Generating Word Grids

Question

Given input n, produce a word grid of size n, in as few bytes as possible.

Details

The number provided will always be odd. The centre square of the grid must always be empty (a space character). The letters that fill the grid must be chosen at random from the English Scrabble letter distribution of letters. That is, each tile must be chosen at random, with uniform probability, from the following 100 characters:

??EEEEEEEEEEEEAAAAAAAAAIIIIIIIIIOOOOOOOONNNNNNRRRRRRTTTTTTLLLLSSSSUUUUDDDDGGGBBCCMMPPFFHHVVWWYYKJXQZ

where ? denotes blank tiles.

As with a Scrabble board, some tiles in this board will also be bonus tiles for a higher score. These tiles are only visible on a board with a size of 9 or more. and should be visible every 3 rows from the centre square in a pattern emanating outwards, but should never appear on the outermost letters. Bonus squares are denoted using lowercase letters, with blank tiles identified as ! instead of ?. Please see this visual demonstration or the reference implementation for more examples on how to correctly distribute bonus tiles.

Examples

Input: 5

Output:

VNZNT
IFOSN
UD VD
ZIOO?
KTLED

Input: 9

Output:

UWDESTKPW
ItDBaDEdI
TERMDYSTR
ROANJLEFT
EkCI OOsT
IPAJPGM?Y
MZLORETVI
G!EGgPUeI
MNROYOEER

Reference implementation.

Rules

This is code-golf so the shortest code in bytes wins.

• Any reasonable format can be used for I/O, assuming it is consistent.
• You should be able to handle grids at least up to 999.
• All standard loopholes are forbidden.

Answer 1

Jelly,  67 65 64 66 64  63 bytes

”?;ØAx“³Ċu~Ṿr¥rṇ⁽ȦƑ’ḃ12¤µŒl⁾?!yW,WKF€
H3ṬṚ¤ṁ‘1¦ṚŒḄ0,0j«þ`ị¢X€€Y

A monadic link taking a number and returning a list of characters, or a full program printing the result.

Try it online! (I prefer it using G rather than Y since that's more square)

How?

”?;ØAx“³Ċu~Ṿr¥rṇ⁽ȦƑ’ḃ12¤µŒl⁾?!yW,WKF€ - Link 1, getLetterSets: no arguments
”?                                    - literal '?'
   ØA                                 - yield uppercase alphabet
  ;                                   - concatenate
                       ¤              - nilad followed by link(s) as a nilad:
      “³Ċu~Ṿr¥rṇ⁽ȦƑ’                  -   base 250 number
                    ḃ12               -   converted to bijective base 12 (frequencies)
     x                                -   times (repeat each)
                        µ             - start a new monadic chain, call that uppers
                         Œl           - to lower-case
                           ⁾?!        - literal ['?','!']
                              y       - translate (change '?'s to '!'s)
                               W      - wrap (that) in a list
                                 W    - wrap (uppers) in a list
                                ,     - pair
                                  K   - join with a space, ' '
                                   F€ - flatten €ach (both flattens the wrapped lists
                                      -               AND makes the lone ' ' into [' '])

