code: def _optimize_runtime_with_given_memory(
      memory: torch.Tensor,
      runtimes: torch.Tensor,
      max_memory: float,
      view_like_ops: List[int],
      inplace_ops: List[Tuple[int, ...]],
      random_ops: List[int],
  ) -> torch.Tensor:
      """
      Given a list of operator names, their corresponding runtimes, and the maximum amount of memory available,
      find the subset of operators that can be optimized to reduce runtime while still fitting within the memory budget.
      Uses https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.milp.html
  
      Args:
          memory (torch.Tensor): Tensor containing the memory usage of each operator.
          runtimes (torch.Tensor): Tensor containing the runtime of each operator.
          max_memory (float): Maximum amount of memory to use.
          view_like_ops ([List[int]): Indices of the view-like ops.
          inplace_ops (List[Tuple[int, int]]): Tuple with the pair of inplace op -> parent of inplace op.
              This will be used to add the constraint that in-place ops need to either be
              stored in memory with the previous op, or recomputed with the previous op.
          random_ops ([List[int]): Indices of the random ops, which will always be recomputed.
      """
      c = -runtimes  # type: ignore[operator]
  
      memory_constraint = LinearConstraint(A=memory, ub=max_memory)
      constraints = [memory_constraint]
  
      # view-like ops should always be recomputed
      for i in view_like_ops:
          A = torch.zeros_like(c)
          A[i] = 1
          constraints.append(LinearConstraint(A=A, lb=0, ub=0))
  
      # inplace ops should always be done in conjuction with its parent op
      # i.e., if we recompute the parent op the inplace should also be
      # recomputed, and vice versa
      for op, op_parent in inplace_ops:
          A = torch.zeros_like(c)
          if op != op_parent:
              A[op_parent] = 1
              A[op] = -1
              constraints.append(LinearConstraint(A=A, lb=0, ub=0))
          else:
              # if op == op_parent, it's because it's the first op
              # that is inplace. Thus never recompute it
              A[op] = 1
              constraints.append(LinearConstraint(A=A, lb=1, ub=1))
  
      # random ops should always be recomputed
      for i in random_ops:
          A = torch.zeros_like(c)
          A[i] = 1
          constraints.append(LinearConstraint(A=A, lb=0, ub=0))
  
      integrality = torch.ones_like(c)
      res = milp(
          c=c,
          constraints=constraints,
          integrality=integrality,
          bounds=Bounds(0, 1),
      )
      x = torch.from_numpy(res.x)
      return x
  
imports: import time
  import weakref
  from collections import defaultdict
  from contextlib import nullcontext
  from copy import deepcopy
  from dataclasses import astuple, dataclass
  from typing import Any, Callable, ContextManager, Dict, List, Optional, Tuple
  import torch
  from torch.testing._internal.composite_compliance import is_inplace, is_inplace_view_fn, is_view_fn
  from torch.utils._python_dispatch import TorchDispatchMode
  from torch.utils._pytree import tree_map
  from torch.utils.checkpoint import get_device_states, set_device_states
label_desc: Use image node_id 7 for calling a global function with example usage: _optimize_runtime_with_given_memory(memory, runtimes, max_memory, view_like_ops, inplace_ops, random_ops) and returns: x