code: def compute_best_placements(
      positions: tp.List[float], min_diff: float
  ) -> tp.List[float]:
      """Provides a list of new positions from a list of initial position, with a minimal
      distance between each position.
  
      Parameters
      ----------
      positions: List[float]
          best positions if minimal distance were 0.
      min_diff: float
          minimal distance allowed between two positions
  
      Returns
      -------
      new_positions: List[float]
          positions after taking into account the minimal distance constraint
  
      Note
      ----
      This function is probably not optimal, but seems a very good heuristic
      """
      assert all(
          v2 >= v1 for v2, v1 in zip(positions[1:], positions[:-1])
      )
      groups = [
          LegendGroup([k], [pos], min_diff)
          for k, pos in enumerate(positions)
      ]
      new_groups: tp.List[LegendGroup] = []
      ready = False
      while not ready:
          ready = True
          for k in range(
              len(groups)
          ):  # pylint: disable=consider-using-enumerate
              if (
                  k < len(groups) - 1
                  and groups[k + 1].bounds[0] < groups[k].bounds[1]
              ):
                  # groups are overlapping: create a new combined group
                  # which will provide new non-overlapping positions around the mean of initial positions
                  new_groups.append(
                      groups[k].combine_with(groups[k + 1])
                  )
                  # copy the rest of the groups and start over from the first group
                  new_groups.extend(groups[k + 2 :])
                  groups = new_groups
                  new_groups = []
                  ready = False
                  break
              new_groups.append(groups[k])
      new_positions = np.array(positions, copy=True)
      for group in groups:
          new_positions[group.indices] = group.get_positions()
      return new_positions.tolist()
  
imports: import os
  import re
  import string
  import hashlib
  import warnings
  import argparse
  import itertools
  from collections import defaultdict
  from pathlib import Path
  import numpy
  import pandas
  from matplotlib import pyplot
  from matplotlib.legend import Legend
  from matplotlib import cm
  from mpl_toolkits.axes_grid1 import make_axes_locatable
  import nevergrad.common.typing
  from .None import utils
  from .exporttable import export_table
label_desc: Use image node_id 12 for calling a global function with example usage: compute_best_placements(positions, min_diff) and returns: new_positions