Quadrants passed through by a line

Question

Task

Given a representation of a line, output the number of quadrants that that line passes through.

Valid Representations of a Line

You can represent a line as

• Three signed integers A, B, and C which share no common factor and where A and B are not both zero, representing the line Ax + By = C,
• Four signed integers X1, Y1, X2, and Y2, representing the line passing through the points (X1, Y1) and (X2, Y2), or
• A data type that describes a line, if your language has one (it must support vertical lines).

You may not take input in any format that does not allow for a vertical line (e.g. slope-intercept form). If you choose to take integers as input, you can assume that they lie in the inclusive range [-127, 128].

Specifications

• The output will always be 0, 2, or 3 (a line can never pass through all four quadrants, nor can it pass through only a single one).
• A line on an axis is considered not to pass through any quadrants. A line through the origin is considered to only pass through 2 quadrants.
• You do not have to return which quadrants are being passed through (though the test cases include them for clarity).
• This is code-golf, so the shortest valid answer (measured in bytes) wins.

Test Cases

You will have to convert these to a suitable format before using them.

1x + 1y = 1   ->  3  (quadrants I, II, and IV)
-2x + 3y = 1  ->  3  (quadrants I, II, and III)
2x + -3y = 0  ->  2  (quadrants III and I)
1x + 1y = 0   ->  2  (quadrants II and IV)
3x + 0y = 6   ->  2  (quadrants I and IV)
-3x + 0y = 5  ->  2  (quadrants II and III)
0x + -8y = 4  ->  2  (quadrants III and IV)
0x + 1y = 0   ->  0  (lies on the x-axis)
1x + 0y = 0   ->  0  (lies on the y-axis)

Answer 1

Python 3, 24 bytes

lambda a:3<<a.count(0)&3

Try it online!

Answer 2

Jelly, 5 bytes

TL’ȧ$

Try it online!

• -1 byte thanks to Challenger5
• -1 byte thanks to Leaky Nun
• -2 bytes thanks to H.PWiz

No longer based off Leaky's answer!

Answer 3

Javascript (ES6), 30 24 22 bytes

This is my first time trying to golf in Javascript. There's gotta be a better way to count zeros...

(a,b,c)=>3<<!a+!b+!c&3

-6 bytes thanks to Herman Lauenstein, -2 bytes to remembering operator precedences.

Alternate 24-bytes solution to return a string instead:

(a,b,c)=>"320"[!a+!b+!c]

Answer 4

05AB1E, 6 bytes

Ƶܹ0¢è

Try it online!

Based on Leaky Nun's answer.

Answer 5

SOGL V0.12, 8 bytes

0233{.‽X

Try it Here!

Based off Leaky Nun's answer.

Answer 6

GolfScript, 16 14 bytes

~{!!}%{+}*.1>*

Try it online!

• @Challenger5 -2 bytes

This program takes an array of 3 integers representing the coefficients in the equation Ax + By = C

Example Input/Output

[1 1 1]   -> 3
[-2 3 1]  -> 3

How it Works

~                       - Eval string (input)
  {  }%                 - Map to array
   !!                   - Double not (equivalent to != 0)
        {+}*            - total array (fold addition)
            .           - Duplicate top of stack
             1>         - Greater than 1?
               *        - Multiply     

This was a little tricky at first for me to figure out a mathematical way to calculate this. However there are only 8 possible configurations such that a != 0 & b != 0 & c != 0

0 0 0 = 0
a 0 0 = 0
0 b 0 = 0
0 0 c = 0
a 0 c = 2
0 b c = 2
a b 0 = 2
a b c = 3

I eventually came to the following function.

F(a,b,c) {
    var r = sign(a)+sign(b)+sign(c);
    if(r > 1)
        r;
    else
        return 0;
}

and the whole thing can be condensed to a single math problem

F(a,b,c) {
    return (sign(a)+sign(b)+sign(c)) * (sign(a)+sign(b)+sign(c) > 1);
}

Answer 7

Retina, 13 bytes

M`\b0
T`d`320

Try it online

Also based on Leaky Nun's answer.

Answer 8

JavaScript, 25 bytes

_=>3<<!_[0]+!_[1]+!_[2]&3

Based off Leaky Nun's answer.

