source code
program meteorshower;
{ The Computer Language Benchmarks Game
http://benchmarksgame.alioth.debian.org/
contributed by Daniel Mantione
modified by Vincent Snijders
}
uses dos;
const N_COL = 5;
N_ROW = 10;
N_CELL = N_COL * N_ROW;
N_PIECE_TYPE = 10;
N_ELEM=5;
N_ORIENT=12;
ALL_PIECE_MASK=[0..N_PIECE_TYPE-1];
SKIP_PIECE=5;
no_piece=high(byte);
L_EDGE_MASK=[0,5,10,15,20,25,30];
R_EDGE_MASK=[4,9,14,19,24,29];
TOP_ROW = [0*N_COL..1*N_COL-1];
SECOND_ROW = [1*N_COL..2*N_COL-1];
THIRD_ROW = [2*N_COL..3*N_COL-1];
FOURTH_ROW = [3*N_COL..4*N_COL-1];
FIFTH_ROW = [4*N_COL..5*N_COL-1];
SIXTH_ROW = [5*N_COL..6*N_COL-1];
LAST_ROW = SIXTH_ROW;
ROW_0_MASK=[0..N_COL-1,10..N_COL+10-1,20..N_COL+20-1,30,31];
ROW_1_MASK=[5..N_COL+5-1,15..N_COL+15-1,25..N_COL+25-1];
BOARD_MASK=[0..29];
type bitvec=set of 0..31;
dimensions=(dimx,dimy);
parity=(even,odd);
goodbad=(good,bad,always_bad);
piecenr=type 0..N_PIECE_TYPE-1;
orientation=type 0..N_ORIENT-1;
piece_placement=record
vec:bitvec;
ipiece:piecenr;
row:byte;
end;
type Soln=object
m_pieces:array[piecenr] of piece_placement;
m_npiece:byte;
m_cells:array[0..N_ROW-1,0..N_COL-1] of piecenr;
m_synched:boolean;
constructor init(fillval:byte);
procedure setCells;
function lessThan(var r:Soln):boolean;
procedure write(var f:text);
procedure fill(value:byte);
procedure spin(var spun:Soln);
function isEmpty:boolean;
procedure popPiece;inline;
procedure pushPiece(Avec:bitvec;AiPiece:piecenr;Arow:byte);
end;
instance=record
m_allowed:set of byte;
m_vec:bitvec;
m_offset:longint;
end;
TPts=array[0..N_ELEM-1,dimensions] of shortint;
piece=object
m_instance:array[parity] of instance;
procedure set_ok_positions(isOdd:parity;w,h:longint);
end;
OkPieces=record
nPieces:array[piecenr] of byte;
pieceVec:array[piecenr,orientation] of bitvec;
end;
type fixed=(OPEN, CLOSED);
islandinfo=record
has_bad:array[fixed,parity] of bitvec;
is_known:array[fixed,parity] of bitvec;
alwaysBad:array[parity] of bitvec;
end;
const MAX_ISLAND_OFFSET=1024;
type cacherec=record
krow,kpiecevec:word;
kboardvec:bitvec;
end;
var s_basePiece:array[piecenr,orientation] of piece;
g_okPieces:array[0..N_ROW-1,0..N_COL-1] of OkPieces;
g_islandInfo:array[0..MAX_ISLAND_OFFSET-1] of islandinfo;
g_nIslandInfo:cardinal=0;
cache:array[0..1024*128-1] of cacherec;
m_curSoln,m_minSoln,m_maxSoln:Soln;
m_nSoln:cardinal;
const basevecs:array [0..9] of bitvec= (
[0,1,2,3,8],
[0,1,3,6,7],
[0,1,2,7,12],
[0,1,2,5,10],
[0,2,5,6,10],
[0,1,2,6,7],
[0,1,5,10,15],
[0,1,2,5,7],
[0,1,2,7,8],
[0,1,2,3,7]
);
constructor soln.init(fillval:byte);
begin
fill(fillval);
end;
procedure Soln.fill(value:byte);
begin
m_synched:=false;
fillchar(m_cells,N_CELL,value);
end;
function soln.isEmpty:boolean;
begin
isempty:=m_nPiece=0;
end;
procedure soln.pushPiece(Avec:bitvec;AiPiece:piecenr;Arow:byte);
begin
with m_pieces[m_npiece] do
begin
vec:=Avec;
iPiece:=AiPiece;
row:=Arow;
end;
inc(m_npiece);
end;
