code: def _compute_table_c(chain: Chain, mmax: int) -> Tuple:
      try:
          from .rotorc import compute_table
  
      # build module if module not found
      except ModuleNotFoundError:
          import os
          import subprocess
          import sys
  
          logger = get_dist_logger()
          logger.info(
              "rotorc hasn't been built! Building library...", ranks=[0]
          )
          this_dir = os.path.dirname(os.path.abspath(__file__))
          result = subprocess.Popen(
              [
                  f"{sys.executable}",
                  f"{os.path.join(this_dir, 'build_c_ext.py')}",
                  "build_ext",
                  f"--build-lib={this_dir}",
              ],
              stdout=subprocess.PIPE,
              stderr=subprocess.PIPE,
          )
          if result.wait() == 0:
              logger.info("rotorc has been built!", ranks=[0])
              from .rotorc import compute_table
          else:
              logger.warning(
                  "rotorc built failed! Using python version!",
                  ranks=[0],
              )
              return CheckpointSolverRotor._compute_table(chain, mmax)
      return compute_table(chain, mmax)
  
imports: from copy import deepcopy
  from typing import Any, List, Tuple
  from torch import Tensor
  from torch.fx import Graph, Node
  from colossalai.auto_parallel.passes.runtime_apply_pass import runtime_apply, runtime_comm_spec_apply
  from colossalai.fx.codegen.activation_checkpoint_codegen import _find_nested_ckpt_regions
  from colossalai.fx.profiler import activation_size, calculate_bwd_time, calculate_fwd_out, calculate_fwd_time, calculate_fwd_tmp
  from colossalai.logging import get_dist_logger
  from .ckpt_solver_base import CheckpointSolverBase
  from .operation import Backward, Chain, ForwardCheck, ForwardEnable, ForwardNograd, Loss, Sequence
label_desc: Use image node_id 11 for calling the CheckpointSolverRotor obj's underlying member method code with example usage: obj._compute_table_c(chain, mmax) and returns: compute_table, CheckpointSolverRotor