Orthodiagonal steps

Question

It's a common problem to navigate in a 2D matrix. We've seen it many times and will see again. So let's help future us and develop the shortest solutions to generate all eight possible steps in a 2D matrix.

Challenge

Your code must output the following 8 pairs of -1,0,1 in any order:

(0,1)
(0,-1)
(1,0)
(-1,0)
(1,1)
(1,-1)
(-1,1)
(-1,-1)

Rules

1. There is no input.
2. Output order is not relevant
3. Output is flexible. Pairs of numbers just need to be distinguishable
4. This is code-golf, so shortest answer in bytes wins

Answer 1

Octave, 24 bytes

dec2base([0:3,5:8],3)-49

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I haven't seen this approach yet.

Creates a list of integers [0, 1, 2, 3, 5, 6, 7, 8], and converts it to ternary, returning a character array:

00
01
02
10
12
20
21
22

Subtracting 49 (ASCII-value for 1) from all characters gives a numeric array:

-1  -1
-1   0
-1   1
 0  -1
 0   1
 1  -1
 1   0
 1   1

Answer 2

T-SQL, 80 78 bytes

SELECT-1n INTO t;INSERT t VALUES(0),(1)SELECT*FROM t,t z WHERE t.n<>0OR z.n<>0

Creates a (permanent) table t containing (-1,0,1), and performs a self-join with a WHERE clause that excludes the 0,0 row. The table t is not cleaned up by my code, you must drop it yourself.

Sadly nearly twice as long as the boring solution (44 bytes), since SQL allows returns in strings:

PRINT'0,1
0,-1
1,0
-1,0
1,1
1,-1
-1,1
-1,-1'

Answer 3

Pure Bash (no external utilities), 36

a=({0,-1,1},{0,-1,1})
echo ${a[@]:1}

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---

Bash with Sed, 35

printf %s\\n {-1..1},{-1..1}|sed 5d

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Answer 4

R, 26 24 bytes

Credits to @JDoe for saving two more bytes with a direct approach:

paste(-1:1,-3:5%/%3)[-5]

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The original asnwer:

outer(-1:1,-1:1,paste)[-5]

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Or for 27 bytes

sapply(-1:1,paste,-1:1)[-5]

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Or for 34 bytes with factors:

(gl(3,3,,-1:1):gl(3,1,9,-1:1))[-5]

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This last solution might be the golfiest if the output could be from 1 to 3 rather than from -1 to 1.

See the other R answer for alternate solutions with expand.grid or with cbind.

Answer 5

Jelly, 8 7 6 bytes

3p_2ẸƇ

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My first ever Jelly answer! Much thanks to Dennis for the final piece of the puzzle.

Now, let's see if I can explain it ... lol.

3p_2ẸƇ   Main program, takes no input.
3p       Product with Range 3, yields [[1,1], [1,2], [1,3], [2,1], [2,2], ...]
  _2     Decrement twice, vectorizes, yields [[-1,-1], [-1,0], [-1,1], [0,-1], ...]
    ẸƇ   Comb, removes those that contain only falsey values, the [0,0]
         Implicit output

-1 byte thanks to Erik; -1 byte thanks to Mr Xcoder and Dennis

Answer 6

Python 2, 33 bytes

i=9;exec"print-i%3-1,i/5;i-=2;"*8

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Dennis saved 3 5 bytes, wow. Thanks!

Answer 7

Haskell, 22 bytes

_:l=mapM(:[1,-1])[0,0]

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Laikoni saved 1 byte.

Answer 8

Japt -Q, 15 13 bytes

I'm sure there's a shorter way, but I liked this approach.

##ü80ì3 mÉ ò
##ü80        // Take 14425280
     ì3      // and turn it into an array of base-3 numbers.
        mÉ   // Subtract one from each digit
           ò // and then split them pairwise.

Shaved off two bytes thanks to Shaggy.

