = -1;
bool completed = true;
for (int y = 0; y < 9; y++)
{
for (int x = 0; x < 9; x++)
{
if (board[y, x] != 0) continue;
row = y;
col = x;
completed = false;
break;
}
if (!completed) break;
}
if (completed)
{
return (true , board);
}
for (int n = 1; n <= 9; n++)
{
// Check if the wanted assignment is valid
if (!IsValid(board, row, col, n)) continue;
// Then assign display and continue solving
board[row, col] = n;
DisplayBoard(board);
var (isSolved, solvedBoard) = Solve(board);
// If the board is solved, return it
if (isSolved) return (true, solvedBoard);
// Otherwise, backtrack (reset the cell to a ready to work value)
board[row, col] = 0;
}
return (false, board);
}
public override (bool, int[]) Solve(int[] board)
{
// TODO
throw new NotImplementedException();
}
}

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namespace EndMove.Sudoku.Solver.Core.Algorithms;
public interface ISolver
{
/// <summary>
/// Check if a number is valid in a cell
/// </summary>
/// <param name="board">The sudoku board (2D Board)</param>
/// <param name="row">New number in x</param>
/// <param name="col">New number in y</param>
/// <param name="n">New number value</param>
/// <returns>True if valid, False otherwise</returns>
public bool IsValid(int[,] board, int row, int col, int n);
/// <summary>
/// Check if a number is valid in a cell
/// </summary>
/// <param name="board">The sudoku board (1D Board)</param>
/// <param name="row">New number in x</param>
/// <param name="col">New number in y</param>
/// <param name="n">New number value</param>
/// <returns>True if valid, False otherwise</returns>
public bool IsValid(int[] board, int row, int col, int n);
/// <summary>
/// Solve the sudoku board
/// </summary>
/// <param name="board">Initial board</param>
/// <returns>Is solved, solved board</returns>
public (bool, int[,]) Solve(int[,] board);
/// <summary>
/// Solve the sudoku board with a 1D array
/// </summary>
/// <param name="board">Initial board</param>
/// <returns>Is solved, solved board</returns>
public (bool, int[]) Solve(int[] board);
}

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namespace EndMove.Sudoku.Solver.Core.Algorithms;
public abstract class SolverBase : ISolver
{
internal readonly Action<int[,]> DisplayBoard;
/// <summary>
/// Constructor for base solver algorithms
/// </summary>
/// <param name="displayBoard">Method to display board in terminal or other</param>
protected SolverBase(Action<int[,]> displayBoard)
{
DisplayBoard = displayBoard;
}
public virtual bool IsValid(int[,] board, int row, int col, int n)
{
// Check Col, Row
for (int i = 0; i < 9; i++)
{
if (board[row, i] == n || board[i, col] == n)
{
return false;
}
}
// Check Box
int xSize = (col / 3) * 3, ySize = (row / 3) * 3;
for (int y = 0; y < 3; y++)
{
for (int x = 0; x < 3; x++)
{
if (board[ySize + y, xSize + x] == n)
{
return false;
}
}
}
return true;
}
public virtual bool IsValid(int[] board, int row, int col, int n)
{
throw new NotImplementedException();
}
public abstract (bool, int[,]) Solve(int[,] board);
public abstract (bool, int[]) Solve(int[] board);
}

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namespace EndMove.Sudoku.Solver.Core;
// PS: I know this class isn't useful at all, I just wanted to play a bit more
public class SudokuStore
{
private readonly List<int[,]> _sudokuBoards;
public SudokuStore()
{
_sudokuBoards = new List<int[,]>();
}
// Add multiple Sudoku boards
public void AddBoard(params int[][,] boards)
{
foreach (var board in boards)
{
AddBoard(board);
}
}
// Add a new Sudoku board
public void AddBoard(int[,] board)
{
if (board.GetLength(0) != 9 || board.GetLength(1) != 9)
{
throw new ArgumentException("Board must be a 9x9 grid.");
}
_sudokuBoards.Add((int[,])board.Clone());
}
// Remove a Sudoku board by index
public void RemoveBoard(int index)
{
if (index < 0 || index >= _sudokuBoards.Count)
{
throw new ArgumentOutOfRangeException(nameof(index), "Invalid board index.");
}
_sudokuBoards.RemoveAt(index);
}
// Get the count of stored Sudoku boards
public int Count => _sudokuBoards.Count;
// Indexer to access Sudoku boards by index
public int[,] this[int index]
{
get
{
if (index < 0 || index >= _sudokuBoards.Count)
{
throw new ArgumentOutOfRangeException(nameof(index), "Invalid board index.");
}
return (int[,])_sudokuBoards[index].Clone();
}
set
{
if (index < 0 || index >= _sudokuBoards.Count)
{
throw new ArgumentOutOfRangeException(nameof(index), "Invalid board index.");
}
if (value.GetLength(0) != 9 || value.GetLength(1) != 9)
{
throw new ArgumentException("Board must be a 9x9 grid.");
}
_sudokuBoards[index] = (int[,])value.Clone();
}
}
}

