Generate Chess960 starting position
You are encouraged to solve this task according to the task description, using any language you may know.
Chess960 is a variant of chess created by world champion Bobby Fischer. Unlike other variants of the game, Chess960 does not require a different material, but instead relies on a random initial position, with a few constraints:
- as in the standard chess game, all eight white pawns must be placed on the second rank.
- White pieces must stand on the first rank as in the standard game, in random column order but with the two following constraints:
- the bishops must be placed on opposite color squares (i.e. they must be an odd number of spaces apart or there must be an even number of spaces between them)
- the King must be between two rooks (with any number of other pieces between them all)
- Black pawns and pieces must be placed respectively on the seventh and eighth ranks, mirroring the white pawns and pieces, just as in the standard game. (That is, their positions are not independently randomized.)
With those constraints there are 960 possible starting positions, thus the name of the variant.
- Task
The purpose of this task is to write a program that can randomly generate any one of the 960 Chess960 initial positions. You will show the result as the first rank displayed with Chess symbols in Unicode: ♔♕♖♗♘ or with the letters King Queen Rook Bishop kNight.
AutoHotkey
<lang AutoHotkey>Loop, 5 Out .= Chess960() "`n" MsgBox, % RTrim(Out, "`n")
Chess960() { P := {} P[K := Rand(2, 7)] := Chr(0x2654) ; King P[Rand(1, K - 1)] := Chr(0x2656) ; Rook 1 P[Rand(K + 1, 8)] := Chr(0x2656) ; Rook 2 Loop, 8 Remaining .= P[A_Index] ? "" : A_Index "`n" Sort, Remaining, Random N P[Bishop1 := SubStr(Remaining, 1, 1)] := Chr(0x2657) ; Bishop 1 Remaining := SubStr(Remaining, 3) Loop, Parse, Remaining, `n if (Mod(Bishop1 - A_LoopField, 2)) Odd .= A_LoopField "`n" else Even .= A_LoopField "`n" X := StrSplit(Odd Even, "`n") P[X.1] := Chr(0x2657) ; Bishop 2 P[X.2] := Chr(0x2655) ; Queen P[X.3] := Chr(0x2658) ; Knight 1 P[X.4] := Chr(0x2658) ; Knight 2 for Key, Val in P Out .= Val return Out }
Rand(Min, Max) { Random, n, Min, Max return n }</lang>
- Output:
♕♘♖♗♗♘♔♖ ♗♖♔♕♘♖♘♗ ♖♗♘♘♗♔♖♕ ♗♗♘♖♔♕♘♖ ♘♗♖♔♗♘♕♖
Befunge
Similar to the Ruby SP-ID solution, this generates the start position for a random number in the Chess960 numbering scheme. <lang befunge>#.#.#.#.065*0#v_1-\>>?1v v,":".:%*8"x"$<^!:\*2<+< >48*,:4%2*1#v+#02#\3#g<< v"B"*2%4:/4p<vg0:+1<\-1< >\0p4/:6%0:0g>68*`#^_\:| v"RKRNN"p11/6$p0\ "Q" \< >"NRNKRRNNKRNRKNRRNKNR"v v"NRNKRNRKNRNRKRNRNNKR"< >"RKRNN"11g:!#v_\$\$\$\v v _v#!`*86:g0:<^!:-1$\$< >$\>,1+ :7`#@_^> v960v <</lang>
- Output:
856 : RBKNBRNQ
C
As noted in the C implementation for the Sparkline in unicode task, unicode output is reliable only on Linux/Unix systems. This implementation thus has compiler directives to check whether the underlying system is Windows or Linux, if Windows, only letters are printed, otherwise Unicode output is displayed. 9 rows are displayed. <lang C>#include<stdlib.h>
- include<locale.h>
- include<wchar.h>
- include<stdio.h>
- include<time.h>
char rank[9];
int pos[8];
void swap(int i,int j){ int temp = pos[i]; pos[i] = pos[j]; pos[j] = temp; }
void generateFirstRank(){ int kPos,qPos,bPos1,bPos2,rPos1,rPos2,nPos1,nPos2,i;
for(i=0;i<8;i++){ rank[i] = 'e'; pos[i] = i; }
do{ kPos = rand()%8; rPos1 = rand()%8; rPos2 = rand()%8; }while((rPos1-kPos<=0 && rPos2-kPos<=0)||(rPos1-kPos>=0 && rPos2-kPos>=0)||(rPos1==rPos2 || kPos==rPos1 || kPos==rPos2));
rank[pos[rPos1]] = 'R'; rank[pos[kPos]] = 'K'; rank[pos[rPos2]] = 'R';
swap(rPos1,7); swap(rPos2,6); swap(kPos,5);
do{ bPos1 = rand()%5; bPos2 = rand()%5; }while(((pos[bPos1]-pos[bPos2])%2==0)||(bPos1==bPos2));
rank[pos[bPos1]] = 'B'; rank[pos[bPos2]] = 'B';
swap(bPos1,4); swap(bPos2,3);
do{ qPos = rand()%3; nPos1 = rand()%3; }while(qPos==nPos1);
rank[pos[qPos]] = 'Q'; rank[pos[nPos1]] = 'N';
for(i=0;i<8;i++) if(rank[i]=='e'){ rank[i] = 'N'; break; } }
void printRank(){ int i;
#ifdef _WIN32 printf("%s\n",rank); #else { setlocale(LC_ALL,""); printf("\n"); for(i=0;i<8;i++){ if(rank[i]=='K') printf("%lc",(wint_t)9812); else if(rank[i]=='Q') printf("%lc",(wint_t)9813); else if(rank[i]=='R') printf("%lc",(wint_t)9814); else if(rank[i]=='B') printf("%lc",(wint_t)9815); if(rank[i]=='N') printf("%lc",(wint_t)9816); } } #endif }
int main() { int i;
srand((unsigned)time(NULL));
for(i=0;i<9;i++){ generateFirstRank(); printRank(); }
return 0; } </lang> Output on Linux :
♗♗♖♕♘♘♔♖ ♘♖♕♔♗♗♖♘ ♖♘♔♖♕♘♗♗ ♘♘♖♗♗♔♖♕ ♗♘♖♘♕♔♖♗ ♕♗♗♘♖♔♘♖ ♕♘♖♔♗♖♘♗ ♗♘♘♕♖♔♖♗ ♖♘♘♕♗♔♖♗
Output on Windows :
BRKNNQRB RBNQNKBR RNQKNBBR RQNKNBBR QBBNRKNR BNRBQKNR BRQKNNRB RNKBNRBQ QNRBBNKR
C++
<lang cpp>#include <iostream>
- include <string>
- include <time.h>
using namespace std;
namespace {
void placeRandomly(char* p, char c)
{
int loc = rand() % 8; if (!p[loc]) p[loc] = c; else placeRandomly(p, c); // try again
}
int placeFirst(char* p, char c, int loc = 0)
{
while (p[loc]) ++loc; p[loc] = c;
return loc; }
string startPos()
{
char p[8]; memset( p, 0, 8 );
// bishops on opposite color p[2 * (rand() % 4)] = 'B'; p[2 * (rand() % 4) + 1] = 'B';
// queen knight knight, anywhere for (char c : "QNN") placeRandomly(p, c);
// rook king rook, in that order placeFirst(p, 'R', placeFirst(p, 'K', placeFirst(p, 'R')));
return string(p, 8);
}
} // leave local
namespace chess960 {
void generate( int c )
{
for( int x = 0; x < c; x++ ) cout << startPos() << "\n";
}
}
int main( int argc, char* argv[] ) {
srand( time( NULL ) ); chess960::generate( 10 ); cout << "\n\n"; return system( "pause" );
} </lang>
- Output:
NQBRNBKR RKBQNBNR RKBRNNQB QRBNNKRB BRKNRBQN QNRBBKNR BQRBKNRN RNBKQBNR QRNKBBRN QRBKNBRN
Clojure
<lang clojure>(ns c960.core
(:gen-class) (:require [clojure.string :as s]))
- legal starting rank - unicode chars for rook, knight, bishop, queen, king, bishop, knight, rook
(def starting-rank [\♖ \♘ \♗ \♕ \♔ \♗ \♘ \♖])
(defn bishops-legal?