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Answer 9

Japt, 13 12 11 bytes

Saved a byte thanks to @Shaggy

9ó8_ìJõ é)Å

Try it online! Uses -R flag to put each item on its own line.

Explanation

9ó8_ìJõ é)Å
9ó8             Create the range [9, 9+8). [9, 10, ..., 16]
   _            Map each item in this range through this function:
     Jõ é)        Generate the range [-1...1] and rotate to get [1, -1, 0].
    ì             Convert the item to an array of base-3 digits,
                  mapping [0,1,2] to [1,-1,0]. [[-1, 1, 1], [-1, 1,-1], [-1, 1, 0],
                                                [-1,-1, 1], [-1,-1,-1], [-1,-1, 0],
                                                [-1, 0, 1], [-1, 0,-1]]
          Å       Remove the first item (gets rid of the leading -1).

Answer 10

Java 8, 83 42 bytes

v->"1,1 1,0 1,-1 0,1 0,-1 -1,1 -1,0 -1,-1"

-41 bytes thanks to @AdmBorkBork by hard-coding..

Try it online.

---

Non hard-coded version as reference (83 72 70 68 bytes):

v->{for(int i=9;i-->1;)System.out.println(~i%3+1+","+(~(i/3)%3+1));}

-11 bytes thanks to @OlivierGrégoire.
-2 bytes creating a port of @ETHproductions's JavaScript (ES6) answer.

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Answer 11

Perl 6, 23 bytes

{(1,-1,0 X 1,-1,0)[^8]}

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Answer 12

05AB1E, 8 7 bytes

2Ý<ãʒĀZ

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Explanation

2Ý<     # Range of 2 decremented, yields [-1, 0, 1]
   ã    # Cartesian product of the list with itself
    ʒ   # Filter by ...
     ĀZ # Maximum of the truthified values, yields 0 only if both values are 0.

-1 byte thanks to Emigna !

Answer 13

Husk, 7 6 bytes

There are a lot of different ways (the tricky/costly part is getting rid of [0,0]), 7 bytes is the shortest I could come up thanks to Leo for pointing out to use decimal conversion (d) as a filter:

fdπ2ṡ1

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Explanation

fdπ2ṡ1  -- constant function (expects no arguments)
    ṡ1  -- symmetric range [-n..n]: [-1,0,1]
  π2    -- cartesian power of 2: [[-1,-1],[-1,0],[0,-1],[-1,1],[0,0],[1,-1],[0,1],[1,0],[1,1]]
f       -- filter only elements that are truthy when
 d      -- | decimal conversion (interpret as polynomial and evaluate at x=10)
        -- : [[-1,-1],[-1,0],[0,-1],[-1,1],[1,-1],[0,1],[1,0],[1,1]]

---

Alternative, 7 bytes

tπ2ṙ1ṡ1

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Explanation

tπ2ṙ1ṡ1  -- constant function (expects no arguments)
     ṡ1  -- symmetric range [-n..n]: [-1,0,1]
   ṙ1    -- rotate by 1: [0,1,-1]
 π2      -- cartesian power of 2: [[0,0],[0,1],[1,0],[0,-1],[1,1],[-1,0],[1,-1],[-1,1],[-1,-1]]
t        -- tail: [[0,1],[1,0],[0,-1],[1,1],[-1,0],[1,-1],[-1,1],[-1,-1]]

Answer 14

MATL, 12 bytes

9:q4X-3YA49-

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Because it's MATL month, here's a MATL port of @Stewie's Octave answer. The sequence [0 1 2 3 5 6 7 8] is generated as the set difference between [0 ... 8] and 4.

Answer 15

R, 27 bytes

expand.grid(-1:1,-1:1)[-5,]

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30 and 35 bytes:

cbind(-1:1,rep(-1:1,e=3))[-5,]
expand.grid(rep(list(-1:1),2))[-5,]

Answer 16

Haskell, 28 27 bytes

tail.mapM id$[0,1,-1]<$"ao"

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Answer 17

JavaScript (ES6)

Two alternate methods, both longer than hardcoding.