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namespace EndMove.Sudoku.Solver.Core.Common;
public static class SudokuUtils
{
/// <summary>
/// Convert a 2D board to a 1D board
/// </summary>
/// <param name="board">2D Board</param>
/// <param name="newBoard">1D Board</param>
public static void TwoDTo1D(int[,] board, out int[] newBoard)
{
int rows = board.GetLength(0), cols = board.GetLength(1);
newBoard = new int[rows * cols];
for (int i = 0; i < rows; i++)
{
for (int j = 0; j < cols; j++)
{
newBoard[i * cols + j] = board[i, j];
}
}
}
/// Display the board in the terminal (1D Board)
public static void DisplayBoard(int[] board)
{
const string separator = "+---+---+---+---+---+---+---+---+---+";
for (int i = 0; i < 81; i++)
{
if (i % 27 == 0)
{
Console.WriteLine(separator);
}
Console.Write("{0} {1} ", (i % 3 == 0) ? '|' : ' ', board[i] == 0 ? "*" : board[i]);
if (i % 9 == 8) Console.WriteLine("|");
}
Console.WriteLine(separator);
}
/// Display the board in the terminal (2D Board)
public static void DisplayBoard(int[,] board)
{
const string separator = "+---+---+---+---+---+---+---+---+---+";
Console.WriteLine(separator);
for (int i = 0; i < 9; i++)
{
Console.Write("|");
for (int j = 0; j < 9; j++)
{
Console.Write(" {0} {1}", board[i, j] == 0 ? "*" : board[i, j], ((j + 1) % 3 == 0) ? '|' : ' ');
}
Console.WriteLine();
if ((i + 1) % 3 == 0)
{
Console.WriteLine(separator);
}
}
}
}

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<Project Sdk="Microsoft.NET.Sdk">
<PropertyGroup>
<OutputType>Exe</OutputType>
<TargetFramework>net8.0</TargetFramework>
<ImplicitUsings>enable</ImplicitUsings>
<Nullable>enable</Nullable>
</PropertyGroup>
</Project>

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using EndMove.Sudoku.Solver.Core.Algorithms;
using EndMove.Sudoku.Solver.Core.Common;
namespace EndMove.Sudoku.Solver.Core
{
public static class Program
{
public static void Main(string[] args)
{
var store = new SudokuStore();
store.AddBoard(new[,]
{
{ 5, 3, 0, 0, 7, 0, 0, 0, 0 },
{ 6, 0, 0, 1, 9, 5, 0, 0, 0 },
{ 0, 9, 8, 0, 0, 0, 0, 6, 0 },
{ 8, 0, 0, 0, 6, 0, 0, 0, 3 },
{ 4, 0, 0, 8, 0, 3, 0, 0, 1 },
{ 7, 0, 0, 0, 2, 0, 0, 0, 6 },
{ 0, 6, 0, 0, 0, 0, 2, 8, 0 },
{ 0, 0, 0, 4, 1, 9, 0, 0, 5 },
{ 0, 0, 0, 0, 8, 0, 0, 7, 9 }
}, new[,]
{
{ 8, 0, 0, 0, 0, 0, 0, 0, 0 },
{ 0, 0, 3, 6, 0, 0, 0, 0, 0 },
{ 0, 7, 0, 0, 9, 0, 2, 0, 0 },
{ 0, 5, 0, 0, 0, 7, 0, 0, 0 },
{ 0, 0, 0, 0, 4, 5, 7, 0, 0 },
{ 0, 0, 0, 1, 0, 0, 0, 3, 0 },
{ 0, 0, 1, 0, 0, 0, 0, 6, 8 },
{ 0, 0, 8, 5, 0, 0, 0, 1, 0 },
{ 0, 9, 0, 0, 0, 0, 4, 0, 0 }
},
new[,]
{
{ 0, 0, 5, 3, 0, 0, 0, 0, 0 },
{ 8, 0, 0, 0, 0, 0, 0, 2, 0 },
{ 0, 7, 0, 0, 1, 0, 5, 0, 0 },
{ 4, 0, 0, 0, 0, 5, 3, 0, 0 },
{ 0, 1, 0, 0, 7, 0, 0, 0, 6 },
{ 0, 0, 3, 2, 0, 0, 0, 8, 0 },
{ 0, 6, 0, 5, 0, 0, 0, 0, 9 },
{ 0, 0, 4, 0, 0, 0, 0, 3, 0 },
{ 0, 0, 0, 0, 0, 9, 7, 0, 0 }
},
new[,]
{
{ 0, 0, 0, 0, 0, 7, 0, 9, 0 },
{ 2, 0, 0, 0, 0, 8, 0, 0, 0 },
{ 0, 3, 0, 0, 0, 0, 0, 6, 0 },
{ 0, 0, 0, 5, 0, 0, 0, 0, 9 },
{ 0, 0, 1, 0, 0, 0, 0, 0, 0 },
{ 9, 0, 0, 0, 0, 0, 0, 0, 0 },
{ 0, 0, 0, 0, 0, 0, 0, 0, 0 },
{ 0, 0, 0, 0, 6, 0, 0, 0, 0 },
{ 0, 5, 0, 0, 9, 0, 0, 0, 0 }
});
SudokuUtils.TwoDTo1D(store[0], out int[] sudoku1D);
SudokuUtils.DisplayBoard(sudoku1D);
// TODO 1D solver with backtracking
ISolver solver = new BackTrackingSolver(SudokuUtils.DisplayBoard);
var (status, lol) = solver.Solve(store[0]);
Console.WriteLine(status);
}
}
}