Algorithm for solving Sudoku

Question

I want to write a code in python to solve a sudoku puzzle. Do you guys have any idea about a good algorithm for this purpose. I read somewhere in net about a algorithm which

Answer 1

Using google ortools - the following will either generate a dummy sudoku array or will solve a candidate. The code is probably more verbose than required, any feedback is appreciated.

The idea is to solve a constraint-programming problem that involves

1. List of 81 variables with integer bounds between 1 and 9.
2. All different constraint for row vector
3. All different constraint for column vector
4. All different constraint for the sub-matrices

In addition, when trying to solve existing sudoku, we add additional constraints on variables that already have assigned value.

from ortools.constraint_solver import pywrapcp
import numpy as np

def sudoku_solver(candidate = None):
    solver = pywrapcp.Solver("Sudoku")

    variables = [solver.IntVar(1,9,f"x{i}") for i in range(81)]
    if len(candidate)>0:
        candidate = np.int64(candidate)
        for i in range(81):
            val = candidate[i]
            if val !=0:
                solver.Add(variables[i] == int(val))

    def set_constraints():
        for i in range(9):
            # All columns should be different
            q=[variables[j] for j in list(range(i,81,9))]
            solver.Add(solver.AllDifferent(q))

            #All rows should be different
            q2=[variables[j] for j in list(range(i*9,(i+1)*9))]
            solver.Add(solver.AllDifferent(q2))

            #All values in the sub-matrix should be different
            a = list(range(81))
            sub_blocks = a[3*i:3*(i+9):9] + a[3*i+1:3*(i+9)+1:9] + a[3*i+2:3*(i+9)+2:9]
            q3 = [variables[j] for j in sub_blocks]
            solver.Add(solver.AllDifferent(q3))
            
    set_constraints()
    db = solver.Phase(variables, solver.CHOOSE_FIRST_UNBOUND, solver.ASSIGN_MIN_VALUE)
    solver.NewSearch(db)    
    
    results_store =[]
    num_solutions =0
    total_solutions = 5
    while solver.NextSolution() and num_solutions

Solve the following sudoku

candidate = np.array([0, 2, 0, 4, 5, 6, 0, 8, 0, 0, 5, 6, 7, 8, 9, 0, 0, 3, 7, 0, 9, 0,
       2, 0, 4, 5, 6, 2, 0, 1, 5, 0, 4, 8, 9, 7, 5, 0, 4, 8, 0, 0, 0, 0,
       0, 3, 1, 0, 6, 4, 5, 9, 7, 0, 0, 0, 5, 0, 7, 8, 3, 1, 2, 8, 0, 7,
       0, 1, 0, 5, 0, 4, 9, 7, 8, 0, 3, 0, 0, 0, 5])


results_store = sudoku_solver(candidate)