49 bytes

_=>[...'11202200'].map((n,i,a)=>[~-n,~-a[i+3&7]])

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51 bytes

f=(n=1679887e3)=>n?[n%4-1,~-(n/4%4)]+' '+f(n>>4):''

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Answer 18

Haskell, 27 bytes

tail$(,)<$>t<*>t
t=[0,1,-1]

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The output is [(0,1),(0,-1),(1,0),(1,1),(1,-1),(-1,0),(-1,1),(-1,-1)].

Answer 19

PowerShell, 41 bytes

(1..-1|%{$i=$_;1..-1|%{"$i,$_"}})-ne'0,0'

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Double-for loop over the range 1..-1, with a -notequals at the end to pull out the extraneous 0,0 entry. They're each individually left on the pipeline and implicit Write-output at program completion gives us newlines for free.

---

Sadly, just the barebones string output is two bytes shorter:

'1,1
1,0
1,-1
0,1
0,-1
-1,1
-1,0
-1,-1'

But that's boring.

Answer 20

Perl 5, 31 bytes

map/1/&&say,<{-1,0,1},{-1,0,1}>

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Answer 21

CJam, 13 bytes

3,:(2m*{2b},`

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Explanation

3,    e# Range [0,3):       [0 1 2]
:(    e# Decrement each:    [-1 0 1]
2m*   e# Cartesian square:  [[-1 -1] [-1 0] [-1 1] [0 -1] [0 0] [0 1] [1 -1] [1 0] [1 1]]
{     e# Filter by
 2b   e#   conversion to binary:
},    e#                    [[-1 -1] [-1 0] [-1 1] [0 -1] [0 1] [1 -1] [1 0] [1 1]]
`     e# Stringify:         "[[-1 -1] [-1 0] [-1 1] [0 -1] [0 1] [1 -1] [1 0] [1 1]]"

Answer 22

Python 2, 39 bytes

n=6;exec'n+=~(n==2);print n/3,n%3-1;'*8

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Answer 23

J, 18 16 bytes

echo}.,{;~0 1 _1

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Answer 24

F# (Mono), 54 bytes

let f=Seq.where((<>)(0,0))(Seq.allPairs[-1..1][-1..1])

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44 bytes - thanks to Laikoni:

let f=Seq.tail(Seq.allPairs[0;-1;1][0;-1;1])

Answer 25

Befunge-93, 24 bytes

11#v91090~9~19~<
9.._@#,

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I feel like this challenge is missing answers from 2D languages, even if most don't move diagonally. This outputs space separated numbers, each pair separated by tabs.

Answer 26

Brachylog, 8 bytes

Ċ{ṡᵐ≜}ᶠb

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Explanation

Ċ           Couple: take a list of two elements [A,B]
 {   }ᶠ     Find all…
    ≜         …possible values of…
  ṡᵐ          …signs of A and B
       b    Behead: remove the first one which is [0,0]

Answer 27

Bash, 30 bytes

echo "
"{-1..1},{-1..1}|grep 1

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Prints a trailing space on each line but the last. (Thanks to @Neil - this originally printed a leading space, but a trailing space is better as per their comment)

Answer 28

MATL, 12 bytes

3:qq2Z^[]5Y(

Try it at MATL Online!

My first ever serious MATL answer! Thanks a lot to Luis Mendo, Sanchises and DJMcMayhem for the help.

How it works

3:qq2Z^[]5Y( – Full program. Outputs to STDOUT.
3:           – Range 3. Push [1 2 3] to the stack.
  qq         – Decrement by 2. Yields [-1 0 1].
    2Z^      – Cartesian power of 2.
         5Y( – Replace the row at index 5 with...
       []    – An empty vector.