"True if Bishops are odd number of indicies apart" [rank] (odd? (apply - (cons 0 (sort > (keep-indexed #(when (= \♗ %2) %1) rank))))))
(defn king-legal?
"True if the king is between two rooks"
[rank]
(let [king-&-rooks (filter #{\♔ \♖} rank)]
(and
(= 3 (count king-&-rooks))
(= \u2654 (second king-&-rooks)))))
(defn c960
"Return a legal rank for c960 chess"
([] (c960 1))
([n]
(->> #(shuffle starting-rank)
repeatedly
(filter #(and (king-legal? %) (bishops-legal? %)))
(take n)
(map #(s/join ", " %)))))
(c960)
- => "♗, ♖, ♔, ♕, ♘, ♘, ♖, ♗"
(c960)
- => "♖, ♕, ♘, ♔, ♗, ♗, ♘, ♖"
(c960 4)
- => ("♘, ♖, ♔, ♘, ♗, ♗, ♖, ♕" "♗, ♖, ♔, ♘, ♘, ♕, ♖, ♗" "♘, ♕, ♗, ♖, ♔, ♗, ♘, ♖" "♖, ♔, ♘, ♘, ♕, ♖, ♗, ♗")</lang>
D
D: Indexing
<lang d>void main() {
import std.stdio, std.range, std.algorithm, std.string, permutations2;
const pieces = "KQRrBbNN";
alias I = indexOf;
auto starts = pieces.dup.permutations.filter!(p =>
I(p, 'B') % 2 != I(p, 'b') % 2 && // Bishop constraint.
// King constraint.
((I(p, 'r') < I(p, 'K') && I(p, 'K') < I(p, 'R')) ||
(I(p, 'R') < I(p, 'K') && I(p, 'K') < I(p, 'r'))))
.map!toUpper.array.sort().uniq;
writeln(starts.walkLength, "\n", starts.front);
}</lang>
- Output:
960 BBNNQRKR
D: Regexp
<lang d>void main() {
import std.stdio, std.regex, std.range, std.algorithm, permutations2;
immutable pieces = "KQRRBBNN";
immutable bish = r"B(|..|....|......)B";
immutable king = r"R.*K.*R";
auto starts3 = permutations(pieces.dup)
.filter!(p => p.match(bish) && p.match(king))
.array.sort().uniq;
writeln(starts3.walkLength, "\n", starts3.front);
}</lang> The output is the same.
D: Correct by construction
<lang d>void main() {
import std.stdio, std.random, std.array, std.range;
// Subsequent order unchanged by insertions.
auto start = "RKR".dup;
foreach (immutable piece; "QNN")
start.insertInPlace(uniform(0, start.length), piece);
immutable bishpos = uniform(0, start.length); start.insertInPlace(bishpos, 'B'); start.insertInPlace(iota(bishpos % 2, start.length, 2)[uniform(0,$)], 'B'); start.writeln;
}</lang>
- Output:
QBNNBRKR
EchoLisp
<lang lisp>(define-values (K Q R B N) (iota 5)) (define *pos* (list R N B Q K B N R)) ;; standard starter
- check opposite color bishops, and King between rooks
(define (legal-pos p)
(and
(> (list-index K p) (list-index R p))
(> (list-index K (reverse p)) (list-index R (reverse p)))
(even? (+ (list-index B p) (list-index B (reverse p))))))
- random shuffle current position until a legal one is found
(define (c960) (set! *pos* (shuffle *pos*)) (if (legal-pos *pos*) (map unicode-piece *pos*) (c960))) </lang>
- Output:
(define (unicode-piece i) (unicode->string (+ 0x2654 i))) (legal-pos *pos*) → #t ;; starter is OK (c960) (♗ ♖ ♔ ♗ ♕ ♘ ♘ ♖) (c960) (♘ ♗ ♗ ♕ ♖ ♘ ♔ ♖) (c960) (♖ ♘ ♗ ♘ ♔ ♕ ♖ ♗) ;; etc.
Elixir
Elixir: shuffle pieces until all regexes match
<lang elixir>defmodule Chess960 do
@pieces ~w(♔ ♕ ♘ ♘ ♗ ♗ ♖ ♖) # ~w(K Q N N B B R R) @regexes [~r/♗(..)*♗/, ~r/♖.*♔.*♖/] # [~r/B(..)*B/, ~r/R.*K.*R/] def shuffle do row = Enum.shuffle(@pieces) |> Enum.join if Enum.all?(@regexes, &Regex.match?(&1, row)), do: row, else: shuffle end
end
Enum.each(1..5, fn _ -> IO.puts Chess960.shuffle end)</lang>
- Output:
♘♗♘♖♗♔♕♖ ♗♖♔♗♕♘♘♖ ♗♗♕♖♔♖♘♘ ♘♗♖♔♗♘♕♖ ♖♕♘♘♗♗♔♖
Elixir: Construct
<lang elixir>defmodule Chess960 do
def construct do
row = Enum.reduce(~w[♕ ♘ ♘], ~w[♖ ♔ ♖], fn piece,acc ->
List.insert_at(acc, :rand.uniform(length(acc)+1)-1, piece)
end)
[Enum.random([0, 2, 4, 6]), Enum.random([1, 3, 5, 7])]
|> Enum.sort
|> Enum.reduce(row, fn pos,acc -> List.insert_at(acc, pos, "♗") end)
|> Enum.join
end
end
Enum.each(1..5, fn _ -> IO.puts Chess960.construct end)</lang>
- Output:
♖♔♗♘♖♕♘♗ ♘♗♘♕♖♔♗♖ ♗♖♔♘♘♗♖♕ ♖♗♘♘♕♔♗♖ ♖♕♗♘♘♗♔♖
Elixir: Generate from SP-ID
<lang elixir>defmodule Chess960 do
@krn ~w(NNRKR NRNKR NRKNR NRKRN RNNKR RNKNR RNKRN RKNNR RKNRN RKRNN)
def start_position, do: start_position(:rand.uniform(960)-1)
def start_position(id) do
pos = List.duplicate(nil, 8)
q = div(id, 4)
r = rem(id, 4)
pos = List.replace_at(pos, r * 2 + 1, "B")
q = div(q, 4)
r = rem(q, 4)
pos = List.replace_at(pos, r * 2, "B")
q = div(q, 6)
r = rem(q, 6)
i = Enum.reject(0..7, &Enum.at(pos,&1)) |> Enum.at(r)
pos = List.replace_at(pos, i, "Q")
krn = Enum.at(@krn, q) |> String.codepoints
Enum.reject(0..7, &Enum.at(pos,&1))
|> Enum.zip(krn)
|> Enum.reduce(pos, fn {i,x},acc -> List.replace_at(acc,i,x) end)
|> Enum.join
end
end
IO.puts "Generate Start Position from ID number" Enum.each([0,518,959], fn id ->
:io.format "~3w : ~s~n", [id, Chess960.start_position(id)]
end) IO.puts "\nGenerate random Start Position" Enum.each(1..5, fn _ -> IO.puts Chess960.start_position end)</lang>
- Output:
Generate Start Position from ID number 0 : BBQNNRKR 518 : BRNKNBRQ 959 : RKRQNNBB Generate random Start Position RQKBBNNR RBBQKNNR RQKNNRBB RKRQBBNN RNBNKQRB
Factor
Using the single-die method: https://en.wikipedia.org/wiki/Chess960_starting_position#Single_die_method <lang factor>USING: io kernel math random sequences ; IN: rosetta-code.chess960
- empty ( seq -- n ) 32 swap indices random ;
- next ( seq -- n ) [ 32 = ] find drop ;
- place ( seq elt n -- seq' ) rot [ set-nth ] keep ;
- white-bishop ( -- elt n ) CHAR: ♗ 4 random 2 * ;
- black-bishop ( -- elt n ) white-bishop 1 + ;