H3ṬṚ¤ṁ‘1¦ṚŒḄ0,0j«þ`ị¢X€€Y - Main link: number, n                 e.g. 13
H                         - halve                                     6.5
    ¤                     - nilad followed by link(s) as a nilad:
 3                        -   literal three                           3
  Ṭ                       -   untruth                                 [0,0,1]
   Ṛ                      -   reverse                                 [1,0,0]
     ṁ                    - mould like (implicit range(int(right)))   [1,0,0,1,0,0]
        ¦                 - sparse application:
       1                  - ...to indices: 1
      ‘                   - ...action: increment                      [2,0,0,1,0,0]
         Ṛ                - reverse                                   [0,0,1,0,0,2]
          ŒḄ              - bounce                          [0,0,1,0,0,2,0,0,1,0,0]
            0,0           - literal [0,0]                             [0,0]
               j          - join                          [0,0,0,1,0,0,2,0,0,1,0,0,0]
                  `       - repeat left argument as right argument with:
                 þ        -   outer product using:       [[0,0,0,0,0,0,0,0,0,0,0,0,0],
                «         -     minimum                   [0,0,0,0,0,0,0,0,0,0,0,0,0],
                          -                               [0,0,0,0,0,0,0,0,0,0,0,0,0],
                          -                               [0,0,0,1,0,0,1,0,0,1,0,0,0],
                          -                               [0,0,0,0,0,0,0,0,0,0,0,0,0],
                          -                               [0,0,0,0,0,0,0,0,0,0,0,0,0],
                          -                               [0,0,0,1,0,0,2,0,0,1,0,0,0],
                          -                               [0,0,0,0,0,0,0,0,0,0,0,0,0],
                          -                               [0,0,0,0,0,0,0,0,0,0,0,0,0],
                          -                               [0,0,0,1,0,0,1,0,0,1,0,0,0],
                          -                               [0,0,0,0,0,0,0,0,0,0,0,0,0],
                          -                               [0,0,0,0,0,0,0,0,0,0,0,0,0],
                          -                               [0,0,0,0,0,0,0,0,0,0,0,0,0]]
                    ¢     - call the last link (1) as a nilad (the letter sets)
                   ị      - index into - gets the correct letter sets for each cell
                     X€€  - random-choice for €ach cell in €ach row
                        Y - join with newlines
                          - if running as a full program: implicit print

Answer 2

R, 288 281 267 257 225 214 bytes

thanks to @cole for -1 byte, reordering the ? to collapse the 2 into rep(2,10)

-10 bytes realizing that row(m) == t(col(m))

-41 bytes thanks to user2390246 for reconfiguring the weights, golfing down the indexing, and some more usual R tips

function(n){m=matrix(sample(el(strsplit("EOAINRTLSUDGBCMPFHVW?YKJXQZ","")),n^2,T,rep(c(12,8,9,6,4:1),c(1,1:4,1,10,5))),,n)
K=n/2+.5
L=col(m)
m[i]=chartr("A-Z?","a-z!",m[i<-(x=!(L-K)%%3&L-1&L-n)&t(x)])
m[K,K]=" "
m}

Try it online!

Returns a matrix. Fairly simple implementation; samples n^2 values with the proper distribution, stores as an nxn matrix.

K is the index of the center.

L=col(m) is a matrix indicating the column number of each element in the matrix. Hence we compute !(L-K)%%3 to get the possible columns (including the edges), i.e., those a multiple of 3 away from the center column. To remove the edges, we consider L-1 and L-n. L-1 is 0 (false) for the first column and L-n is 0 for the last column. Applying & (element-wise boolean AND) to these three yields a matrix with TRUE in those columns a multiple of three away from the center, excluding the edges. We store this result as x.

If we take the transpose of x, t(x), we get the same matrix, but for the rows, hence x&t(x) is a matrix we save as i containing: TRUE indices for the required cells, and FALSE everywhere else.

Then we use chartr to perform the required transformation on m[i] and save the result as m[i], change the center cell to a space, and return the matrix.

Importantly as user2390246 pointed out, we don't need to test n>=9 because for n<7, there aren't any cells a multiple of 3 away from the center (apart from the center which is changed to a space anyway), and for n==7, the only cells a multiple of 3 from the center are on the edge so they are excluded. Neat!

Answer 3

JavaScript (ES6), 247 242 bytes

-5 bytes with help from @Shaggy

n=>[...Array(p=n*n)].map((_,i)=>i==p>>1?" ":g(i/n|0)&g(i%n,c="AI9O8NRTEE6LSUD4G3BCMPFHVWY?2KJXQZ".replace(/(\D+)(\d)/g,(_,c,i)=>c.repeat(i))[Math.random()*100|0])?c<"A"?"!":c.toLowerCase():++i%n?c:c+`
`,g=x=>x&&x<n-1&((n>>1)-x)%n%3==0).join``

Test Snippet

let f=
n=>[...Array(p=n*n)].map((_,i)=>i==p>>1?" ":g(i/n|0)&g(i%n,c="AI9O8NRTEE6LSUD4G3BCMPFHVWY?2KJXQZ".replace(/(\D+)(\d)/g,(_,c,i)=>c.repeat(i))[Math.random()*100|0])?c<"A"?"!":c.toLowerCase():++i%n?c:c+`
`,g=x=>x&&x<n-1&((n>>1)-x)%n%3==0).join``

