Python: Simple 4 number Solver?

Question

I'm trying to make a simple number solver of 4 numbers. The solver replaces the "0" with a number between 1-4. All numbers in the one layered grid must be unique.

Start [2, 0, 3, 0]

The end result should be [2, 1, 3, 4] or [2, 4, 3, 1]

I need to know how to create a loop that does this? The loop should check the 0s and replace them with the correct number, cycling through 1-4, and then print the correct grid list.

import numpy as np

grid = [2, 0, 3, 0]
        
#checks that the number is not the same as existing number 
def possible(y,n):
    if grid[y] == n:
        return False
    else:
        return True

# loop that checks all 4 numbers and then replaces the 0's with the correct number    
for num in grid:  
    if possible == False:
        for n in grid(1,4):
            print(grid)

Answer 1

This will output a valid solution:

grid = [2, 0, 3, 0]
all_nums = {1,2,3,4}
for i in range(len(grid)):
    if grid[i] == 0:
        non_zero_numbers_already_taken = set()
        for j in range(len(grid)):
            if grid[j] != 0:
                non_zero_numbers_already_taken.add(grid[j])
        # assigns an available number to replace the 0 at index i
        grid[i] = (all_nums - non_zero_numbers_already_taken).pop()
print(grid) 
# output : [2, 1, 3, 4]

You can adapt the logic to output all possible solutions..

Answer 2

This is an alternative

    def replace_zeros(plist):
        numbers = [4,3,2,1]
        outcome = []
        for num in plist:
            if num in numbers:
                numbers.remove(num)

        print(f'these are the missing numbers: {numbers}')
        for num in plist:
            if num == 0:
                outcome.append(numbers.pop())
            else:
                outcome.append(num)
        return outcome

    new_grid = replace_zeros([1,0,3,0])
    print(new_grid)
    #these are the missing numbers: [4,2]
    # [1,2,3,4]