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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def add_sub_directory(self, key, path):
 """Adds a sub-directory to the results directory. Parameters key: str A look-up key for the directory path. path: str The relative path from the root of the results directory to the sub-directory. Returns ------- str: The absolute path to the sub-directory. """

        sub_dir_path = os.path.join(self.results_root, path)
        os.makedirs(sub_dir_path, exist_ok=True)
        self._directories[key] = sub_dir_path
        return sub_dir_path