- queen ( seq -- seq elt n ) CHAR: ♕ over empty ;
- knight ( seq -- seq elt n ) CHAR: ♘ over empty ;
- rook ( seq -- seq elt n ) CHAR: ♖ over next ;
- king ( seq -- seq elt n ) CHAR: ♔ over next ;
- chess960 ( -- str )
" " clone black-bishop place white-bishop place queen place knight place knight place rook place king place rook place ;
- chess960-demo ( -- ) 5 [ chess960 print ] times ;
MAIN: chess960-demo</lang>
- Output:
♕♖♗♘♔♘♖♗ ♕♗♖♘♗♘♔♖ ♗♘♕♖♔♗♖♘ ♘♖♗♕♔♗♘♖ ♗♗♘♖♘♔♕♖
Forth
<lang forth>\ make starting position for Chess960, constructive
\ 0 1 2 3 4 5 6 7 8 9 create krn S" NNRKRNRNKRNRKNRNRKRNRNNKRRNKNRRNKRNRKNNRRKNRNRKRNN" mem,
create pieces 8 allot
- chess960 ( n -- )
pieces 8 erase 4 /mod swap 2* 1+ pieces + 'B swap c! 4 /mod swap 2* pieces + 'B swap c! 6 /mod swap pieces swap bounds begin dup c@ if swap 1+ swap then 2dup > while 1+ repeat drop 'Q swap c! 5 * krn + pieces 8 bounds do i c@ 0= if dup c@ i c! 1+ then loop drop cr pieces 8 type ;
0 chess960 \ BBQNNRKR ok 518 chess960 \ RNBQKBNR ok 959 chess960 \ RKRNNQBB ok
960 choose chess960 \ random position</lang>
Fortran
This implementation simply iterates through all 960 positions. <lang fortran>program chess960
implicit none integer, pointer :: a,b,c,d,e,f,g,h integer, target :: p(8) a => p(1) b => p(2) c => p(3) d => p(4) e => p(5) f => p(6) g => p(7) h => p(8)
king: do a=2,7 ! King on an internal square
r1: do b=1,a-1 ! R1 left of the King
r2: do c=a+1,8 ! R2 right of the King
b1: do d=1,7,2 ! B1 on an odd square
if (skip_pos(d,4)) cycle
b2: do e=2,8,2 ! B2 on an even square
if (skip_pos(e,5)) cycle
queen: do f=1,8 ! Queen anywhere else
if (skip_pos(f,6)) cycle
n1: do g=1,7 ! First knight
if (skip_pos(g,7)) cycle
n2: do h=g+1,8 ! Second knight (indistinguishable from first)
if (skip_pos(h,8)) cycle
if (sum(p) /= 36) stop 'Loop error' ! Sanity check
call write_position
end do n2
end do n1
end do queen
end do b2
end do b1
end do r2
end do r1
end do king
contains
logical function skip_pos(i, n)
integer, intent(in) :: i, n
skip_pos = any(p(1:n-1) == i)
end function skip_pos
subroutine write_position
integer :: i, j
character(len=15) :: position = ' '
character(len=1), parameter :: names(8) = ['K','R','R','B','B','Q','N','N']
do i=1,8
j = 2*p(i)-1
position(j:j) = names(i)
end do
write(*,'(a)') position
end subroutine write_position
end program chess960 </lang>
- Output:
The first ten positions:
R K R B B Q N N R K R B B N Q N R K R B B N N Q R K R Q B B N N R K R N B B Q N R K R N B B N Q R K R Q B N N B R K R N B Q N B R K R N B N Q B R K R B Q N B N
FreeBASIC
<lang freebasic> Randomize Timer For i As Byte = 1 To 10
Dim As String inicio = "RKR", pieza = "QNN"
Dim As Byte posic
For n As Byte = 1 To Len(pieza)
posic = Int(Rnd*(Len(inicio) + 1)) + 1
inicio = Left(inicio, posic-1) + _
Mid(pieza, n, 1) +_
Right(inicio, Len(inicio) - posic + 1)
Next n
posic = Int(Rnd*(Len(inicio) + 1)) + 1
inicio = Left(inicio, posic-1) + "B" + Right(inicio, Len(inicio) - posic + 1)
posic = posic + 1 + 2 * Int(Int(Rnd*(Len(inicio) - posic)) / 2)
inicio = Left(inicio, posic-1) + "B" + Right(inicio, Len(inicio) - posic + 1)
Print inicio
Next i </lang>
Go
<lang go>package main
import (
"fmt" "math/rand"
)
type symbols struct{ k, q, r, b, n rune }
var A = symbols{'K', 'Q', 'R', 'B', 'N'} var W = symbols{'♔', '♕', '♖', '♗', '♘'} var B = symbols{'♚', '♛', '♜', '♝', '♞'}
var krn = []string{
"nnrkr", "nrnkr", "nrknr", "nrkrn", "rnnkr", "rnknr", "rnkrn", "rknnr", "rknrn", "rkrnn"}
func (sym symbols) chess960(id int) string {
var pos [8]rune
q, r := id/4, id%4
pos[r*2+1] = sym.b
q, r = q/4, q%4
pos[r*2] = sym.b
q, r = q/6, q%6
for i := 0; ; i++ {
if pos[i] != 0 {
continue
}
if r == 0 {
pos[i] = sym.q
break
}
r--
}
i := 0
for _, f := range krn[q] {
for pos[i] != 0 {
i++
}
switch f {
case 'k':
pos[i] = sym.k
case 'r':
pos[i] = sym.r
case 'n':
pos[i] = sym.n
}
}
return string(pos[:])
}
func main() {
fmt.Println(" ID Start position")
for _, id := range []int{0, 518, 959} {
fmt.Printf("%3d %s\n", id, A.chess960(id))
}
fmt.Println("\nRandom")
for i := 0; i < 5; i++ {
fmt.Println(W.chess960(rand.Intn(960)))
}
}</lang>
- Output:
ID Start position 0 BBQNNRKR 518 RNBQKBNR 959 RKRNNQBB Random ♗♘♖♗♘♔♕♖ ♕♘♖♔♘♖♗♗ ♖♘♗♔♖♕♘♗ ♘♘♖♕♗♔♖♗ ♗♕♘♗♘♖♔♖
Haskell
<lang Haskell>import Data.List import qualified Data.Set as Set
data Piece = K | Q | R | B | N deriving (Eq, Ord, Show)
isChess960 :: [Piece] -> Bool isChess960 rank =
(odd . sum $ findIndices (== B) rank) && king > rookA && king < rookB where Just king = findIndex (== K) rank [rookA, rookB] = findIndices (== R) rank
main :: IO () main = mapM_ (putStrLn . concatMap show) . Set.toList . Set.fromList
. filter isChess960 $ permutations [R,N,B,Q,K,B,N,R]</lang>
- Output:
QRKRBBNN QRKRBNNB QRKRNBBN QRKRNNBB QRKBRNBN ...
J
Build a table of the starting positions then pick one at random. There are 40320 distinct permutations of 8 items and 5040 distinct permutations of these chess pieces and (as the task name points out) only 960 permutations which also satisfy the constraints on bishop and rook position, so little memory is needed to generate the table. Also, since the table is built at "compile time", execution is fast (though "compilation" is reasonably fast also).
