# Python Sequence elements comparison

I have these two functions:

```def comparison(a, b):
return [-1, 0, 1].index(cmp(b, a))

def base_3(seq):
return [comparison(a, b) for a, b in itertools.combinations(seq, 2)]
```

The function comparison returns a comparison number based on this:

1. 0 if a > b
2. 1 if a = b
3. 2 if a < b

The function base_3 returns the comparison among all combined elements.

For instance:

```x = [0, 1, 2]
y = [1, 2, 0]
z = [0, 1, 0]

>>> base_3(x)
[2, 2, 2]

>>> base_3(y)
[2, 0, 0]

>>> base_3(z)
[2, 1, 0]
```

I need a function that return a sequence from a given base_3, when possible:

```>>> base_3_to_seq([2, 2, 2])
[0, 1, 2]

>>> base_3_to_seq([2, 1, 0])
[0, 1, 0]

>>> base_3_to_seq([0, 2, 1])
"Impossible"
```

How can I write this function base_3_to_seq?

## Answers

This is a brute force way:

```def base_3_to_seq(base3):
for seq in itertools.product(range(3), repeat=3):
if base_3(seq) == base3:
return seq
return "Impossible"
```

Depending upon which way you're calling it most, you could speed the code up for long runs by memoizing either base_3 or base_3_to_seq.

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