import numpy as np

# Solve the generated sudoku!
def solve(problem) -> list : 
    
    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 : # Generates the semi-grid where checking is to be done

                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])

           
    np_problem = np_problem.tolist()
    full_numbers = []

    for x_ in np_problem :
         for y_ in x_ : full_numbers.append(y_)

    #return full_numbers
    full_numbers = [full_numbers[9*x : 9*(x+1)] for x in range(9)]
    return full_numbers