procedure soln.popPiece;inline;
begin
dec(m_nPiece);
m_synched := false;
end;
procedure soln.write(var f:text);
var x,y:byte;
begin
for y:=0 to N_ROW-1 do
begin
{indent every second line}
if y mod 2=1 then
system.write(f,' ');
for x:=0 to N_COL-1 do
if m_cells[y,x]=no_piece then
system.write(f,'. ')
else
system.write(f,char(byte('0')+m_cells[y,x]),' ');
writeln(f);
end;
end;
procedure Soln.setCells;
var c,i,x,y,newcells:byte;
begin
if m_synched then
exit;
for i:=1 to m_nPiece do
with m_pieces[i-1] do
begin
newcells:=0;
c:=0;
for y:=row to N_ROW do
begin
for x:=0 to N_COL-1 do
begin
if c in vec then
begin
m_cells[y,x]:=ipiece;
inc(NewCells);
end;
inc(c);
end;
if NewCells=N_ELEM then
break;
end;
end;
m_synched:=true;
end;
function Soln.lessThan(var r:Soln):boolean;
var x,y,lval,rval:byte;
begin
if m_pieces[0].iPiece<>r.m_pieces[0].iPiece then
begin
lessthan:=m_pieces[0].iPiece < r.m_pieces[0].iPiece;
exit;
end;
setCells();
r.setCells();
for y:=0 to N_ROW-1 do
for x:=0 to N_COL-1 do
begin
lval:=m_cells[y,x];
rval:=r.m_cells[y,x];
if lval <> rval then
begin
lessthan:=lval<rval;
exit;
end;
end;
lessthan:=false; {solutions are equal}
end;
procedure Soln.spin(var spun:Soln);
var x,y:byte;
begin
setCells;
{swap cells}
for y:=0 to N_ROW-1 do
for x:=0 to N_COL-1 do
spun.m_cells[y,x]:=m_cells[N_ROW-y-1,N_COL-x-1];
{swap first and last pieces (the rest aren't used)}
spun.m_pieces[0].iPiece:=m_pieces[N_PIECE_TYPE-1].iPiece;
spun.m_synched:=true;
end;
function floor(top,bot:longint):longint;
begin
floor:=top div bot;
{negative numbers should be rounded down, not towards zero}
if (floor*bot<>top) and ((top<0) xor (bot<=0)) then
dec(floor);
end;
const s_firstOne:array[0..31] of byte=(
0, 0, 1, 0, 2, 0, 1, 0,
3, 0, 1, 0, 2, 0, 1, 0,
4, 0, 1, 0, 2, 0, 1, 0,
3, 0, 1, 0, 2, 0, 1, 0
);
function first_set_bit(v:bitvec):cardinal;inline;
{$ifdef endian_little}
const l=0;
h=1;
{$else}
const l=1;
h=0;
{$endif}
var d:double;
u:array[0..1] of bitvec absolute d;
begin
first_set_bit:=0;
if v<>[] then
begin
u[l]:=v;
u[h]:=[30,25,24,21,20];
d:=d-4503599627370496;
first_set_bit:=cardinal(u[h]) shr 20-$3ff;
end;
end;
function count_ones(v:bitvec):cardinal;inline;
begin
count_ones:=0;
while v<>[] do
begin
inc(count_ones);
cardinal(v):=cardinal(v) and (cardinal(v)-1);
end;
end;
procedure setCoordList(vec:bitvec;var pts:Tpts);
var iPt,n:longint;
x,y:byte;
begin
iPt:=0;
n:=0;
for y:=0 to N_ROW-1 do
for x:=0 to N_COL-1 do
begin
if n in vec then
begin
pts[iPt,dimx]:=x;
pts[iPt,dimy]:=y;
inc(iPt);
end;
inc(n);
if n=32 then
exit;
end;
end;
function toBitVector(const pts:Tpts):bitvec;
var x,y,iPt:byte;
begin
tobitvector:=[];
for iPt:=low(pts) to high(pts) do
begin
x:=pts[iPt,dimx];
y:=pts[iPt,dimy];
include(tobitvector,y*N_COL+x);
end;
end;
procedure shiftUpLines(var pts:Tpts;shift:longint);
var iPt:byte;
begin
{vertical shifts have a twist}
for iPt:=low(pts) to high(pts) do
begin
if pts[iPt,dimy] and shift and 1<>0 then