Answer 29

Batch, 77 bytes

@for %%x in (-1 0 1)do @for %%y in (-1 0 1)do @if not %%x%%y==00 echo %%x %%y

63 bytes if a nonstandard separator is allowed:

@for %%x in (-1/-1 -1/0 -1/1 0/-1 0/1 1/-1 1/0 1/1)do @echo %%x

Answer 30

Jelly, 6 bytes

;Ø+p`Ḋ

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-1 thanks to Dennis.

Answer 31

Pyth, 11 9 bytes

t^+U2_1 2

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Explanation

t^+U2_1 2
  +U2_1     [0, 1, -1]
 ^      2   Product with itself.
t           Exclude the first.

Equivalently, we could use t*J+U2_1J, but that's not any shorter.

Answer 32

JavaScript (ES6), 45 bytes

f=(n=8)=>n?[...f(n-1),[1+~n%3,1+~(n/3)%3]]:[]

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Another alternative to hardcoding, still not as short though...

Answer 33

Japt, 14 13 bytes

[J1T]ê à2 s1J

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Answer 34

Stax, 10 bytes

τÄêdD┘│çû╢

Run and debug it

Explanation (unpacked):

1:r2|^{|af|u Full program
1:r          Push [-1, 0, 1]
   2|^       Join with self
   c|*        Alternative: copy and join
      {  f   Filter:
       |a      Any truthy (not 0)?
          |u Representation

Answer 35

PHP, 79, 76, 73 Bytes

76 Bytes thanks to Dom Hastings

Try it online (79 Bytes) using base 16 (Original answer)

Try it online (77 Bytes) using base 36

Try it online (73 Bytes) using base 36

Tried to avoid any kind of loop

<?=strtr(chunk_split(base_convert("18qfremyq6",36,4),3,"
"),[2=>-1,',']);
//as the starting index is 2, next will be 3, no need for 3=>','

Output

1,0
-1,0
1,1
1,-1
-1,1
-1,-1
0,1
0,-1

Explanation

Basically "72c75eb6e34e" 18qfremyq6 is the base 16 36 representation of a base 4 number 130230131132231232031032, every 3 represents a "," and 2 a -1

Chunk split, adds a line break every 3 characters.

Shorter with an output without the comma, 79 Bytes

<?=strtr(chunk_split(base_convert("10fcb5c",16,3),2,"
"),[2=>-1]);

Output

10
-10
11
1-1
-11
-1-1
01
0-1

Answer 36

Gaia, 8 bytes

3…(¦:×ỵ⁈

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This generates the list in this order:

[[-1 -1] [-1 0] [-1 1] [0 -1] [0 1] [1 -1] [1 0] [1 1]]

Explanation

3…(¦:×ỵ⁈ – Full program. Outputs to STDOUT.
3…       – Push [0 1 2] to the stack.
  (¦     – Decrement each; yields [-1 0 1].
    :    – Duplicate.
     ×   – Cartesian product.
       ⁈ – Filter-reject those that:
      ỵ  – Have no truthy element.

An alternative to this would be 3…(¦2*ỵ⁈.

Answer 37

Japt, 9 7 bytes

4 Japt solutions to one challenge; that has to be a first :)

Jõ ï fd

Test it

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Original, 9 bytes

4#ô²ìJõ)ò

Test it

---

Explanation

Using the number Nit found for his solution (14425280) as a starting point, I converted it to base-3, split it to an array of 2 character strings and then tested each permutation to see if any of them produced a perfect square or cube when rejoined to a string and converted back to base-10. That gave me the perfect squares 15366400, 18011536 & 18421264 and, of those, only 18011536 had a square root that would allow me to save a byte thanks to Japt's trick of using # to build numbers, that being 4244.

