Sudoku Strategy

A Python library for representing, analysing, and solving Sudoku puzzles using human style solving techniques.

The project is designed around a simple distinction between:

• Grid state: the current digits and candidates in a puzzle.
• Grid analysis: information that can be derived from the current state.
• Strategies: human solving techniques that analyse a grid and identify deductions.
• Deductions: explanations of the changes that can be made to the puzzle.
• Grid modification: applying deductions to progress the puzzle.

The aim is not simply to produce a completed Sudoku grid, but to provide useful, explainable solving steps that can be presented as hints.

Installation

Install from PyPI with:

pip install sudoku_strategy

Quick Start

from sudoku_strategy import GridState, Solver
from sudoku_strategy.grid import GridModifier

# Puzzle digits is an 81 length tuple representing the starting state of the
# puzzle. `0` is used to represent an empty cell.
puzzle_digits = (0, 0, 5, 4, 0, ...)

grid = GridState.new_puzzle(puzzle_digits)

# Add any user entered digits to the puzzle
modifier = GridModifier(grid)
modifier.write_digit(5, Cell(7, 8))

# Compute all candidates
modifier.compute_candidates()

# Get the next move
solver = Solver()

deduction = solver.find_next(grid)

if deduction is not None:
    print(deduction.explanation)

A deduction's explanation might look like:

Cell R4C7 is a naked single with value 5

This makes the solver suitable for applications where the user wants to understand why a move can be made rather than simply being given the answer.

Representing a Sudoku

Cells

A Sudoku consists of 81 cells arranged into:

• 9 rows
• 9 columns
• 9 boxes

Cells are represented using zero-based row and column coordinates:

from sudoku_strategy import Cell

cell = Cell(row=3, col=6)

This corresponds to R4C7 when displayed using the conventional one-based Sudoku notation.

Cells can also be created from their zero-based position in the grid with zero being the top left cell, counting along each row, with cell 80 being in the bottom right:

cell = Cell.from_index(33)

Grid

GridState represents the current state of a Sudoku puzzle. It stores:

• Puzzle's initial digits
• Entered digits
• Candidates for each cell

An empty grid can be created with:

from sudoku_strategy import GridState

grid = GridState.create_empty()

The state can be queried:

digit = grid.digit(cell)

if grid.cell_empty(cell):
    print("Cell is empty")

if grid.is_complete():
    print("Puzzle is complete")

Modifying a Grid

Editing a Sudoku grid is achieved with GridModifier It allows digits and candidates to be added or removed from a grid:

from sudoku_strategy.grid import GridModifier

modifier = GridModifier(grid)

# Write 8 to R9C4
modifier.add_digit(5, Cell(8, 3))

# Calculate all candidate for the puzzle
modifier.update_candidates()

# Remove the candidate 6 from R3C8
modifier.remove_candidate(6, Cell(2, 7))

Analysing a Grid

GridAnalysis provides higher level queries over a GridState. It is deliberately separate from the state itself. Analysis does not modify the puzzle. For example:

from sudoku_strategy.grid import GridAnalysis

analysis = GridAnalysis(grid)

# Query the candidates for a cell
candidates = analysis.get_candidates_for_cell(cell)

# Count how many candidates are in a cell
count = analysis.count_candidates_in_cell(cell)

# You can search a collection of cells (e.g. row 4) for a particular
# candidate (e.g. 5)
row_4 = analysis.iterate.row(3)
cells_with_five = analysis.cells_with_candidate(row_4, 5)
count = analysis.count_cells_with_candidate(row_4, 5)

Solving Strategies

A solving strategy analyses a grid and produces a deduction when it finds one. Strategies implement the AbsStrategy interface:

class AbsStrategy(ABC):
    @abstractmethod
    def find(self, analysis) -> Deduction | None: ...

For example, the naked single strategy looks for an empty cell with exactly one remaining candidate:

from sudoku_strategy.strategy import NakedSingleStrategy

strategy = NakedSingleStrategy()

deduction = strategy.find(analysis)

If a naked single is found, the strategy returns a Deduction. If no naked single exists, it returns None.

Deductions

A deduction represents a conclusion reached by a solving strategy. A deduction can either show a cell that can have a digit entered, or provide a list of candidates that can be eliminated. For example:

from sudoku_strategy.strategy import DigitDeduction, EliminationDeduction

Deduction(
    strategy="Naked Single",
    assignment=CellDigit(Cell(3, 6), 5),
    explanation="Cell R4C7 is a naked single with value 5.",
)

A deduction contains both the information required to make the change, and an explanation suitable for displaying to user.

Finding a Hint

The Solver can search its configured strategies for the next available deduction

from sudoku_strategy import Solver

solver = Solver()

deduction = solver.find_next(grid)

if deduction is None:
    print("No known next step")
else:
    print(deduction.explanation)

Strategies are evaluated in order. The first strategy to produce a deduction determines the next step. This means the order of strategies can be used to control the solving approach. For example:

strategies = (
    NakedSingleStrategy(),
    HiddenSingleStrategy(),
)
solver = Solver(
    strategies=strategies,
)

Solving a Puzzle

The solver can also repeatedly find and apply deductions until the puzzle is complete or no further supported deduction can be found:

deductions = solver.solve(grid)

The returned list contains the deductions that were made. This allows the solution to be displayed as a sequence of human-readable steps rather than only displaying the final grid.

For example:

for deduction in deductions:
    print(deduction.explanation)

The original grid is preserved while solving - the solver works on a copy of the supplied grid.

Reading and Writing Puzzles

Puzzles can be read and written in various formats using GridFileWriter and GridFileReader which convert file to/from a GridState:

from sudoku_strategy import GridFileWriter, GridFileReader

# Load a file into a GridState
grid = GridFileReader().load(path)

# Manipulate the grid
...

# Write the updated grid back to a file
GridFileWriter().save(grid, path)

Supported formats:

• Susser: saved in .txt files
• Json: saved in .json files

Susser Format

A string of 81 characters representing cells in the grid, starting in the top left, and working along the rows to the bottom right. Filled cells are given the number 1-9, and empty cells use a placeholder character, e.g. '.'

Json Format

The json format consists of an object with three fields:

• Puzzle digits
  • A list of 81 digits representing the puzzle's starting state. 0 is used to represent an empty cell
• digits
  • A list of 81 digits representing digits added to the grid. These include the digits defined in puzzle digits. 0 is used to represent an empty cell
• Candidates Values
  • A list of 81 lists. Each sub list can contain the numbers 1-9 representing the candidates for the associated cell.