How does Recursive Backtracking work? Computerphile sodoku solver

Question

I'm so confused by backtracking because when the recursive call returns, won't you replace the solution found by replacing the grid back to zero. So even if you find the solution would it not be erased because after calling the solve function you are canceling what you did by replacing the value back to zero. I get the fact that you are backtracking but on the final recursive call that contains all the correct values are you not just replacing everything to 0?

# grid = .....    # defined as a global value,
                  # a list of 9 lists, 9-long each
def solve():
    global grid
    for y in range (0, 9):
        for x in range (0, 9):
            if grid[y][x] == 0:
                for n in range(1,10):
                    if possible(y, x, n):
                        grid[y][x] = n
                        solve()
                        grid[y][x] = 0
                return

    # edit: missed this final line:
    print (np.matrix(grid))

This was the code on Computerphile video by Prof. Thorsten Altenkirch.

Answer 1

This is weird code, but should work with some adaptations:

def solve():
    global grid
    for y in range(0, 9):
        for x in range(0, 9):
            if grid[y][x] == 0:
                for n in range(1,10):
                    if possible(y, x, n):
                        grid[y][x] = n
                        if solve():
                            return True  # return without reset
                        grid[y][x] = 0
                return False  # exhausted all options
            return True  # this is the deepest and last call with no more zeroes