inc(pts[iPt,dimx]);
dec(pts[iPt,dimy],shift);
end;
end;
function shiftToX0(var pts:Tpts;var Ainstance:instance;offsetRow:longint):shortint;
var x,y,xmin,xmax,iPt,offset:shortint;
begin
{ .. determine shift}
xMin:=pts[0,dimx];
xMax:=xMin;
for iPt:=low(pts)+1 to high(pts) do
begin
x:=pts[iPt,dimx];
y:=pts[iPt,dimy];
if x<xMin then
xMin:=x
else if x > xMax then
xMax:=x;
end;
offset:=N_ELEM;
for iPt:=low(pts) to high(pts) do
begin
dec(pts[iPt,dimx],xMin);
{check offset -- leftmost cell on top line}
if (pts[iPt,dimy]=offsetRow) and (pts[iPt,dimx]<offset) then
offset:=pts[iPt,dimx];
end;
Ainstance.m_offset := offset;
Ainstance.m_vec := toBitVector(pts);
shifttox0:=xMax - xMin;
end;
function badregion(var to_fill:bitvec;rnew:bitvec):boolean;
var region,even_region,odd_region:bitvec;
cell_count:cardinal;
begin
{Grow empty region, until it doesn't change any more.}
repeat
region:=rnew;
even_region:=region*(ROW_0_MASK*([0..31]-L_EDGE_MASK));
odd_region:=region*(ROW_1_MASK*([0..31]-R_EDGE_MASK));
rnew:=to_fill*(rnew
{simple grow up/down}
+bitvec(cardinal(region) shr N_COL)
+bitvec(cardinal(region) shl N_COL)
{grow right/left}
+bitvec(cardinal(region) and not cardinal(L_EDGE_MASK) shr 1)
+bitvec(cardinal(region) and not cardinal(R_EDGE_MASK) shl 1)
{tricky growth}
+bitvec(cardinal(even_Region) shr (N_COL+1))
+bitvec(cardinal(even_Region) shl (N_COL-1))
+bitvec(cardinal(odd_Region) shr (N_COL-1))
+bitvec(cardinal(odd_Region) shl (N_COL+1))
);
until (rnew=to_fill) or (rnew=region);
{Subtract empty region from board.}
to_fill:=to_fill-rnew;
cell_count:=count_ones(to_fill);
{Optimize 'cell_count mod 5<>0' by hand...}
badregion:=cell_count<>((cell_count*$cccd) shr 18)*5;
end;
function has_bad_islands_single(boardVec:bitvec;row:longint):boolean;
var tofill,startregion,bmask:bitvec;
isodd:boolean;
begin
tofill:=[0..31]-boardvec;
isOdd:=row and 1<>0;
if isOdd then
begin
dec(row);
toFill:=bitvec(cardinal(tofill) shl N_COL); {shift to even aligned}
toFill:= tofill + TOP_ROW;
end;
startRegion := TOP_ROW;
bMask := BOARD_MASK; {all but the first two bits}
if row>=4 then
cardinal(bMask):=cardinal(bmask) shr ((row-4)*N_COL)
else if isOdd or (row = 0) then
startRegion := LAST_ROW;
toFill:=tofill*bMask;
startRegion:=startregion*toFill;
has_bad_islands_single:=true;
while toFill<>[] do
begin
if badRegion(toFill, startRegion) then
exit;
startRegion:=[first_set_bit(toFill)];
end;
has_bad_islands_single:=false;
end;
procedure piece.set_ok_positions(isOdd:parity;w,h:longint);
var x,y,xpos,pos:byte;
begin
pos:=byte(isodd)*N_COL;
with m_instance[isOdd] do
begin
m_allowed:=[];
y:=byte(isOdd);
while y<N_ROW-h do
begin
if m_offset<>0 then
inc(pos,m_offset);
for xPos:=0 to N_COL-1-m_offset do
begin
{check if the new position is on the board}
if (xPos<N_COL-w) and not has_bad_islands_single(bitvec(cardinal(m_vec) shl xPos),y) then
begin
{position is allowed}
include(m_allowed,pos);