<lang J>row0=: u: 9812+2}.5|i.10 king=: u:9812 rook=: u:9814 bish=: u:9815 pos=: I.@e. bishok=: 1=2+/ .| pos&bish rookok=: pos&rook -: (<./,>./)@pos&(rook,king) ok=: bishok*rookok perm=: A.&i.~ ! valid=: (#~ ok"1) ~.row0{"1~perm 8 gen=: valid {~ ? bind 960</lang>
Example use:
<lang J> gen ♘♗♖♔♗♕♖♘
gen
♗♘♘♗♖♔♖♕
gen
♖♗♔♘♘♕♗♖
gen
♖♔♕♗♗♘♖♘</lang>
Java
Regex inspired by (original) Python Regexp, prints ten examples. <lang java5>import java.util.Arrays; import java.util.Collections; import java.util.List;
public class Chess960{ private static List<Character> pieces = Arrays.asList('R','B','N','Q','K','N','B','R');
public static List<Character> generateFirstRank(){ do{ Collections.shuffle(pieces); }while(!check(pieces.toString().replaceAll("[^\\p{Upper}]", ""))); //List.toString adds some human stuff, remove that
return pieces; }
private static boolean check(String rank){ if(!rank.matches(".*R.*K.*R.*")) return false; //king between rooks if(!rank.matches(".*B(..|....|......|)B.*")) return false; //all possible ways bishops can be placed return true; }
public static void main(String[] args){ for(int i = 0; i < 10; i++){ System.out.println(generateFirstRank()); } } }</lang>
- Output:
[R, N, K, N, R, B, B, Q] [B, B, Q, R, N, K, N, R] [R, K, Q, N, N, R, B, B] [N, B, B, N, R, K, Q, R] [R, Q, B, B, K, N, N, R] [R, K, B, Q, N, B, N, R] [N, N, R, K, Q, B, B, R] [R, N, K, Q, N, B, B, R] [N, R, B, K, Q, B, N, R] [N, Q, N, R, K, B, B, R]
JavaScript
This conforms to Altendörfer's single die method[1], though the die will give no "needless" numbers. <lang javaScript>function ch960startPos() {
var rank = new Array(8),
// randomizer (our die)
d = function(num) { return Math.floor(Math.random() * ++num) },
emptySquares = function() {
var arr = [];
for (var i = 0; i < 8; i++) if (rank[i] == undefined) arr.push(i);
return arr;
};
// place one bishop on any black square
rank[d(2) * 2] = "♗";
// place the other bishop on any white square
rank[d(2) * 2 + 1] = "♗";
// place the queen on any empty square
rank[emptySquares()[d(5)]] = "♕";
// place one knight on any empty square
rank[emptySquares()[d(4)]] = "♘";
// place the other knight on any empty square
rank[emptySquares()[d(3)]] = "♘";
// place the rooks and the king on the squares left, king in the middle
for (var x = 1; x <= 3; x++) rank[emptySquares()[0]] = x==2 ? "♔" : "♖";
return rank;
}
// testing (10 times) for (var x = 1; x <= 10; x++) console.log(ch960startPos().join(" | "));</lang>
- Output:
The test-output (exemplary each):
♖ | ♗ | ♗ | ♔ | ♘ | ♖ | ♘ | ♕
♗ | ♗ | ♕ | ♖ | ♔ | ♘ | ♘ | ♖
♖ | ♕ | ♘ | ♗ | ♗ | ♔ | ♘ | ♖
♖ | ♗ | ♔ | ♘ | ♗ | ♕ | ♘ | ♖
♗ | ♖ | ♕ | ♔ | ♘ | ♗ | ♘ | ♖
♖ | ♗ | ♗ | ♕ | ♔ | ♘ | ♖ | ♘
♗ | ♘ | ♖ | ♗ | ♔ | ♘ | ♕ | ♖
♕ | ♘ | ♗ | ♖ | ♔ | ♗ | ♖ | ♘
♗ | ♘ | ♖ | ♘ | ♕ | ♗ | ♔ | ♖
♘ | ♗ | ♖ | ♔ | ♗ | ♘ | ♖ | ♕
Julia
<lang julia>function generateposition()
# Placeholder knights rank = ['♘', '♘', '♘', '♘', '♘', '♘', '♘', '♘'] lrank = length(rank)
# Check if a space is available isfree(x::Int) = rank[x] == '♘'
# Place the King rank[indking = rand(2:lrank-1)] = '♔'
# Place rooks
rank[indrook = rand(filter(isfree, 1:lrank))] = '♖'
if indrook > indking
rank[rand(filter(isfree, 1:indking-1))] = '♖'
else
rank[rand(filter(isfree, indking+1:lrank))] = '♖'
end
# Place bishops rank[indbish = rand(filter(isfree, 1:8))] = '♗' pbish = filter(iseven(indbish) ? isodd : iseven, 1:lrank) rank[rand(filter(isfree, pbish))] = '♗'
# Place queen rank[rand(filter(isfree, 1:lrank))] = '♕' return rank
end
@show generateposition()</lang>
- Output:
generateposition() = ['♘', '♗', '♗', '♖', '♕', '♔', '♘', '♖']
Kotlin
<lang scala>object Chess960 : Iterable<String> {
override fun iterator() = patterns.iterator()
private operator fun invoke(b: String, e: String) {
if (e.length <= 1) {
val s = b + e
if (s.is_valid()) patterns += s
} else {
for (i in 0 until e.length) {
invoke(b + e[i], e.substring(0, i) + e.substring(i + 1))
}
}
}
private fun String.is_valid(): Boolean {
val k = indexOf('K')
return indexOf('R') < k && k < lastIndexOf('R') &&
indexOf('B') % 2 != lastIndexOf('B') % 2
}
private val patterns = sortedSetOf<String>()
init {
invoke("", "KQRRNNBB")
}
}
fun main(args: Array<String>) {
Chess960.forEachIndexed { i, s -> println("$i: $s") }
}</lang>
- Output:
0: BBNNQRKR 1: BBNNRKQR 2: BBNNRKRQ ... 957: RQNNBKRB 958: RQNNKBBR 959: RQNNKRBB
Lua
<lang Lua>-- Insert 'str' into 't' at a random position from 'left' to 'right' function randomInsert (t, str, left, right)
local pos repeat pos = math.random(left, right) until not t[pos] t[pos] = str return pos
end
-- Generate a random Chess960 start position for white major pieces function chess960 ()
local t, b1, b2 = {}
local kingPos = randomInsert(t, "K", 2, 7)
randomInsert(t, "R", 1, kingPos - 1)
randomInsert(t, "R", kingPos + 1, 8)
b1 = randomInsert(t, "B", 1, 8)
b2 = randomInsert(t, "B", 1, 8)
while (b2 - b1) % 2 == 0 do
t[b2] = false
b2 = randomInsert(t, "B", 1, 8)
end
randomInsert(t, "Q", 1, 8)
randomInsert(t, "N", 1, 8)
randomInsert(t, "N", 1, 8)
return t
end
-- Main procedure math.randomseed(os.time()) print(table.concat(chess960()))</lang>
- Output:
NNRQBBKR
Mathematica / Wolfram Language
Generates all possible initial conditions, filters for validity, and chooses a random element.
