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# Turning Digit Soup into an Answer

We’ve got yet another problem to solve. We have many candidates for the last 12 digits of the barcode. In addition, we need to use the parities of the first six digits to figure out what the first digit is. Finally, we need to ensure that our answer’s check digit makes sense.

This seems quite challenging! We have a lot of uncertain data; what should we do? It’s reasonable to ask if we could perform a brute-force search. Given the candidates we saw in th preceding ghci session, how many combinations would we have to examine?

````ghci> ``product . map length . candidateDigits \$ input`
34012224
```

So much for that idea. Once again, we’ll initially focus on a subproblem that we know how to solve and postpone worrying about the rest.

## Solving for Check Digits in Parallel

Let’s abandon the idea of searching for now, and focus on computing a check digit. The check digit for a barcode can assume 1 of 12 possible values. For a given parity digit, which input sequences can cause that digit to be computed?

```-- file: ch12/Barcode.hs
type Map a = M.Map Digit [a]```

In this map, the key is a check digit, and the value is a sequence that evaluates to this check digit. We have two further map types based on this definition:

```-- file: ch12/Barcode.hs
type DigitMap = Map Digit
type ParityMap = Map (Parity Digit)```

We’ll generically refer to these as solution maps, because they show us the digit sequence that solves for each check digit.

Given a single digit, here’s how we can update an existing ...

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