import numpy as np problem = [] for x in range(9): i = input() l = [int(v) for v in i] problem.append(l) #print(problem) np_problem = np.array(problem) fixed_coordinates = [] # first getting the coordinates where fixed numbers are present empty_coordinates = [] for i , sub_array in enumerate(problem) : temp = [[i , c] for c , sub_element in enumerate(sub_array) if sub_element > 0] temp2 = [[i , j] for j , sub_element2 in enumerate(sub_array) if sub_element2 == 0] for z in temp : fixed_coordinates.append(z) for w in temp2 : empty_coordinates.append(w) l , m , r = [0 , 3 , 6] , [1 , 4 , 7] , [2 , 5 , 8] avoid_dict = {idx : [] for idx in list(range(0 , len(empty_coordinates)))} def generate_bounds(r , c) -> list: lower_bound_c = c if c in l else c - 1 if c in m else c - 2 upper_bound_c = c + 3 if c in l else c + 2 if c in m else c + 1 lower_bound_r = r if r in l else r - 1 if r in m else r - 2 upper_bound_r = r + 3 if r in l else r + 2 if r in m else r + 1 return [lower_bound_c , upper_bound_c , lower_bound_r , upper_bound_r] def backtrack(return_coordinates) : n_r , n_c = empty_coordinates[empty_coordinates.index(return_coordinates) - 1] # getting back element coordinates while [n_r , n_c] != empty_coordinates[empty_coordinates.index(return_coordinates) + 1]: if np_problem[n_r , n_c] != 0 : avoid_dict[empty_coordinates.index([n_r , n_c])].append(np_problem[n_r , n_c]) fix_flag = False r , c = n_r , n_c for num in range(1 , 10) : l_b_c , u_b_c , l_b_r , u_b_r = generate_bounds(r , c) if all([num not in np_problem[l_b_r : u_b_r , l_b_c : u_b_c] , num not in np_problem[r , :] , num not in np_problem[: , c]]) : if num not in avoid_dict.get(empty_coordinates.index([n_r , n_c])) : np_problem[n_r , n_c] , fix_flag = num , True break if fix_flag : n_r , n_c = empty_coordinates[empty_coordinates.index([n_r , n_c]) + 1] if not fix_flag : np_problem[n_r , n_c] = 0 avoid_dict[empty_coordinates.index([n_r , n_c])].clear() n_r , n_c = empty_coordinates[empty_coordinates.index([n_r , n_c]) - 1] for r in range(9) : for c in range(9) : if [r , c] not in fixed_coordinates : fix_flag = False for num in range(1 , 10) : l_b_c , u_b_c , l_b_r , u_b_r = generate_bounds(r , c) if all([num not in np_problem[l_b_r : u_b_r , l_b_c : u_b_c] , num not in np_problem[r , :] , num not in np_problem[: , c]]) : np_problem[r , c] , fix_flag = num , True break if not fix_flag : backtrack([r , c]) print(np_problem)