This is a fairly simple question in concept. Shouldn't be too hard to make a simple program for - the tricky part is finding how to shave off those extra characters. Good luck! ## Task Input is a string of indeterminate length, composed of any number of eight characters; [ ⭢⭠⭡⭣⭧⭨⭦⭩ ] For a pointer starting at (0,0) on a Cartesian plane, of the form (X, Y), below is the list of what each of the arrows will do to the pointer. |Input | Hex Value | Action | Cartesian| |:-:|:-:| :-- |:-:| |⭠|0x2b60| X decreases by 1.|(-1,0) |⭡|0x2b61| Y increases by 1.|(0,+1)| |⭢|0x2b62| X increases by 1.|(+1,0)| |⭣|0x2b63| Y decreases by 1.|(0,-1)| |⭦|0x2b66| Perform ⭡ and ⭠.|(-1,+1)| |⭧|0x2b67| Perform ⭡ and ⭢.|(+1,+1)| |⭨|0x2b68| Perform ⭣ and ⭢.|(+1,-1)| |⭩|0x2b69| Perform ⭣ and ⭠.|(-1,-1)| The output should print where this pointer ends up. ## Sample Test Cases | Input | Output| | :-: | :-: | |⭠⭠⭣⭧⭨⭢⭢⭩⭡ | (1,-1)| |⭡⭣⭨⭨⭦⭩⭦⭩⭩⭠⭡⭡ | (-4,-1)| |⭡⭡⭡ | (0,3)| | [blank string] | (0,0) |

# [APL (Dyalog Unicode)], 28 bytes ([SBCS]) [SBCS]:https://github.com/abrudz/SBCS +/∘×9 11∘.○0j¯1*.5⊥7 10⊤⎕UCS [Try it online!][TIO-k69z6lrw] [APL (Dyalog Unicode)]: https://www.dyalog.com/ [TIO-k69z6lrw]: https://tio.run/##SyzI0U2pTMzJT///X1v/UceMw9MtFQwNgQy9R9O7DbIOrTfU0jN91LXUXMHQ4FHXkkd9U0Odg/@nPWqb8Ki3D8jz9H/U1XxovfGjtolAXnCQM5AM8fAEKlFQf7R2waO1Cx@tXfRo7eJHa5c9Wrv80doVj9auVOeCSS4Ay0CEF4HRSqAOdQWFR71zFQwVgLZDlC4Eq1sBRsvAiiDkSpgVMD2H1pug6EKSMlAwBgnDeQYA "APL (Dyalog Unicode) – Try It Online" ### How it works First, observe that the decimal values have a pattern: | Input | Hex value | Decimal value | `a=(n/10)%7` | `b=n%10` | `c=a/2+b` | `(-i)**c` | | :-: | :-: | :-: | :-: | :-: | :-: | :-: | | ⭠ | 0x2b60 | 11104 | 4 | 4 | 6 | $-1$ | | ⭡ | 0x2b61 | 11105 | 4 | 5 | 7 | $i$ | | ⭢ | 0x2b62 | 11106 | 4 | 6 | 8 | $1$ | | ⭣ | 0x2b63 | 11107 | 4 | 7 | 9 | $-i$ | | ⭦ | 0x2b66 | 11110 | 5 | 0 | 2.5 | $(-1+i)/\sqrt2$ | | ⭧ | 0x2b67 | 11111 | 5 | 1 | 3.5 | $(1+i)/\sqrt2$ | | ⭨ | 0x2b68 | 11112 | 5 | 2 | 4.5 | $(1-i)/\sqrt2$ | | ⭩ | 0x2b69 | 11113 | 5 | 3 | 5.5 | $(-1-i)/\sqrt2$ | If we represent the movements with a complex number, we can see that clockwise rotation (power of `-i`) on ⭠ and ⭦ gives the other arrows in the respective group. And ⭦ can also be derived from ⭠ by 45° rotation followed by scaling. +/∘×9 11∘.○0j¯1*.5⊥7 10⊤⎕UCS ⎕UCS ⍝ Convert to Unicode codepoints 7 10⊤ ⍝ a=(n/10)%7 and b=n%10 for each n .5⊥ ⍝ .5×a+b for each n 0j¯1* ⍝ Power of -i 9 11∘.○ ⍝ Extract real and imaginary parts × ⍝ Signum of each number; effectively scale 45deg-rotations +/∘ ⍝ Sum of real and imaginary part respectively

