Queueing With Friends

Question

You're with your best bud, Jim, at the amusement park and as your favorite ride comes into view, you and Jim exchange glances. Naturally you race to get in line. Unfortunately he wins because you're a golfer and he plays a real sport (sorry friends). In fact, you're so far behind that you and Jim are separated by x people. Assuming the line is length n and you're at the back and the line zigs and zags every j people, at what positions in the line will you and Jim be in the same column allowing you to chat (only one row apart)?

Input

3 Integers

• n - The length of the line. This number will always be greater than or equal to j and will be in the form y * j where y is a positive integer (the number of rows in the queue).
• j - The number of people in one row of the line (the number of columns in one row). This number will always be greater than 0.
• x - The number of people between you and Jim such that 0 <= x < 2j - 1. Hint: If this number is odd, then your output should be empty.

Output

A list of integer positions in the line at which Jim is in the same column as you.
_{¹ These integers can be 0 or 1-indexed as long as you specify in your answer.
² These integers can assume you start at position 0 or position n-1 as long as you specify in your answer.}

Example

In this example, the input would be n = 9, j = 3, x = 0. The output should be 2, 5 because your position is 2 or 5 when you're in the same column as Jim

Test Cases

[9, 3, 0] -> [2, 5]
[12, 3, 0] -> [2, 5, 8]
[9, 3, 1] -> []
[9, 3, 2] -> [1, 4]
[14, 7, 10] -> [1]
[24, 4, 6] -> [0, 4, 8, 12, 16]

Scoring

This is code-golf, so the shortest answer (in bytes) wins.

Answer 1

Python 2, 45 41 40 37 bytes

lambda n,j,x:range(j-x/2,x%2or n-x,j)

Pretty much the trivial solution. I just quickly scanned for patterns and found a pattern. 1-indexed, 1 is at the back of the queue.

-4 bytes by avoiding ternaries and using an array for the values instead
-1 byte thanks to some inspiration from @DeadPossum, by using and instead of ternaries or array selectors
-3 bytes by switching to or in the opposite order. Only works because of 1-indexing

Also, crossed out 4 is still 4 on all of the 4s :(

Try it online!

Answer 2

Pip, 22 21 bytes

20 bytes of code, +1 for -p flag.

c%2?lv-c/2+b*\,a/b-1

Takes n, j, and x as command-line arguments. 0-indexed, starting at position 0. Try it online!

Explanation

This is my original 22-byte version because it's a bit more understandable.

                       a, b, c are cmdline args; l is [] (implicit)
c%2?                   Test c mod 2
    l                  If it's 1 (truthy), return empty list; else:
                a/b-1  Number of rows in the queue minus 1
               ,       Range(^)
             b*        Multiply each element by b
     b-1-c/2+          Add (b-1)-c/2 to each element
                       Output in [1;2;3] format (implicit, -p flag)

The formula was obtained by observing the pattern for n=9, j=3:

x Output
0 [2;5]
2 [1;4]
4 [0;3]

If we take x/2 (0,1,2), subtract it from j-1 (2,1,0), and add that to [0;3], we get the correct result in all cases.

Answer 3

Java 8 lambda, 101 bytes

(n,j,x)->{int[]i=new int[n/j-1];int c=0,k=j-x/2;for(;k<n-x;k+=j)i[c++]=k;return x/2==0?i:new int[0];}

Almost-direct port of my Python answer. Range doesn't exist in Java though.

Answer 4

Haskell, 43 bytes

(n#j)x|odd$round x=[]|m<-j-x/2=[m,m+j..n-x]

Pretty much directly ported from the Python answer from HyperNeutrino

More well-formatted code:

f n j x |odd$round x = []
        |otherwise   = let m=j-x/2 in [m,m+j..n-x]

EDIT: Forgot to mention it was one-indexed

Answer 5

C# - 91 bytes

int[]r=new int[n/j-1];for(int i=1;i<n/j;i++){r[i-1]=i*j-x/2-1;}return(x%2==0)?r:new int[0];