;(R.onclick=L.onchange=I.oninput=function(){let n=+I.value,res=f(n);O.innerText=n+"\n"+(L.checked?res.replace(/[A-Z\?]/g,".").replace(/[a-z!]/g,"#"):res);})()

<label><input id=L type=checkbox> Layout only</label> <button id=R>Rerun</button><br><input id=I type=range min=9 max=53 step=2 value=9 style="width:100%">
<pre id=O></pre>

Answer 4

Perl 6, 162 161 154 153 bytes

{(my@b=0,|(-$^m..$m).map({$_%%3+!$_}),0).map:{((my$e='AIJKQXZG'~'NRTBCFHMPVWYG'x 2~'EEEAAIIOONRTUSLD'x 4)~'??',$e.lc~'!!',' ')[@b Xmin$_]».comb».roll}}

Try it online!

Takes (n-3)/2 as input, returns a list of lists of letters.

Explanation:

-> $m {
    # Idea stolen from @Xcali's answer.
    my $e = 'AIJKQXZG' ~ 'NRTBCFHMPVWYG' x 2 ~ 'EEEAAIIOONRTUSLD' x 4;
    # Array containing 1 for bonus tiles, 2 for middle element, like
    #     (0,1,0,0,1,0,0,2,0,0,1,0,0,1,0)
    my @b = 0, |(-$m..$m).map({ $_ %% 3 + !$_ }), 0;
    # Map column vector.
    @b.map: {
        # Compute element-wise minimum of row vector and value from
        # column vector. Select character pools accordingly and get
        # random items.
        ($e~'??', $e.lc~'!!', ' ')[@b Xmin $_]».comb».roll
    }
}

Answer 5

Perl 5, 246 244 + 1 (-n) = 247 245 bytes

$m=($n=$_-$_%2)/2;for(@a=(U x++$n)x$n){$_=(LUU,ULU,UUL)[$m%3]x($n/3).U x($n%3)if$z%@a&&$z%3==$m%3;substr$_,$m,1,$"if$m==$z++;s/L/-U/g;s/U/substr"EEAIONRT"x6 .AIJKQXZG."AIO?BCFHMPVWYGUUSSLLDD"x2,rand 100,1/ge;s/^-//;s/-\?/!/g;s/-(.)/lc$1/ge;say}

Try it online!

Answer 6

[C64 basic v2, 210 209 bytes]

1t$="2?9E3E9A9I8O6N6R6T4L4S4U4D3G2B2C2M2P2F2H2V2W2Y1K1J1X1Q1Z":rEn
3fOx=1ton:fOy=1ton:a=rN(0)*100:b=1
4c=aS(mI(t$,b,1))-48:d=aS(mI(t$,b+1,1)):b=b+2:ifc>atH6
5a=a-c:gO4
6pO983+40*y+x,c:nE:nE:pO1003.5+n*20.5,32

An input n 5 can be specified like

0dA5

That "5" to the end should be changed to any odd number. Don't give more than 25, then the program will overwrite itself.

---

How to try it: google for "vice c64 emulator", install it, and copy-paste this basic code into it. To start the program, type: RUN. To clear the screen, press shift/home.

And the result:

Answer 7

Python 3, 214 236 240 bytes

lambda n:[[[choice([s,[[c.lower(),'!'][c<'A']for c in s]][((i-n//2)%3+(j-n//2)%3<1)*(i*j>0)*(i<n-1)*(j<n-1)])," "][i==j==n//2]for j in range(n)]for i in range(n)]
from random import*
s=(("OIAE"*2+"SDLUNTRE")*2+"HVBMCYPWF?GNTR")*2+"ZXJQKGIA"

Try it online!

The multiplicity of each character is expressed as sum of powers of two, e.g 12 = 8 + 4 => "E"*12 = "E"*2*2*2 + "E"*2*2.

((i-n//2)%3+(j-n//2)%3<1)*(i*j>0)*(i<n-1)*(j<n-1) may probably be golfed.