end;
inc(pos);
end;
y:=y+2;
{Skip row with wrong parity:}
inc(pos,N_COL);
end;
end;
end;
procedure gen_orientation(vec:bitvec;iOrient:cardinal;var target:Piece);
var pts:Tpts;
x,y,ymin,ymax,h,w:shortint;
rot,iPt:byte;
flip:boolean;
begin
{get (x,y) coordinates}
setCoordList(vec, pts);
rot := iOrient mod 6;
flip := iOrient >= 6;
if flip then
for iPt:=0 to N_ELEM-1 do
pts[iPt,dimy]:=-pts[iPt,dimy];
{rotate as necessary}
while rot>0 do
begin
for iPt:=0 to N_ELEM-1 do
begin
x:=pts[iPt,dimx];
y:=pts[iPt,dimy];
pts[iPt,dimx]:=floor(2*x-3*y+1,4);
pts[iPt,dimy]:=floor(2*x+y+1,2);
end;
dec(rot);
end;
{determine vertical shift}
yMin := pts[0,dimy];
yMax := yMin;
for iPt:= 1 to N_ELEM-1 do
begin
y := pts[iPt,dimy];
if y < yMin then
yMin := y
else if y > yMax then
yMax := y;
end;
h:=yMax-yMin;
shiftUpLines(pts, yMin);
w := shiftToX0(pts, target.m_instance[EVEN], 0);
target.set_ok_positions(EVEN, w, h);
cardinal(target.m_instance[EVEN].m_vec) := cardinal(target.m_instance[EVEN].m_vec) shr target.m_instance[EVEN].m_offset;
{shift down one line}
shiftUpLines(pts, -1);
w := shiftToX0(pts, target.m_instance[ODD], 1);
{shift the bitmask back one line}
cardinal(target.m_instance[ODD].m_vec) :=cardinal(target.m_instance[ODD].m_vec) shr N_COL;
target.set_ok_positions(ODD, w, h);
cardinal(target.m_instance[ODD].m_vec):= cardinal(target.m_instance[ODD].m_vec) shr target.m_instance[ODD].m_offset;
end;
function getPiece(iPiece,iOrient:cardinal;iParity:parity):instance;inline;
begin
getpiece:=s_basePiece[iPiece][iOrient].m_instance[iParity];
end;
procedure gen_all_orientations;
var ipiece:piecenr;
iorient:orientation;
irow,icol:byte;
refpiece:bitvec;
n,npiece:byte;
begin
for iPiece:=low(ipiece) to high(ipiece) do
begin
refPiece:=BaseVecs[iPiece];
for iOrient:=low(iorient) to high(iorient) do
begin
gen_orientation(refPiece, iOrient, s_basePiece[iPiece,iOrient]);
with s_basePiece[iPiece,iOrient] do
begin
if (iPiece=SKIP_PIECE) and (iOrient in [3..5,9..11]) then
begin
m_instance[odd].m_allowed := [];
m_instance[even].m_allowed := [];
end;
end;
end;
end;
for iPiece:=low(ipiece) to high(ipiece) do
begin
for iOrient:=low(iorient) to high(iorient) do
begin
n:=0;
for iRow:=0 to N_ROW-1 do
begin
with getPiece(iPiece, iOrient, parity(iRow and 1)) do
for iCol:=0 to N_COL-1 do
begin
if n in m_allowed then
begin
nPiece:=g_okPieces[iRow,iCol].nPieces[iPiece];
g_okPieces[iRow,iCol].pieceVec[iPiece,nPiece]:=bitvec(cardinal(m_vec) shl iCol);
inc(g_okPieces[iRow,iCol].nPieces[iPiece]);
end;
inc(n);
end;
end
end
end
end;
procedure init_board;
begin
m_cursoln.init(NO_PIECE);
m_minsoln.init(NO_PIECE);
m_maxsoln.init(NO_PIECE);
m_nsoln:=0;
end;
const g_firstRegion:array[0..31] of bitvec=(
[], [0], [1], [0,1],
[2], [0], [1,2], [0,1,2],
[3], [0], [1], [0,1],
[2,3], [0], [1,2,3], [0,1,2,3],
[4], [0], [1], [0,1],
[2], [0], [1,2], [0,1,2],
[3,4], [0], [1], [1,2],
[2,3,4], [0], [1,2,3,4], [0,1,2,3,4]
