How to generates a list which elements are at a fix distance from a desired list

Question

I have a list of possibilities and a desired input:

possibles = [20, 30, 40, 50, 60, 70, 80, 100]
desired = [20, 30, 40]

I want to generate the close by lists. Example:

# Distance of 1 (i.e. 1 element changes to a close-by)
[30, 30, 40]
[20, 40, 40]
[20, 30, 30]
[20, 30, 50]

# Distance of 2:
[40, 30, 40]
[30, 30, 50]
[30, 40, 40]
...

My current version is only varying one element at a time, thus, as soon as the distance is above 1, I'm missing a lot of combination.

def generate_close_by(possibles, desired):
    for k in range(1, 4):
        for i, elt in enumerate(desired):
            id = possibles.index(elt)

            new = desired[:]
            if id < len(possibles)-k-1:
                new[i] = possibles[id+k]
                yield (new)

            if id > k:
                new[i] = possibles[id-k]
                yield (new)

# Output
[30, 30, 40]
[20, 40, 40]
[20, 30, 50]
[20, 30, 30]
[40, 30, 40]
[20, 50, 40]
[20, 30, 60]
[50, 30, 40]
[20, 60, 40]
[20, 30, 70]

I'm quite sure a module should already exist to do this kind of iteration (itertools?), could you point me to the write function?

Thanks.

EDIT:

Update on the tries...

I'm trying to generate a list the same size of desired in which each element correspond to how much I have to move the element of desired.

desired = [20, 30, 40]
# Distance of 1:
distance = [1, 0, 0]
distance = [0, 1, 0]
distance = [0, 0, 1]
distance = [-1, 0, 0]
distance = [0, -1, 0]
distance = [0, 0, -1]

And then plan was to try to create the new list, and if it can't (out of bounds), it just continues. Not working yet, but might be a good approach.

Answer 1

I guess I will show a more long winded approach that can be more easily generalizable.

I first write down the problem.

possible_pts = [20, 30, 40, 50, 60, 70, 80, 100]
starting_pt_in_idx = [0, 1, 2]
distance = 2

There are 3 axes that can "change". I first find the combinations of axis changes.

N = len(starting_pt_in_idx)
axis = list(range(N))

import itertools
axismoves = list(itertools.combinations_with_replacement(axis, distance))
print(axismoves)

Next, we bin it. For example, if I see axis-0 appearing twice, it becomes [2,0,0].

abs_movements = []
for combi in axismoves:
    move_bin = [0] * N
    for i in combi:
        move_bin[i] += 1
    abs_movements.append(move_bin)
print(abs_movements)

The above gave the absolute movements. To find the actual movement, we must take into consideration the change can be positive or negative along that axis.

import copy
actual_movements = []
for movement in abs_movements:
    actual_movements.append(movement)
    for i, move in enumerate(movement):
        if move != 0:
            _movement = copy.deepcopy(movement)
            _movement[i] = - move
            actual_movements.append(_movement)
print(actual_movements)

The final step is to translate the index into actual positions. So first we write this helper function.

def translate_idx_to_pos(idx_vect, points):
    idx_bounds = [0, len(points) - 1]
    pos_point = [0] * len(idx_vect)
    for i, idx_pos in enumerate(idx_vect):
        if idx_pos < idx_bounds[0] or idx_pos > idx_bounds[1]:
            return None
        else:
            pos_point[i] = points[idx_pos]
    return pos_point

Using the actual movements to act on the starting point index, then translating it back to the positions.

from operator import add
final_pts = []
for movement in actual_movements:
    final_pt_in_idx = list(map(add, starting_pt_in_idx, movement))
    final_point = translate_idx_to_pos(final_pt_in_idx, possible_pts)
    if final_point is not None:
        final_pts.append(final_point)

print(final_pts)

This gives

[40, 30, 40]
[30, 40, 40]
[30, 20, 40]
[30, 30, 50]
[30, 30, 30]
[20, 50, 40]
[20, 40, 50]
[20, 20, 50]
[20, 40, 30]
[20, 30, 60]
[20, 30, 20]

Answer 2

Yes you are right, itertools is gonna be really useful here. What you want is find all subsets of desired length of the possibles list WITH duplicates, and the function that does that is itertools.product

from itertools import product

possibles = [20, 30, 40, 50, 60, 70, 80, 100]
desired = [20, 30, 40]

def fake_hamming(cur, desired, possibles):
    assert len(cur) == len(desired)

    hamm = 0
    for i in range(len(cur)):
        assert cur[i] in possibles
        assert desired[i] in possibles
        hamm += abs(possibles.index(cur[i]) - possibles.index(desired[i]))

    return hamm

def generate_close_by(desired, possibles, dist):
    all_possible_lists = product(possibles, repeat=len(desired))
    return [l for l in all_possible_lists if fake_hamming(l, desired, possibles) == dist]

print(generate_close_by(desired, possibles,1))
>>> [(20, 20, 40), (20, 30, 30), (20, 30, 50), (20, 40, 40), (30, 30, 40)]

Edit There you go, changed combinations for product (see @tobias_k comment below), and also here is the fake_hamming function xD Also it is true that it will be slow for big lists, but this is the most generic way to do it

Answer 3

def distribute(number, bucket):
  if bucket == 1:
    yield [number]
    if number != 0:
      yield [-1 * number]
  elif number == 0:
    yield [0]*bucket
  else:
    for i in range(number+1):
      for j in distribute(number-i, 1):
        for k in distribute(i, bucket-1):
          yield j+k

def generate(possibles, desired, distance):
  for index_distance_tuple in distribute(distance, len(desired)):
    retval = desired[:]
    for i, index in enumerate(index_distance_tuple):
      if index + i < 0 or index + i >= len(possibles):
        break
      retval[i] = possibles[index + i]
    else:
      yield retval

For distance 1:

for i in generate(possibles, desired, 1):
  print(i)

Output :

[30, 30, 40]
[20, 40, 40]
[20, 20, 40]
[20, 30, 50]
[20, 30, 30]

For distance 2 :

for i in generate(possibles, desired, 2):
  print(i)

Output :

[40, 30, 40]
[30, 40, 40]
[30, 20, 40]
[30, 30, 50]
[30, 30, 30]
[20, 50, 40]
[20, 40, 50]
[20, 40, 30]
[20, 20, 50]
[20, 20, 30]
[20, 30, 60]
[20, 30, 20]