<lang Mathematica>Print[StringJoin[
RandomChoice[
Select[Union[
Permutations[{"\[WhiteKing]", "\[WhiteQueen]", "\[WhiteRook]",
"\[WhiteRook]", "\[WhiteBishop]", "\[WhiteBishop]",
"\[WhiteKnight]", "\[WhiteKnight]"}]],
MatchQ[#, {___, "\[WhiteRook]", ___, "\[WhiteKing]", ___,
"\[WhiteRook]", ___}] &&
OddQ[Subtract @@ Flatten[Position[#, "\[WhiteBishop]"]]] &]]]];</lang>
Objeck
<lang objeck>class Chess960 {
function : Main(args : String[]) ~ Nil {
Generate(10);
}
function : Generate(c : Int) ~ Nil {
for(x := 0; x < c; x += 1;) {
StartPos()->PrintLine();
};
}
function : StartPos() ~ String {
p := Char->New[8];
# bishops
b1 : Int; b2 : Int;
while(true) {
b1 := GetPosition(); b2 := GetPosition();
b1c := b1 and 1; b2c := b2 and 1;
c := b1c = 0 & b2c <> 0;
if(c) {
break;
};
};
p[b1] := 0x2657; p[b2] := 0x2657;
# queen, knight, knight
q := false;
for(x := 0; x < 3; x += 1;) {
do {
b1 := GetPosition();
} while( p[b1] <> '\0');
if(<>q) {
p[b1] := 0x2655; q := true;
}
else {
p[b1] := 0x2658;
};
};
# rook king rook
q := false;
for(x := 0; x < 3; x += 1;) {
a := 0;
while(a < 8) {
if(p[a] = '\0') {
break;
};
a += 1;
};
if(<>q) {
p[a] := 0x2656; q := true;
}
else {
p[a] := 0x2654; q := false;
};
};
s := "";
for(x := 0; x < 8; x += 1;) { s->Append(p[x]); };
return s;
}
function : GetPosition() ~ Int {
return (Float->Random() * 1000)->As(Int) % 8;
}
}</lang>
Output:
♗♖♕♔♖♗♘♘ ♕♗♖♔♗♘♖♘ ♖♘♔♘♕♖♗♗ ♖♗♔♘♖♘♗♕ ♖♔♖♘♕♗♗♘ ♗♘♖♕♔♘♖♗ ♗♖♔♕♖♘♘♗ ♗♖♔♘♘♖♕♗ ♖♕♔♖♘♘♗♗ ♗♖♘♔♘♖♕♗
PARI/GP
<lang parigp>chess960() = {
my (C = vector(8), i, j, r);
C[random(4) * 2 + 1] = C[random(4) * 2 + 2] = "B";
for (i = 1, 3, while (C[r = random(8) + 1],); C[r] = Vec("NNQ")[i]);
for (i = 1, 8, if (!C[i], C[i] = Vec("RKR")[j++]));
C
}</lang>
Output:
gp > for(i=1, 10, print(chess960())); ["N", "R", "Q", "K", "N", "R", "B", "B"] ["R", "K", "N", "B", "N", "R", "B", "Q"] ["B", "R", "K", "N", "R", "B", "Q", "N"] ["R", "B", "Q", "K", "B", "N", "R", "N"] ["R", "B", "K", "N", "N", "Q", "B", "R"] ["N", "Q", "N", "R", "B", "K", "R", "B"] ["N", "Q", "R", "B", "K", "R", "B", "N"] ["N", "R", "B", "K", "R", "N", "Q", "B"] ["R", "K", "Q", "N", "B", "N", "R", "B"] ["B", "B", "R", "N", "K", "R", "N", "Q"]
Alternatively with recent version of PARI/GP >= 2.9:
gp > M=Map(["B","♗";"K","♔";"N","♘";"Q","♕";"R","♖"]); gp > for(i=1,10,print(concat(apply((c)->mapget(M,c),chess960())))); ♗♖♘♔♕♗♖♘ ♕♖♘♔♖♗♗♘ ♖♕♘♔♘♖♗♗ ♘♘♗♖♕♗♔♖ ♘♘♖♗♗♔♖♕ ♗♖♘♔♘♕♖♗ ♖♔♘♗♗♕♘♖ ♘♖♗♘♔♗♕♖ ♖♔♕♗♗♘♖♘ ♕♗♖♔♗♘♘♖
Perl
Directly generates a configuration by inserting pieces at random appropriate places. Each config has an equal chance of being produced. <lang perl>sub rnd($) { int(rand(shift)) }
sub empties { grep !$_[0][$_], 0 .. 7 }
sub chess960 { my @s = (undef) x 8; @s[2*rnd(4), 1 + 2*rnd(4)] = qw/B B/;
for (qw/Q N N/) { my @idx = empties \@s; $s[$idx[rnd(@idx)]] = $_; }
@s[empties \@s] = qw/R K R/; @s } print "@{[chess960]}\n" for 0 .. 10;</lang>
- Output:
R N B K R N Q B N N R K B R Q B N N Q R K R B B Q R N K B N R B R K R B N Q B N B R K B Q N R N B R N B Q K N R R B Q N N K B R N R N Q K R B B R Q N K R B B N R K N Q B B R N
Perl 6
First, using a list with three rooks and no king, we keep generating a random piece order until the two bishops are on opposite colors. Then we sneakily promote the second of the three rooks to a king. <lang perl6>repeat until m/ '♗' [..]* '♗' / { $_ = < ♖ ♖ ♖ ♕ ♗ ♗ ♘ ♘ >.pick(*).join } s:2nd['♖'] = '♔'; say .comb;</lang>
- Output:
♕ ♗ ♖ ♘ ♔ ♖ ♗ ♘
Here's a more "functional" solution that avoids side effects <lang perl6>sub chess960 {
.subst(:nth(2), /'♜'/, '♚') given first rx/ '♝' [..]* '♝' /, < ♛ ♜ ♜ ♜ ♝ ♝ ♞ ♞ >.pick(*).join xx *;
}
say chess960;</lang>
- Output:
♛♝♜♚♝♞♞♜
We can also pregenerate the list of 960 positions, though the method we use below is a bit wasteful, since it generates 40320 candidates only to throw most of them away. This is essentially the same filtering algorithm but written in the form of a list comprehension rather than nested map and grep. (The list comprehension is actually faster currently.) Note that the constant is calculated at compile time, because, well, it's a constant. Just a big fancy one.
<lang perl6>constant chess960 =
< ♛ ♜ ♜ ♜ ♝ ♝ ♞ ♞ >.permutations».join.unique.grep( / '♝' [..]* '♝' / )».subst(:nth(2), /'♜'/, '♚');
.say for chess960;</lang> Here's a much faster way (about 30x) to generate all 960 variants by construction. No need to filter for uniqueness, since it produces exactly 960 entries. <lang perl6>constant chess960 = gather for 0..3 -> $q {
(my @q = <♜ ♚ ♜>).splice($q, 0, '♛');
for 0 .. @q -> $n1 {
(my @n1 = @q).splice($n1, 0, '♞');
for $n1 ^.. @n1 -> $n2 {
(my @n2 = @n1).splice($n2, 0, '♞');
for 0 .. @n2 -> $b1 {
(my @b1 = @n2).splice($b1, 0, '♝');
for $b1+1, $b1+3 ...^ * > @b1 -> $b2 {
(my @b2 = @b1).splice($b2, 0, '♝');
take @b2.join;
}
}
}
}
}
CHECK { note "done compiling" } note +chess960; say chess960.pick;</lang>
- Output:
done compiling 960 ♜♚♝♜♞♛♞♝
If you run this you'll see that most of the time is spent in compilation, so in the case of separate precompilation the table of 960 entries merely needs to be deserialized back into memory. Picking from those entries guarantees uniform distribution over all possible boards.
Phix
Examines all 40320 permutations for validity and saves them in a list, which is easy to pick random entries from.
Using a dictionary (as commented out) is a little faster, but harder to extract random entries from.
For something faster, and truer to the task description, just use the commented out permute(rand(factorial(8) line,
and quit as soon as you find a valid one (but I wanted to check that I had found exactly 960).
<lang Phix>sequence solutions = {}
--integer d = new_dict()
for i=1 to factorial(8) do
sequence s = permute(i,"RNBQKBNR")
-- sequence s = permute(rand(factorial(8),"RNBQKBNR")
integer b1 = find('B',s),
b2 = find('B',s,b1+1)
if and_bits(b2-b1,1)=1 then
integer k = find('K',s)
integer r1 = find('R',s)
integer r2 = find('R',s,r1+1)
if r1<k and k<r2 then
if find(s,solutions)=0 then
-- if getd_index(s,d)=0 then -- setd(s,0,d)
solutions = append(solutions,s)
end if
end if
end if
end for printf(1,"Found %d solutions\n",{length(solutions)}) for i=1 to 5 do
?solutions[rand(length(solutions))]
end for</lang>
- Output:
Found 960 solutions "QRNNKRBB" "BQRNKBNR" "BRQBNNKR" "QBNRBKRN" "RNKBBQRN"
PicoLisp
<lang PicoLisp>(load "@lib/simul.l")
(seed (in "/dev/urandom" (rd 8)))
(loop
(match
'(@A B @B B @C)
(shuffle '(Q B B N N 0 0 0)) )
(NIL (bit? 1 (length @B))) )
(let Rkr '(R K R)
(for I (append @A '(B) @B '(B) @C)
(prin (if (=0 I) (pop 'Rkr) I)) )
(prinl) )
(bye)</lang>
PowerShell
<lang PowerShell>function Get-RandomChess960Start
{
$Starts = @()
ForEach ( $Q in 0..3 ) {
ForEach ( $N1 in 0..4 ) {
ForEach ( $N2 in ($N1+1)..5 ) {
ForEach ( $B1 in 0..3 ) {
ForEach ( $B2 in 0..3 ) {
$BB = $B1 * 2 + ( $B1 -lt $B2 )
$BW = $B2 * 2
$Start = [System.Collections.ArrayList]( '♖', '♔', '♖' )
$Start.Insert( $Q , '♕' )
$Start.Insert( $N1, '♘' )
$Start.Insert( $N2, '♘' )
$Start.Insert( $BB, '♗' )
$Start.Insert( $BW, '♗' )
$Starts += ,$Start
}}}}}
$Index = Get-Random 960 $StartString = $Starts[$Index] -join return $StartString }
Get-RandomChess960Start Get-RandomChess960Start Get-RandomChess960Start Get-RandomChess960Start </lang>
- Output:
♘♕♖♔♖♘♗♗ ♗♕♘♖♔♗♖♘ ♖♗♔♕♗♖♘♘ ♘♖♔♖♕♗♗♘
Python
Python: Indexing
This uses indexing rather than regexps. Rooks and bishops are in upper and lower case to start with so they can be individually indexed to apply the constraints. This would lead to some duplication of start positions if not for the use of a set comprehension to uniquify the, (upper-cased), start positions.