4#ô           :4244
   ²          :Square
     Jõ       :Array [-1,0,1]
    ì  )      :Convert to a digit array in that base
        ò     :Split on every second element

Answer 38

Ruby, 40 bytes

([*-1..1]*2).permutation(2).uniq-[[0,0]]

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Answer 39

K (ngn/k), 15 bytes

{(+1-!x#3)^,&x}

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 x:2 / for testing
 x#3 / that many 3s
3 3
 !x#3 / all vectors of 0 1 2 as the columns of a matrix
(0 0 0 1 1 1 2 2 2
 0 1 2 0 1 2 0 1 2)
 +!x#3 / transpose
(0 0
 0 1
 0 2
 1 0
 1 1
 1 2
 2 0
 2 1
 2 2)
 &x / that many 0s
0 0
 (+!x#3)^,&x / remove the all-zero vector
(0 1
 0 2
 1 0
 1 1
 1 2
 2 0
 2 1
 2 2)

Answer 40

Wolfram Language (Mathematica), 29 bytes

Print@Rest@Tuples[{0,1,-1},2]

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Answer 41

JavaScript (Node.js), 42 bytes

_=>`1,1
1,0
1,-1
0,1
0,-1
-1,1
-1,0
-1,-1`

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Explanation :

Does nothing basically no input and prints the string separated by new lines using string literal.

Answer 42

Retina, 24 bytes

K`_ _
_
_$"0
+0`_
1$%"-1

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Answer 43

GolfScript, 26 19 18 bytes

9,[4]-{.3/(\3%(n}/

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My first GolfScript submission, any help is appreciated! Outputs one element per line, and removes the 0, 0 element.

For nicer printing, I found this 20 byte solution:

9,[4]-{[.3/(\3%(]p}%

which prints one array per line.

Answer 44

brainfuck, 86 bytes

+[[<+>->->>---<<<]>]>---.>.<.>.<-.+.>.-.<-.>.+.<.>..<.+.>..<-.>.<+.>.<-.>.-.<.>.<+.>+.

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Prints pairs of numbers separated by commas.

Answer 45

JavaScript (Most browsers), 42 40 bytes

for(x=9;x;)--x-4&&alert([~(-x/3),x%3-1])

Only works in DevTools in browsers. As per New users' guides to golfing rules in specific languages this should be valid (Full browser JS program).

If the one above is anyway considered a snippet, then 47 45 bytes:

_=>{for(x=9;x;)--x-4&&alert([~(-x/3),x%3-1])}

Answer 46

Whitespace, 219 bytes

[S S S T    T   N
_Push_3][S S T  T   N
_Push_-1][S S S N
_Push_0][S S S T    T   N
_Push_3][S S T  T   N
_Push_-1][S S S T   N
_Push_1][S S S T    T   N
_Push_3][S S S N
_Push_0][S S S T    T   N
_Push_3][S S T  T   N
_Push_-1][S S S T   N
_Push_1][S S S T    T   N
_Push_3][S S T  T   N
_Push_-1][S S S N
_Push_0][S S S T    T   N
_Push_3][S S S T    N
_Push_1][S S S T    T   N
_Push_3][S S S N
_Push_0][S S S T    T   N
_Push_3][S S S T    N
_Push_1][S S S T    S N
_Push_2][S S S N
_Push_0][S S S T    T   N
_Push_3][S S T  T   N
_Push_-1][S S S T   N
_Push_1][S S S T    S N
_Push_2][S S S N
_Push_0][S S S T    T   N
_Push_3][S S S T    N
_Push_1][S S S T    T   N
_Push_3][S S T  T   N
_Push_-1][S S S N
_Push_0][S S S T    S N
_Push_2][S S S T    N
_Push_1][S S S T    T   N
_Push_3][S S S N
_Push_0][S S S T    S N
_Push_2][N
S S N
_Create_Label_LOOP][S S S T S T T   T   S N
_Push_46][T S S S _Add_top_two][T   N
S S _Print_as_character][N
S N
N
_Jump_to_Label_LOOP]

Letters S (space), T (tab), and N (new-line) added as highlighting only.
[..._some_action] added as explanation only.

