A simple sudoku solver.

sudoku.py

'''
A simple sudoku solver
'''
from typing import List
from typing import Tuple
from typing import Union

class sudoku:
	def __init__(self, puzzel:List[List[int]]):
		self.puzzel = puzzel
		self._is_solved:bool = self.solve()

	def _completed(self) -> bool:
		for r in range(0, 9):
			for c in range(0, 9):
				if self.puzzel[r][c] == -1:
					return False
		return True

	def _is_valid(self, row:int, column:int, value:int) -> bool:
		if value in self.puzzel[row]:
			return False

		if value in [self.puzzel[row][c] for c in range(0, 9)]:
			return False

		ro = (row//3) * 3
		co = (column//3) * 3

		for r in range(ro, ro+3):
			for c in range(co, co+3):
				if self.puzzel[r][c] == value:
					return False
		return True


	def _find_next(self) -> Union[Tuple[int, int], Tuple[None, None]]:
		for r in range(0, 9):
			for c in range(0, 9):
				if self.puzzel[r][c] == -1:
					return r,c
		return None, None

	def solve(self) -> bool:
		if self._completed():
			return True

		r, c = self._find_next()

		for value in range(1,10):
			if self._is_valid(r, c, value):
				self.puzzel[r][c] = value
				return self.solve()

		return False

	@property
	def is_solved(self) -> bool:
		return self._is_solved
	
	@property
	def solution(self) -> List[List[int]]:
		return self.puzzel

if __name__ == '__main__':
	puzzel =[[5,1,7,6,-1,-1,-1,3,4],
		[2,8,9,-1,-1,4,-1,-1,-1],
		[3,4,6,2,-1,5,-1,9,-1],
		[6,-1,2,-1,-1,-1,-1,1,-1],
		[-1,3,8,-1,-1,6,-1,4,7],
		[-1,-1,-1,-1,-1,-1,-1,-1,-1],
		[-1,9,-1,-1,-1,-1,-1,7,8],
		[7,-1,3,4,-1,-1,5,6,-1],
		[-1,-1,-1,-1,-1,-1,-1,-1,-1]
	]

	d = sudoku(puzzel)

	if d.is_solved:
		print(d.solution)