<lang python>>>> from itertools import permutations >>> pieces = 'KQRrBbNN' >>> starts = {.join(p).upper() for p in permutations(pieces)
if p.index('B') % 2 != p.index('b') % 2 # Bishop constraint
and ( p.index('r') < p.index('K') < p.index('R') # King constraint
or p.index('R') < p.index('K') < p.index('r') ) }
>>> len(starts) 960 >>> starts.pop() 'QNBRNKRB' >>></lang>
Python: Regexp
This uses regexps to filter permutations of the start position pieces rather than indexing. <lang python>>>> import re >>> pieces = 'KQRRBBNN' >>> bish = re.compile(r'B(|..|....|......)B').search >>> king = re.compile(r'R.*K.*R').search >>> starts3 = {p for p in (.join(q) for q in permutations(pieces))
if bish(p) and king(p)}
>>> len(starts3) 960 >>> starts3.pop() 'QRNKBNRB' >>></lang>
Python: Correct by construction
Follows Perl algorithm of constructing one start position randomly, according to the rules. (See talk page for tests). <lang python>from random import choice
def random960():
start = ['R', 'K', 'R'] # Subsequent order unchanged by insertions.
#
for piece in ['Q', 'N', 'N']:
start.insert(choice(range(len(start)+1)), piece)
#
bishpos = choice(range(len(start)+1))
start.insert(bishpos, 'B')
start.insert(choice(range(bishpos + 1, len(start) + 1, 2)), 'B')
return start
return .join(start).upper()
print(random960())</lang>
- Output:
['N', 'R', 'K', 'N', 'B', 'Q', 'R', 'B']
Python: Generate all positions then choose one randomly
<lang python>from random import choice
def generate960():
start = ('R', 'K', 'R') # Subsequent order unchanged by insertions.
# Insert QNN in all combinations of places
starts = {start}
for piece in ['Q', 'N', 'N']:
starts2 = set()
for s in starts:
for pos in range(len(s)+1):
s2 = list(s)
s2.insert(pos, piece)
starts2.add(tuple(s2))
starts = starts2
# For each of the previous starting positions insert the bishops in their 16 positions
starts2 = set()
for s in starts:
for bishpos in range(len(s)+1):
s2 = list(s)
s2.insert(bishpos, 'B')
for bishpos2 in range(bishpos+1, len(s)+2, 2):
s3 = s2[::]
s3.insert(bishpos2, 'B')
starts2.add(tuple(s3))
return list(starts2)
gen = generate960() print(.join(choice(gen)))</lang>
- Output:
NRBQNKRB
R
<lang rsplus> pieces <- c("R","B","N","Q","K","N","B","R")
generateFirstRank <- function() {
attempt <- paste0(sample(pieces), collapse = "")
while (!check_position(attempt)) {
attempt <- paste0(sample(pieces), collapse = "")
}
return(attempt)
}
check_position <- function(position) {
if (regexpr('.*R.*K.*R.*', position) == -1) return(FALSE)
if (regexpr('.*B(..|....|......|)B.*', position) == -1) return(FALSE)
TRUE
}
convert_to_unicode <- function(s) {
s <- sub("K","\u2654", s)
s <- sub("Q","\u2655", s)
s <- gsub("R","\u2656", s)
s <- gsub("B","\u2657", s)
s <- gsub("N","\u2658", s)
}
cat(convert_to_unicode(generateFirstRank()), "\n") </lang>
- Output:
♘♗♘♖♗♕♔♖
Racket
Constructive:
<lang racket>#lang racket (define white (match-lambda ['P #\♙] ['R #\♖] ['B #\♗] ['N #\♘] ['Q #\♕] ['K #\♔])) (define black (match-lambda ['P #\♟] ['R #\♜] ['B #\♝] ['N #\♞] ['Q #\♛] ['K #\♚]))
(define (piece->unicode piece colour)
(match colour ('w white) ('b black)) piece)
(define (find/set!-random-slot vec val k (f values))
(define r (f (random k)))
(cond
[(vector-ref vec r)
(find/set!-random-slot vec val k f)]
[else
(vector-set! vec r val)
r]))
(define (chess960-start-position)
(define v (make-vector 8 #f)) ;; Kings and Rooks (let ((k (find/set!-random-slot v (white 'K) 6 add1))) (find/set!-random-slot v (white 'R) k) (find/set!-random-slot v (white 'R) (- 7 k) (curry + k 1))) ;; Bishops -- so far only three squares allocated, so there is at least one of each colour left (find/set!-random-slot v (white 'B) 4 (curry * 2)) (find/set!-random-slot v (white 'B) 4 (compose add1 (curry * 2))) ;; Everyone else (find/set!-random-slot v (white 'Q) 8) (find/set!-random-slot v (white 'N) 8) (find/set!-random-slot v (white 'N) 8) (list->string (vector->list v)))
(chess960-start-position)</lang>
- Output:
"♖♘♗♕♔♗♘♖"
Well that's embarassing... the stupid thing has only gone and randomly generated a classic chess starting position.
Try again:
"♘♖♔♕♗♗♖♘"
REXX
Random starting position is correct by construction (both REXX entries).
