DigitMask | Topcoder Archive

Problem Statement

You will be given a list of patterns. Each pattern will contain only digits ('0'-'9'), question marks ('?'), and may potentially begin or end (but not both) with a hyphen ('-'). You must return the number of strings of length len that match all of the patterns. A digit must be matched with the same digit. A question mark can be matched with any digit. If the pattern ends with a hyphen, the pattern is describing a prefix. Similarly, if the pattern begins with a hyphen it describes a suffix. If there are no hyphens, the matched string must have the same length as the pattern. Said differently, a hyphen matches 0 or more digits.

Definition

Class:: DigitMask
Method:: howMany
Parameters:: String[], int
Returns:: int
Method signature:: int howMany(String[] patterns, int len)
(be sure your method is public)

Constraints

patterns will contain between 1 and 50 elements, inclusive.
Each element of patterns will contain between 1 and 50 characters, inclusive.
Each character in patterns will be a digit ('0'-'9'), a question mark ('?'), or a hyphen ('-');
Each element of patterns will contain at most 1 hyphen, and it must occur at the beginning or the end of the element.
len will be between 1 and 50, inclusive.
The return value will be between 0 and 1,000,000,000, inclusive.
No element of patterns will be "-" (quotes for clarity).

Examples

```
{"???"}
```
```
3
```
```
Returns: 1000
```
Every 3 digit string is possible.
```
{"9??","??7"}
```
```
3
```
```
Returns: 10
```
The first digit must be 9 and the last must be 7.
```
{"9??","??7"}
```
```
4
```
```
Returns: 0
```
The patterns say that the string must have length 3.
```
{"9??-","-???7"}
```
```
4
```
```
Returns: 100
```
The first pattern says the string begins with a 9 and has at least 3 digits. The second pattern says the string ends with a 7 and has at least 4 digits.

{
"??????????????????????????????????????????????????",
"?????????????????????????????????????????????????9",
"?????????????????????????????????????????????????8"
}

Returns: 0

```
{
"-?????"
}
```
```
4
```
```
Returns: 0
```

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