# [Golfscript](https://http://www.golfscript.com/), ~~71 bytes~~ 58 bytes Line breaks are stylistic and for readability, they do not contribute to character count. ~~This is not a particularly elegant solution, but it works and is likely very shrinkable.~~ Shrunk by 13 characters using a rotating array. My guess is a nested block loop that can somehow generate these particular arrays without needing to spell them out. ~~In a perfect world, you wouldn't need to duplicate the original array, meaning we could cut out the whole third line and another few characters.~~ Kinda half-done. Still wanna get rid of the loop, I think this can be brought down to 40 characters. Will continue optimizing - just wanted to get a concrete solution out. ~~One character can be shaved by swapping the order of the arrays, but it's less clear, and I'd like it to be clear until I've golfed it much lower.~~ This is no longer true. ``` 2\+.[-1 1 1 -1 -1 0 1 0]:a; {10%a\=+}*\ {10%a(+\=+}* {50-\}2* ``` Explanation; ``` 2\+. # Put an ASCII 50 at the start of the given array. [-1 1 1 -1 -1 0 1 0]:a; # Remember this encoding of directionality for later. { # Open a block (X encoding) 10% # Mod the arrows by 10 a\= # Check that number against a, as the index + # Add it to our running tally at the front (to the 50) }* # Do this to every element in the array, iterating, # and pumping out a value. This is a bit tricky to # explain, but in essence, this is a weird workaround # the usual loop command, since that loop outputs # a bunch of non-arrayed elements, which we can't # handle effectively. This lets us output one number # (The sum of them all), but skips the first element. # This is why we added 2 at the beginning, since it's # read as ASCII 50. We subtract that later. \ # Take our duplicated string {10%a(+\=+}* # Repeat the previous process with the Y array. {50-\}2* # Take away that pesky 50 from the sum of both indices ``` Then our stack is X, Y, which gets automatically outputted. This is more elegant that my previous solution, but the array itself takes a lot of space, and I'd like to shorten it.

# LuaTeX, ~~191~~ 190 bytes This is just a simple switch cases answer. The string should be delimited by `~` on the left and `⭤` (U+2b64) on the right end. Function definition: ```tex \def~#1{\catcode`#1"D}~:~;~.~,~|\let|\def\let:\newcount:.:,|:{\advance.}|;{\advance,}|~#1{\ifcase\numexpr`#1-`⭠:-1|;1|:1|;-1|\2||:-1;1|:1;1|:1;-1|:-1;-1\fi~}|\2#1~{ \fi\the. \the,}\let|\or ``` Complete script: ```tex \def~#1{\catcode`#1"D}~:~;~.~,~|\let|\def\let:\newcount:.:,|:{\advance.}|;{\advance,}|~#1{\ifcase\numexpr`#1-`⭠:-1|;1|:1|;-1|\2||:-1;1|:1;1|:1;-1|:-1;-1\fi~}|\2#1~{ \fi\the. \the,}\let|\or ~⭠⭠⭣⭧⭨⭢⭢⭩⭡⭤ .0,0%reset counters ~⭡⭣⭨⭨⭦⭩⭦⭩⭩⭠⭡⭡⭤ .0,0%reset counters ~⭡⭡⭡⭤ .0,0%reset counters ~⭤ \bye ``` Output (as PDF): ![cg_directions2.png](/image?hash=69177df5a63fe41f9d5f2290d1806e7478e6397231dace9aed1045af934e5219)

# [Jelly], 19 bytes Od⁵%7H+ɗ/ı-*)ÆiṠSṁ2 [Try it online!][TIO-khqk820w] [Jelly]: https://github.com/DennisMitchell/jelly [TIO-khqk820w]: https://tio.run/##y0rNyan8/98/5VHjVlVzD@2T0/WPbNTV0jzclvlw54Lghzsbjf7///9o7cJHaxc/WrsCjJY9WrsSRgLRArDsQgA "Jelly – Try It Online" **Translation of Bubbler's amazing APL answer.** ## Explanation Od⁵%7H+ɗ/ı-*ÆiṠ)Sṁ2 Main monadic link ) Map over each character O Codepoint d⁵ Divmod 10 / Fold over ɗ ( %7 Left argument modulo 7 H Halve + Add right argument ɗ ) ı-* -i to the power Æi List of real and imaginary part Ṡ Sign S Sum ṁ2 Reshape to have 2 elements