generates one random position
<lang rexx>/*REXX program generates a random starting position for the Chess960 game. */ parse arg seed . /*allow for (RANDOM BIF) repeatability.*/ if seed\== then call random ,,seed /*if SEED was specified, use the seed.*/ @.=. /*define the first rank as being empty.*/ r1=random(1,6) /*generate the first rook: rank 1. */ @.r1='R' /*place the first rook on rank1. */
do until r2\==r1 & r2\==r1-1 & r2\==r1+1
r2=random(1,8) /*find placement for the 2nd rook. */
end /*forever*/
@.r2='r' /*place the second rook on rank 1. */ k=random(min(r1, r2)+1, max(r1, r2)-1) /*find a random position for the king. */ @.k='K' /*place king between the two rooks. */
do _=0 ; b1=random(1,8); if @.b1\==. then iterate; c=b1//2
do forever; b2=random(1,8) /* c=color of bishop ►──┘ */
if @.b2\==. | b2==b1 | b2//2==c then iterate /*is a bad position?*/
leave _ /*found position for the 2 clergy*/
end /*forever*/ /* [↑] find a place for the 1st bishop*/
end /* _ */ /* [↑] " " " " " 2nd " */
@.b1='B' /*place the 1st bishop on rank 1. */ @.b2='b' /* " " 2nd " " " " */
/*place the two knights on rank 1. */ do until @._='N'; _=random(1,8); if @._\==. then iterate; @._='N'; end do until @.!='n'; !=random(1,8); if @.!\==. then iterate; @.!='n'; end
_= /*only the queen is left to be placed. */
do i=1 for 8; _=_ || @.i; end /*construct the output: first rank only*/
say translate(translate(_, 'q', .)) /*stick a fork in it, we're all done. */</lang> output
NRQKBRNB
generates all 960 positions randomly
<lang rexx>/*REXX program generates all random starting positions for the Chess960 game. */ parse arg seed . /*allow for (RANDOM BIF) repeatability.*/ if seed\== then call random ,,seed /*if SEED was specified, use the seed.*/ x.=0; #=0; rg='random generations: ' /*initialize game placeholder; # games.*/
/*▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒*/
do t=1 /* [↓] display every 1,000 generations*/ /*▒*/ if t//1000==0 then say right(t,9) rg # " unique starting positions." /*▒*/ @.=. /*define the first rank as being empty.*/ /*▒*/ r1=random(1,6) /*generate the first rook: rank 1. */ /*▒*/ @.r1='R' /*place the first rook on rank1. */ /*▒*/
do until r2\==r1 & r2\==r1-1 & r2\==r1+1 /*▒*/
r2=random(1,8) /*find placement for the 2nd rook. */ /*▒*/
end /*forever*/ /*▒*/
@.r2='r' /*place the second rook on rank 1. */ /*▒*/ k=random(min(r1, r2)+1, max(r1, r2)-1) /*find a random position for the king. */ /*▒*/ @.k='K' /*place king between the two rooks. */ /*▒*/
do _=0 ; b1=random(1,8); if @.b1\==. then iterate; c=b1//2 /*▒*/
do forever; b2=random(1,8) /* c=color of bishop ►──┘ */ /*▒*/
if @.b2\==. | b2==b1 | b2//2==c then iterate /*is a bad position?*/ /*▒*/
leave _ /*found position for the 2 clergy*/ /*▒*/
end /*forever*/ /* [↑] find a place for the 1st bishop*/ /*▒*/
end /* _ */ /* [↑] " " " " " 2nd " */ /*▒*/
@.b1='B' /*place the 1st bishop on rank 1. */ /*▒*/ @.b2='b' /* " " 2nd " " " " */ /*▒*/
/*place the two knights on rank 1. */ /*▒*/ do until @._='N'; _=random(1,8); if @._\==. then iterate; @._='N'; end /*▒*/ do until @.!='n'; !=random(1,8); if @.!\==. then iterate; @.!='n'; end /*▒*/
_= /*only the queen is left to be placed. */ /*▒*/
do i=1 for 8; _=_ || @.i; end /*construct the output: first rank only*/ /*▒*/
upper _ /*uppercase all the chess pieces. */ /*▒*/ if x._ then iterate /*This position found before? Skip it.*/ /*▒*/ x._=1 /*define this position as being found. */ /*▒*/
- =#+1 /*bump the # of unique positions found,*/ /*▒*/
if #==960 then leave /*▒*/ end /*t ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒*/
say # 'unique starting positions found after ' t "generations."
/*stick a fork in it, we're all done. */ /**/</lang>
output
1000 random generations: 515 unique starting positions.
2000 random generations: 707 unique starting positions.
3000 random generations: 796 unique starting positions.
4000 random generations: 849 unique starting positions.
5000 random generations: 883 unique starting positions.
6000 random generations: 900 unique starting positions.
7000 random generations: 922 unique starting positions.
8000 random generations: 935 unique starting positions.
9000 random generations: 942 unique starting positions.
10000 random generations: 946 unique starting positions.
11000 random generations: 953 unique starting positions.
12000 random generations: 957 unique starting positions.
13000 random generations: 959 unique starting positions.
14000 random generations: 959 unique starting positions.
960 unique starting positions found after 14639 generations.
version 3 COMPUTE all possibilities
<lang rexx>/*---------------------------------------------------------------
- Compute the 960 possible solutions
- There must be at least one field between the rooks
- The king is positioned on any field between the rooks
- The queen is placed on any unoccupied field
- bishops are placed so that they are on different colored fields
- what remains are the kNights...
- --------------------------------------------------------------*/
cnt.=0 Call time 'R' Do r1=1 To 6
Do r2=r1+1 To 8
Do kk=r1+1 To r2-1
poss=space(translate('12345678',' ',r1||kk||r2),0)
Call rest
End
End
End
say cnt.1 'solutions' Say time('E') Exit
rest: Do i=1 To 5
q=substr(poss,i,1)
br=space(translate(poss,' ',q),0)
Do b1i=1 To 3
Do b2i=b1i+1 To 4
Call finish
End
End
End
Return
finish:
b1=substr(br,b1i,1) b2=substr(br,b2i,1) If (b1+b2)//2>0 Then Call out Return
out:
pos.='N'
pos.r1='R'
pos.r2='R'
pos.kk='K'
pos.q='Q'
pos.b1='B'
pos.b2='B'
ol=
Do k=1 To 8
ol=ol||pos.k
End
cnt.1=cnt.1+1
If cnt.1<4 |,
cnt.1>957 Then
Say format(cnt.1,3) poss r1 kk r2 ol
If cnt.1=4 Then
Say ' ...'
Return</lang>
- Output:
1 45678 1 2 3 RKRQBBNN
2 45678 1 2 3 RKRQBNNB
3 45678 1 2 3 RKRQNBBN
...
958 12345 6 7 8 BNNBQRKR
959 12345 6 7 8 NBBNQRKR
960 12345 6 7 8 NNBBQRKR
960 solutions
Ruby
Ruby: shuffle pieces until all regexes match
Translation of Tcl. <lang ruby>pieces = %i(♔ ♕ ♘ ♘ ♗ ♗ ♖ ♖) regexes = [/♗(..)*♗/, /♖.*♔.*♖/] row = pieces.shuffle.join until regexes.all?{|re| re.match(row)} puts row</lang>
- Output:
♕♖♗♘♔♖♘♗
Ruby: Construct
Uses the Perl idea of starting with [R,K,R] and inserting the rest: <lang ruby>row = [:♖, :♔, :♖] [:♕, :♘, :♘].each{|piece| row.insert(rand(row.size+1), piece)} [[0, 2, 4, 6].sample, [1, 3, 5, 7].sample].sort.each{|pos| row.insert(pos, :♗)}
puts row</lang>
- Output:
♗♘♕♘♖♗♔♖
Ruby: Generate from SP-ID
Chess960 numbering scheme <lang ruby>KRN = %w(NNRKR NRNKR NRKNR NRKRN RNNKR RNKNR RNKRN RKNNR RKNRN RKRNN)
def chess960(id=rand(960))
pos = Array.new(8)
q, r = id.divmod(4)
pos[r * 2 + 1] = "B"
q, r = q.divmod(4)
pos[r * 2] = "B"
q, r = q.divmod(6)
pos[pos.each_index.reject{|i| pos[i]}[r]] = "Q"
krn = KRN[q].each_char
pos.each_index {|i| pos[i] ||= krn.next}
pos.join
end
puts "Generate Start Position from id number" [0,518,959].each do |id|
puts "%3d : %s" % [id, chess960(id)]
end
puts "\nGenerate random Start Position" 5.times {puts chess960}</lang>
- Output:
Generate Start Position from id number 0 : BBQNNRKR 518 : RNBQKBNR 959 : RKRNNQBB Generate random Start Position RNBNKBRQ RKRNBBNQ BBRNQKNR NBRKNRBQ BRKQNNRB
Rust
<lang rust>use std::collections::BTreeSet;
struct Chess960 ( BTreeSet<String> );
impl Chess960 {
fn invoke(&mut self, b: &str, e: &str) {
if e.len() <= 1 {
let s = b.to_string() + e;
if Chess960::is_valid(&s) { self.0.insert(s); }
} else {
for (i, c) in e.char_indices() {
let mut b = b.to_string();
b.push(c);
let mut e = e.to_string();
e.remove(i);
self.invoke(&b, &e);
}
}
}
fn is_valid(s: &str) -> bool {
let k = s.find('K').unwrap();
k > s.find('R').unwrap() && k < s.rfind('R').unwrap() && s.find('B').unwrap() % 2 != s.rfind('B').unwrap() % 2
}
}
// Program entry point. fn main() {
let mut chess960 = Chess960(BTreeSet::new());
chess960.invoke("", "KQRRNNBB");
for (i, p) in chess960.0.iter().enumerate() {
println!("{}: {}", i, p);
}
}</lang>
Scala
Functional Programming, tail recursive, Unicode, RegEx
<lang Scala>import scala.annotation.tailrec
object Chess960 extends App {
private val pieces = List('♖', '♗', '♘', '♕', '♔', '♘', '♗', '♖')
@tailrec
private def generateFirstRank(pieces: List[Char]): List[Char] = {
def check(rank: String) =
rank.matches(".*♖.*♔.*♖.*") && rank.matches(".*♗(..|....|......|)♗.*")
val p = scala.util.Random.shuffle(pieces)
if (check(p.toString.replaceAll("[^\\p{Upper}]", "")))
generateFirstRank(pieces)
else p
}
loop(10)
@tailrec
private def loop(n: Int): Unit = {
println(generateFirstRank(pieces))
if (n <= 0) () else loop(n - 1)
}
}</lang>
- Output:
See it running in your browser by ScalaFiddle (JavaScript, non JVM) or by Scastie (JVM).
