如何优化数独解算器中涉及回溯的函数运行速度

def solve_sudoku(board):
    def is_valid(board, row, col, num):
        for x in range(9):
            if board[row][x] == num or board[x][col] == num:
                return False
        start_row, start_col = 3 * (row // 3), 3 * (col // 3)
        for i in range(3):
            for j in range(3):
                if board[i + start_row][j + start_col] == num:
                    return False
        return True

    def find_empty(board):
        for i in range(9):
            for j in range(9):
                if board[i][j] == 0:
                    return (i, j)
        return None

    def solve():
        empty = find_empty(board)
        if not empty:
            return True
        row, col = empty
        for num in range(1, 10):
            if is_valid(board, row, col, num):
                board[row][col] = num
                if solve():
                    return True
                board[row][col] = 0
        return False

    solve()
    return board

# 示例数独板
board = [
    [5, 3, 0, 0, 7, 0, 0, 0, 0],
    [6, 0, 0, 1, 9, 5, 0, 0, 0],
    [0, 9, 8, 0, 0, 0, 0, 6, 0],
    [8, 0, 0, 0, 6, 0, 0, 0, 3],
    [4, 0, 0, 8, 0, 3, 0, 0, 1],
    [7, 0, 0, 0, 2, 0, 0, 0, 6],
    [0, 6, 0, 0, 0, 0, 2, 8, 0],
    [0, 0, 0, 4, 1, 9, 0, 0, 5],
    [0, 0, 0, 0, 8, 0, 0, 7, 9]
]

solved_board = solve_sudoku(board)
for row in solved_board:
    print(row)