);
function calc_bad_islands(boardVec:bitvec;row:longint):goodbad;
var tofill,boardmask,bottom,startregion:bitvec;
filled:boolean;
begin
toFill:=[0..31]-boardVec;
{Compensate for odd rows.}
if row and 1<>0 then
begin
dec(row);
cardinal(toFill):=cardinal(tofill) shl N_COL;
end;
boardMask := BOARD_MASK; {all but the first two bits}
if row>4 then
cardinal(boardMask):=cardinal(boardmask) shr ((row-4)*N_COL);
toFill:=tofill*boardMask;
{a little pre-work to speed things up}
filled:=toFill*LAST_ROW=LAST_ROW;
bottom:=LAST_ROW;
while bottom*toFill=bottom do
begin
toFill:=tofill-bottom;
cardinal(bottom):=cardinal(bottom) shr N_COL;
end;
if filled or (row<4) then
startRegion := bottom * toFill
else
begin
startRegion := g_firstRegion[cardinal(toFill*TOP_ROW)];
if startRegion=[] then
begin
startRegion := bitvec(cardinal(toFill) shr N_COL)*TOP_ROW;
startRegion := g_firstRegion[cardinal(startRegion)];
cardinal(startRegion) := cardinal(startregion) shl N_COL;
end;
startRegion:=startregion+bitvec(cardinal(startRegion) shl N_COL)*toFill;
end;
while toFill<>[] do
begin
if badRegion(toFill, startRegion) then
begin
if toFill<>[] then
calc_bad_islands:=ALWAYS_BAD
else
calc_bad_islands:=BAD;
exit;
end;
startRegion := [first_set_bit(toFill)];
end;
calc_bad_islands:=GOOD;
end;
function has_bad_islands(boardvec:bitvec;row:longint):goodbad;
var last_row:bitvec;
isodd:parity;
isclosed:fixed;
begin
{skip over any filled rows}
while boardVec*TOP_ROW=TOP_ROW do
begin
cardinal(boardVec):=cardinal(boardvec) shr N_COL;
inc(row);
end;
has_bad_islands:=bad;
with g_islandInfo[cardinal(boardvec*(TOP_ROW+SECOND_ROW))] do
begin
last_row:=bitvec(cardinal(boardvec) shr (2*N_COL))*TOP_ROW;
isOdd:=parity(row and 1);
if not(cardinal(last_row) in alwaysBad[parity(row and 1)]) then
if boardVec*bitvec(cardinal(cardinal(TOP_ROW) shl N_COL*3))=[] then
begin
isClosed:=fixed(row>6); {because we track 3 rows}
if not(cardinal(last_row) in is_known[isClosed,isOdd]) then
if boardVec<>[] then
begin
has_bad_islands:=calc_bad_islands(boardvec,row);
include(is_known[isClosed,isOdd],cardinal(last_row));
if has_bad_islands<>good then
include(is_known[isClosed,isOdd],cardinal(last_row));
end
else
has_bad_islands:=good
else
if not(cardinal(last_row) in has_bad[isClosed,isOdd]) then
has_bad_islands:=good;
end
else
has_bad_islands:=calc_bad_islands(boardvec,row);
end;
end;
const g_flip:array[0..31] of bitvec=(
[], [4], [3], [3,4],
[2], [2,4], [2,3], [2,3,4],
[1], [1,4], [1,3], [1,3,4],
[1,2], [1,2,4], [1,2,3], [1,2,3,4],
[0], [0,4], [0,3], [0,3,4],
[0,2], [0,2,4], [0,2,3], [0,2,3,4],
[0,1], [0,1,4], [0,1,3], [0,1,3,4],
[0,1,2], [0,1,2,4], [0,1,2,3], [0,1,2,3,4]
);
function flipTwoRows(bits:bitvec):bitvec;inline;
var flipped:cardinal;
begin
flipped:=cardinal(g_flip[cardinal(bits) shr N_COL]) shl N_COL;
fliptworows:=bitvec(flipped or cardinal(g_flip[cardinal(bits*TOP_ROW)]));
end;