Imperative Programming
<lang scala>object Chess960 extends App {
private def apply(b: String, e: String) {
if (e.length <= 1) {
val s = b + e
if (is_valid(s)) patterns += s
} else
for (i <- 0 until e.length)
apply(b + e(i), e.substring(0, i) + e.substring(i + 1))
}
private def is_valid(s: String) = {
val k = s.indexOf('K')
if (k < s.indexOf('R')) false
else k < s.lastIndexOf('R') && s.indexOf('B') % 2 != s.lastIndexOf('B') % 2
}
private val patterns = scala.collection.mutable.SortedSet[String]()
apply("", "KQRRNNBB")
for ((s, i) <- patterns.zipWithIndex) println(s"$i: $s")
}</lang>
Scheme
<lang Scheme>(import (scheme base) (scheme write)
(srfi 1) ; list library
(srfi 27)) ; random numbers
(random-source-randomize! default-random-source)
- Random integer in [start, end)
(define (random-between start end)
(let ((len (- end start 1)))
(if (< len 2)
start
(+ start (random-integer len)))))
- Random item in list
(define (random-pick lst)
(if (= 1 (length lst)) (car lst) (list-ref lst (random-integer (length lst)))))
- Construct a random piece placement for Chess960
(define (random-piece-positions)
(define (free-indices positions) ; return list of empty slot indices
(let loop ((i 0)
(free '()))
(if (= 8 i)
free
(loop (+ 1 i)
(if (string=? "." (vector-ref positions i))
(cons i free)
free)))))
;
(define (place-king+rooks positions)
(let ((king-posn (random-between 1 8)))
(vector-set! positions king-posn "K")
; left-rook is between left-edge and king
(vector-set! positions (random-between 0 king-posn) "R")
; right-rook is between right-edge and king
(vector-set! positions (random-between (+ 1 king-posn) 8) "R")))
;
(define (place-bishops positions)
(let-values (((evens odds) (partition even? (free-indices positions))))
(vector-set! positions (random-pick evens) "B")
(vector-set! positions (random-pick odds) "B")))
;
(let ((positions (make-vector 8 ".")))
(place-king+rooks positions)
(place-bishops positions)
;; place the queen in a random remaining slot
(vector-set! positions (random-pick (free-indices positions)) "Q")
;; place the two knights in the remaining slots
(for-each (lambda (idx) (vector-set! positions idx "N"))
(free-indices positions))
positions))
(display "First rank: ") (display (random-piece-positions)) (newline) </lang>
- Output:
Ten sample runs:
First rank: #(R N N Q K R B B) First rank: #(R K N N Q R B B) First rank: #(Q R B N N B K R) First rank: #(Q R B N N K R B) First rank: #(R K N Q R B B N) First rank: #(R K N B Q R B N) First rank: #(R N K N B B R Q) First rank: #(R B K Q B N R N) First rank: #(B Q R N K N R B) First rank: #(R B B Q N N K R)
Seed7
<lang seed7>$ include "seed7_05.s7i";
const proc: main is func
local
var string: start is "RKR";
var char: piece is ' ';
var integer: pos is 0;
begin
for piece range "QNN" do
pos := rand(1, succ(length(start)));
start := start[.. pred(pos)] & str(piece) & start[pos ..];
end for;
pos := rand(1, succ(length(start)));
start := start[.. pred(pos)] & "B" & start[pos ..];
pos := succ(pos) + 2 * rand(0, (length(start) - pos) div 2);
start := start[.. pred(pos)] & "B" & start[pos ..];
writeln(start);
end func;</lang>
- Output:
NQBNRBKR
Sidef
<lang ruby>func is_valid_960 (backrank) {
var king = backrank.index('♚')
var (rook1, rook2) = backrank.indices_of('♜')...
king.is_between(rook1, rook2) || return false
var (bishop1, bishop2) = backrank.indices_of('♝')...
bishop1+bishop2 -> is_odd
}
func random_960_position(pieces = <♛ ♚ ♜ ♜ ♝ ♝ ♞ ♞>) {
pieces.shuffle.permutations {|*a|
return a if is_valid_960(a)
}
}
say random_960_position().join(' ')</lang>
- Output:
♝ ♝ ♜ ♚ ♞ ♛ ♜ ♞
Tcl
Using regular expressions to filter a random permutation.
<lang tcl>package require struct::list
proc chess960 {} {
while true {
set pos [join [struct::list shuffle {N N B B R R Q K}] ""] if {[regexp {R.*K.*R} $pos] && [regexp {B(..)*B} $pos]} { return $pos }
}
}
- A simple renderer
proc chessRender {position} {
string map {P ♙ N ♘ B ♗ R ♖ Q ♕ K ♔} $position
}
- Output multiple times just to show scope of positions
foreach - {1 2 3 4 5} {puts [chessRender [chess960]]}</lang>
- Output:
♕♖♘♔♗♗♘♖ ♖♔♘♘♗♕♖♗ ♘♖♗♗♕♔♘♖ ♘♕♗♖♔♖♘♗ ♘♘♖♔♗♗♕♖
Yabasic
<lang Yabasic>start$ = "RKR" piece$ = "QNN"
for piece = 1 to len(piece$)
pos = int(ran(len(start$) + 1)) + 1 start$ = left$(start$, pos-1) + mid$(piece$, piece, 1) + right$(start$, len(start$) - pos + 1)
next pos = int(ran(len(start$) + 1)) + 1 start$ = left$(start$, pos-1) + "B" + right$(start$, len(start$) - pos + 1) pos = pos + 1 + 2 * int(int(ran(len(start$) - pos)) / 2) start$ = left$(start$, pos-1) + "B" + right$(start$, len(start$) - pos + 1) print start$ </lang>
zkl
<lang zkl>const pieces="KQRrBbNN"; starts:=pieces:Utils.Helpers.permuteW(_).filter(fcn(p){
I:=p.index;
I("B") % 2 != I("b") % 2 and // Bishop constraint.
// King constraint.
((I("r") < I("K") and I("K") < I("R")) or
(I("R") < I("K") and I("K") < I("r")))
}).pump(List,"concat","toUpper"):Utils.Helpers.listUnique(_);</lang> <lang zkl>N:=starts.len(); println(N); glyphs:=Dictionary("K","\u2654", "Q","\u2655", "R","\u2656", "B","\u2657", "N","\u2658"); // pick some random starts and transform BBNRKQRN to glyphs do(10){ starts[(0).random(N)].apply(glyphs.find).println() }</lang>
- Output:
960 ♗♕♘♖♘♔♖♗ ♖♘♗♔♖♗♘♕ ♖♗♘♔♗♕♖♘ ♘♖♘♗♗♔♕♖ ♘♘♗♖♕♔♖♗ ♘♖♕♔♗♖♘♗ ♘♖♗♘♕♔♖♗ ♖♘♗♔♕♘♖♗ ♖♔♖♕♘♘♗♗ ♕♗♖♘♗♔♘♖
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