What size is the digit?

Question

7-segment digits can be represented in ASCII using _| characters. Here are the size 1 digits:

   _  _       _   _   _   _   _   _ 
|  _| _| |_| |_  |_    | |_| |_| | |
| |_  _|   |  _| |_|   | |_|  _| |_|

Larger sizes are formed by making each segment proportionately longer. Here are a couple size 3 digits.

 ___    ___    ___    ___    ___    ___    ___ 
|   |  |          |  |          |  |   |  |   |
|   |  |          |  |          |  |   |  |   |
|___|  |___       |  |___    ___|  |   |  |___|
|   |  |   |      |      |      |  |   |      |
|   |  |   |      |      |      |  |   |      |
|___|  |___|      |   ___|   ___|  |___|   ___|

Goal

In this challenge, you are to write a program/function that can take a single digit as input and identify its size. The catch: if the input is not a valid digit, then your program should output 0.

This is code-golf, fewest bytes wins.

You can write either a program or a function, which can receive the digit either as STDIN or an argument, and print/return the value.

Digits will be provided as a multi-line string, padded with the minimal amount of trailing whitespace needed to make it a perfect rectangle. The trailing newline is an optional part of input. There will be no unneeded leading spaces.

When a non-digit is passed, it will still be comprised of _| characters, padded to a rectangle, and have no unneeded leading spaces. There will be no blank lines. You won't have to deal with empty input.

Output should be a single non-negative integer, with optional trailing newline. If the input is not a proper digit of any size, output 0. Else, output the size.

Here is a handy guide for the widths and heights of each digit for a given size N.

Digit  Height  Width (not counting newlines)
1      2N      1
2      2N+1    N+2
3      2N+1    N+1
4      2N      N+2
5      2N+1    N+2
6      2N+1    N+2
7      2N+1    N+1
8      2N+1    N+2
9      2N+1    N+2
0      2N+1    N+2

I/O Examples

In:

__ 
  |
__|
  |
__|

Out:

2

In:

|
|
|

Out:

0  //because it is of an invalid height.  Either 1 char too short or tall.

In:

|    |
|    |
|    |
|____|
     |
     |
     |
     |

Out:

4

In:

 ___ 
|    
|___ 
|   |
|___|

Out:

0 //1 char too wide

In:

 _ 
|_|
| |

Out:

0 //it's not a digit

In:

 __ 
|   
|__ 
   |
 __|

Out:

2

In:

 _  _ 
 _| _|
|_  _|

Out:

0  //both would be valid individually, but input should be a *single* digit

In:

 _ 
|_|
|_|

Out:

1

In:

|
|

Out:

1

In:

__|_
 |  
 _ |
  _ 
|__ 

Out:

0

---

This is approximately the inverse of Transform number into 7-segment display pattern, from 3 years back.

Answer 1

Ruby, 250

->x{d=y=0
x.size.downto(0){|n|y=n
a=["|
"*2*n]
"XNRDqpm@A".bytes{|z|p=[?|,' ','']
h=s=""
(n*2).times{|i|
i%n<1&&(d=z>>i/n*3&7)&&h=[?_,' '][d/3%2]*n
s=p[d%3]+h+p[d/6]+"
"+s
h=' '*n}
z!=68&&s=' '*(1-d%3/2)+?_*n+" 
"+s
a<<s};puts a
a.index(x)&&break}
y}

Given that there are so many possible invalid inputs, the only way to do this was to generate all the correct digits and check to see if the input matches.

I build each digit up from bottom to top, in 2 halves plus the top line. Although there are 12 possibilities (considering that the left segment can be on, off, or in the case of 3and 7completely absent) only 7 are actually present and careful choice of encoding enables all info (except the top line) to be encoded into a single character.

the digit 1 doesn't really fit the pattern and is handled separately, being used to initialize the array.

Ungolfed in test program

This version uses . instead of spaces for diagnostic reasons.

#Encoding used for half-digits (radix 3,2,2 most significant digit at right)

#000    |_|  0

#100    ._|  1  . = space

#200    X_|  2  X = no space (for digits 3 and 7)  

#010    |.|  3

#110    ..|  4

#210    X.|  5

#001    |_.  6


f=->x{d=y=0                                        #d and y required to be intialized for scoping reasons
  x.size.downto(0){|n|y=n                          #Assume max possible size of character = length of input and iterate down through all possible sizes n   
    a=["|\n"*2*n]                                  #Make an array containing the digit 1 (different shape to others)
    "XNRDqpm@A".bytes{|z|                          #Each character encodes the pattern for a digit. Iterate through them
      p=['|','.','']                               #Possible components for left and right of digit
      h=s=""                                       #h initialized for scoping reasons. s will contain the digit string 
      (n*2).times{|i|                              #For each row
        i%n<1&&                                    #If i%n==1 we are at the bottom of a half digit
        (d=z>>i/n*3&7)&&                           #so extract info from z and store in d
        h=[?_,'.'][d/3%2]*n                        #h is the horizontal part of the half digit, either _ or spaces 
        s=p[d%3]+h+p[d/6]+"\n"+s                   #Build one row of digit, working upwards: left,middle,right
        h='.'*n                                    #If row i%n!=0 (not bottom row of half digit)the middle section must contain spaces
      }                                            #We now have both halves of the digit, only the top segment missing 
      z!=68&&s='.'*(1-d%3/2)+?_*n+".\n"+s          #If z!=68 (digit 4) add a top to the digit, with appropriate leading and trailing spaces        
      a<<s                                         #Add the completed digit of size n to a
    }
    #puts a                                        #Diagnostic: uncomment to print all the strings checked
    a.index(x)&&break                              #If string x is in a, break

  }
y                                                  #and return last value of n 
}


# digit 7, size 2. Trailing newline required. Outputs 2
puts f[
"__.
..|
..|
..|
..|
"]