Python dictionary with list keyword

Question

I'm coding a N'th order markov chain.

It goes something like this:

class Chain:
 def __init__(self, order):
  self.order = order
  self.state_table = {}
 def train(self, next_state, *prev_states):
  if len(prev_states) != self.order: raise ValueError("prev_states does not match chain order")
  if prev_states in self.state_table:
   if next_state in self.state_table[prev_states]:
    self.state_table[prev_states][next_state] += 1
   else:
    self.state_table[prev_states][next_state] = 0
  else:
   self.state_table[prev_states] = {next_state: 0}

Unfortunally, list and tuples are unhashable, and I cannot use them as keywords in dicts... I have hopefully explained my problem well enough for you to understand what I try to achieve.

Any good ideas how I can use multiple values for dictionary keyword?

Followup question:

I did not know that tuples are hashable. But the entropy for the hashes seem low. Are there hash collisions possible for tuples?!

Answer 1

Tuples are hashable when their contents are.

>>> a = {}
>>> a[(1,2)] = 'foo'
>>> a[(1,[])]
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: unhashable type: 'list'

As for collisions, when I try a bunch of very similar tuples, I see them being mapped widely apart:

>>> hash((1,2))
3713081631934410656
>>> hash((1,3))
3713081631933328131
>>> hash((2,2))
3713082714462658231
>>> abs(hash((1,2)) - hash((1,3)))
1082525
>>> abs(hash((1,2)) - hash((2,2)))
1082528247575

Answer 2

You can use tuples as dictionary keys, they are hashable as long as their content is hashable (as @larsman said).

Don't worry about collisions, Python's dict takes care of it.

>>> hash('a')
12416037344
>>> hash(12416037344)
12416037344
>>> hash('a') == hash(12416037344)
True
>>> {'a': 'one', 12416037344: 'two'}
{'a': 'one', 12416037344: 'two'}

In this example I took a string and an integer. But it works the same with tuples. Just didn't have any idea how to find two tuples with identical hashes.