Answer 9

Haskell, 22 bytes

f l="320"!!sum[1|0<-l]

Try it online!

Point-free solution, 27 bytes

("320"!!).(\l->sum[1|0<-l])

Try it online!

Answer 10

Perl 6, 18 bytes

{3+<@_.grep(0)+&3}

Answer 11

ABCR, 30 bytes

Input is in the form A,B,C where the commas can be replaced by any non-numeric, non-- character.

BBi7baxci7baxci7bax@7)A7(xxo

No online interpreter yet, but here's an explanation:

BB                                Add two values to the B queue. (Values are unimportant)
  i7 ax                           Read in a number.  If it's non-zero...
    b                             Dequeue one item from the B queue.
       c                          Read in the delimiter...
        i                         ... And promptly overwrite it with the next number.
         7baxci7bax               Repeat the whole "if 0, dequeue from B" for the
                                     other two input numbers.
                   @              Get the current length of the B queue. [2, 1, or 0]
                    7             If the length isn't 0...
                     )            ... Increment it to our required [3,2,0]
                      A           ... And enqueue it to A.
                                  (We don't need to add to A otherwise, because it defaults
                                    to 0 already if there's no value in it.
                                    I used that to exit the queue with 7_ax earlier.)
                       7(xx       Set the register to 0 to exit from loop.
                           o      Peek A and print as a number.

Answer 12

APL (Dyalog Unicode), 14 11 bytes

0⌈3-×⍨+/0=⎕

Try it online!

⎕IO is 0. Thanks to @Adám for -3 bytes!

Answer 13

Deorst, 12 bytes

l0EN))A:k?Z+

Try it online!

Somewhat based off Leaky's answer; uses the same premise, but a different mapping method.

How it works

Deorst has a count occurrences builtin, but doesn't (for some reason) have an indexing command, so I had to create the following mapping, where the left is a.count(0) and the right is the wanted result

0 -> 3
1 -> 2
2 -> 0

The program itself works like this (example input of [1,1,1])

l0           - Push 0;     STACK = [[1 1 1] 0]
  EN         - Count;      STACK = [0]
    ))       - Subtract 2; STACK = [-2]
      A      - Absolute;   STACK = [2]
       :     - Duplicate;  STACK = [2 2]
        k?Z  - Positive?;  STACK = [2 1]
           + - Sum;        STACK = [3]

Answer 14

Add++, 23 bytes

D,f,@@@,!$!@!s2$_|d0$>+

Try it online!

Based off both my Deorst answer and Leaky's Python answer

How it works

D,f,@@@,  - Create a triadic function. 
            Example arguments;   [1 1 1]
        ! - Logical NOT; STACK = [1 1 0]
        $ - Swap;        STACK = [1 0 1]
        ! - Logical NOT; STACK = [1 0 0]
        @ - Reverse;     STACK = [0 0 1]
        ! - Logical NOT; STACK = [0 0 0]
        s - Sum;         STACK = [0]
        2 - Push 2;      STACK = [0 2]
        $ - Swap;        STACK = [2 0]
        _ - Subtract;    STACK = [-2]
        | - Absolute;    STACK = [2]
        d - Duplicate;   STACK = [2 2]
        0 - Push 0;      STACK = [2 2 0]
        $ - Swap;        STACK = [2 0 2]
        > - Greater to;  STACK = [2 1]
        + - Sum;         STACK = [3]

However, I think I've been using functions too much in Add++, rather than the main code body. So I attempted to do this using both functions, and the code body, and resulted in a much nicer 50 byte piece (yes, that is the longest answer here):

# Example input: 1 1 1;
# x and y are the accumulators

D,f,@@@,!$!@!s # Count the 0s
$f>?>?>?       # Call f with the input.
-2   # Subtract 2;    x: -2;  y: 0
^2   # Square;        x: 4;   y: 0
S    # Square root;   x: 2.0; y: 0
\1   # To integer;    x: 2;   y: 0
y:x  # Assign x to y; x: 2;   y: 2
}    # Switch to y;   x: 2;   y: 2
>0   # Is positive?;  x: 2;   y: 1
}    # Switch to x;   x: 2;   y: 1
+y   # Add y to x;    x: 3;   y: 1
O    # Print x

Try it online!