procedure mark_bad(var info:IslandInfo;n:byte;eo:parity;always:boolean);inline;
begin
with info do
begin
include(has_bad[OPEN,eo],n);
include(has_bad[CLOSED,eo],n);
if always then
include(alwaysBad[eo],n);
end;
end;
procedure calc_always_bad;
var i,iWord:cardinal;
boardvec:bitvec;
hasbad:goodbad;
always:boolean;
flipped:^islandinfo;
begin
for iWord:=1 to MAX_ISLAND_OFFSET-1 do
begin
flipped := @g_islandInfo[cardinal(flipTwoRows(bitvec(iWord)))];
for i:=0 to 31 do
begin
boardvec:=bitvec((i shl (2*N_COL)) or iWord);
if not(i in g_islandInfo[iWord].is_known[OPEN,EVEN]) then
begin
hasBad:=calc_bad_islands(boardvec,0);
if hasBad<>good then
begin
always:=hasBad=ALWAYS_BAD;
mark_bad(g_islandInfo[iWord], i, EVEN, always);
mark_bad(flipped^,cardinal(g_flip[i]), ODD, always);
end;
end;
end;
flipped^.is_known[OPEN,odd]:=[0..31];
g_islandInfo[iWord].is_known[OPEN,even]:=[0..31];
end
end;
procedure record_solution(var s:Soln);
var spun:soln;
begin
s.setcells;
inc(m_nSoln,2); {add solution and its rotation}
if m_minSoln.isEmpty then
begin
m_minSoln := s;
m_maxSoln := s;
exit;
end;
if s.lessThan(m_minSoln) then
m_minSoln := s
else if m_maxSoln.lessThan(s) then
m_maxSoln := s;
s.spin(spun);
if spun.lessThan(m_minSoln) then
m_minSoln := spun
else if m_maxSoln.lessThan(spun) then
m_maxSoln := spun;
end;
function gen_all_solutions(boardVec,placedPieces:bitvec;row:byte):cardinal;
var ipiece:piecenr;
iorient:byte;
piece:bitvec;
begin
while boardVec*TOP_ROW=TOP_ROW do
begin
cardinal(boardVec):=cardinal(boardvec) shr N_COL;
inc(row);
end;
gen_all_solutions:=0;
with cache[((cardinal(boardvec)*
(cardinal(placedpieces) {shl 3} + 1)
xor row shl 5)) mod 131071] do
if (krow<>row) or (bitvec(cardinal(kpiecevec))<>placedpieces) or (kboardvec<>boardvec) then
begin
with g_okpieces[row,s_firstOne[cardinal([0..N_COL-1]-boardVec)]] do
for ipiece:=0 to N_PIECE_TYPE-1 do
if not(ipiece in placedpieces) then
for iorient:=1 to npieces[ipiece] do {start with 1, npieces[x] can be zero}
begin
piece:=pieceVec[iPiece,iOrient-1];
{check if piece conflicts with other pieces or if we get a bad island.}
if (piece*boardVec=[]) and (has_bad_islands(boardVec+piece,row)=good) then
begin
m_curSoln.pushPiece(piece,iPiece,row);
{recurse or record solution}
if placedPieces+[ipiece]<>ALL_PIECE_MASK then
inc(gen_all_solutions,gen_all_solutions(boardVec+piece,placedPieces+[ipiece],row))
else
begin
record_solution(m_curSoln);
inc(gen_all_solutions);
end;
m_curSoln.popPiece();
end;
end;
if gen_all_solutions=0 then
begin
krow:=row;
kpiecevec:=word(cardinal(placedpieces));
kboardvec:=boardvec;
end;
end;
end;
begin
if paramcount > 2 then
halt(1); {spec says this is an error}
textrec(output).flushfunc:=nil;
gen_all_orientations;
calc_always_bad;
init_board;
filldword(cache,sizeof(cache) shr 2,$ffffffff);
gen_all_solutions([], [], 0);
writeln(m_nSoln,' solutions found');
writeln;
m_minSoln.write(output);
writeln;
m_maxSoln.write(output);
writeln;
end.