Try it online (with raw spaces, tabs and new-lines only).

Prints with a . delimiter between each number, and / between each pair of numbers. Since the codepoints of both . and / are between - and 01, these are the shortest delimiters to use with this approach.

Uses this Whitespace tip of mine to print the output. The optimal constant 46 is generated by this Java program.

NOTE: Hard-coded with tab and newline delimiters (since their codepoints are pretty short, being 9 and 10 respectively) would be 332 bytes instead.

Answer 47

Tcl, 44 bytes

puts "-1 -1
0 -1
1 -1
-1 0
1 0
-1 1
0 1
1 1"

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---

Tcl, 77 bytes

set j -1
time {set i -2
time {puts [expr [incr i]|$j?"$i $j":""]} 3
incr j} 3

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Answer 48

TI-Basic, 32 bytes

For(A,-1,1
For(B,-1,1
If A≠2B
Disp A,B,"
End
End

Prints pairs as two lines, separated by empty lines.

TI-Basic is a tokenized language, all tokens used here are one-byte.

Explanation:

For(A,-1,1 # First number from -1 to 1 (inclusive)
For(B,-1,1 # Second number from -1 to 1 (inclusive)
If A≠2B    # If the pair is not 0,0
Disp A,B," # Print the first number, then the second, then
           # an empty string (each on its own line)
End        # End second number loop
End        # End first number loop

Output

-1
-1

-1
0

-1
1

0
-1

0
1

1
-1

1
0

1
1

Answer 49

Yabasic, 49 bytes

An anonymous function that takes no input and outputs to the console.

For i=-1To 1
For j=-1To 1
If i Or j?i,j
Next
Next

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Output

-1 -1
-1 0
-1 1
0 -1
0 1
1 -1
1 0
1 1

Answer 50

VBA, 66 bytes

An anonymous function that takes no input and outputs to the console.

For i=-1To 1:For j=-1To 1:?IIf(i Or j,i &" "&j &vbCr,"");:Next j,i

Output

-1 -1
-1 0
-1 1
0 -1
0 1
1 -1
1 0
1 1

Answer 51

Ruby, 31 bytes

p (w=*-1..1).product(w)-[[0,0]]

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Answer 52

Julia 0.6, 24 bytes

[(A=[0:3;5:8])%3 A÷3]-1

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Generate [0,1,2,0,2,0,1,2] in the first column and [0,0,0,1,1,2,2,2] in the second (excluding 4%3 and 4÷3 to avoid 0 0), then subtract 1 from all the values.

Other methods I tried:

[(i,j)for i=-1:1,j=-1:1 if i|j!=0]

[[s...].-'1'for s=base.(3,[0:3;5:8],2)] (based on Stewie Griffin's Octave solution)

[(i,j)for i=-1:1,j=-1:1][(1:9).!=5]

Answer 53

MathGolf, 7 5 bytes

1╤╫■╞

-2 bytes by porting @ბიმო's second Husk answer, so make sure to upvote him!

Try it online.

Explanation:

1╤     # Push list [-1,0,1] (push 1; pop and push a list in the range [-n,n])
  ╫    # Rotate it once towards the left: [0,1,-1]
   ■   # Take the cartesian product with itself, creating all possible pairs
    ╞  # Discard the first item of this list (the [0,0] pair)
       # (after which the entire stack joined together is output implicitly)

Answer 54

05AB1E, 6 bytes

T®šã¨

Port of @ბიმო's second Husk answer, so make sure to upvote him!

Try it online.

Explanation:

T      # Push 10
 ®š    # Prepend -1 as list: [-1,1,0]
   ã   # Take the cartesian product of this list with itself, generating all pairs
    ¨  # Remove the last one, which is the [0,0]
       # (after which the result is output implicitly)