function [moves, vine] = solver(board, limit)
[m,n] = size(board);
% Gwendolyn's neat board-tuning
if limit > 0
original = board;
board(board<median(board(:))/114)=0;
end
%Allocate result cell
resultcell(:,3) = num2cell(-inf(10,1));
id = reshape( 1:m*n, m, n);
limitlimit = 15100;
if limit < limitlimit
[resultcell{1,1}, resultcell{1,2}, resultcell{1,3}] = alfi(rot90(board,3), limit);
idtemp = rot90(id,3);
resultcell{1,1} = idtemp(resultcell{1,1});
resultcell{1,2} = idtemp(resultcell{1,2});
end
largestValue = max(board(:));
if largestValue > 200
if limit > 0
[movestemp, vinetemp, resultcell{2,3}] = robert(fliplr(board),limit); % monotonous should work good on flipping lr/ud as well
idtemp = fliplr(id);
resultcell{2,1} = idtemp(movestemp);
resultcell{2,2} = idtemp(vinetemp);
[movestemp, vinetemp, resultcell{3,3}] = robert((board),limit);
idtemp = (id);
resultcell{3,1} = idtemp(movestemp);
resultcell{3,2} = idtemp(vinetemp);
[movestemp, vinetemp, resultcell{10,3}] = robert(flipud(board),limit);
idtemp = flipud(id);
resultcell{10,1} = idtemp(movestemp);
resultcell{10,2} = idtemp(vinetemp);
[resultcell{9,1}, resultcell{9,2}, resultcell{9,3}] = dofilter(board,limit);
end
doclusters=any(any(board(:,2:end)==board(:,1:end-1)))||any(any(board(1:end-1,:)==board(2:end,:))); %%%%
if doclusters && limit<numel(board)
[resultcell{4,2}, resultcell{4,3}] = real_kurt(board);
end
[resultcell{5,1}, resultcell{5,2}, resultcell{5,3}] = nick(board,limit);
[movestemp, vinetemp, resultcell{7,3}] = nick(rot90(board,2),limit);
idtemp = rot90(id,2);
resultcell{7,1} = idtemp(movestemp);
resultcell{7,2} = idtemp(vinetemp);
if max(cell2mat(resultcell([5 7],3))) < 2 * max(cell2mat(resultcell([1 2 3 4 9 10],3)))
[movestemp, vinetemp, resultcell{6,3}] = nick(board',limit);
idtemp = id';
resultcell{6,1} = idtemp(movestemp);
resultcell{6,2} = idtemp(vinetemp);
[movestemp, vinetemp, resultcell{8,3}] = nick(rot90(board,3),limit);
idtemp = rot90(id,3);
resultcell{8,1} = idtemp(movestemp);
resultcell{8,2} = idtemp(vinetemp);
end
end
[~,best_index]=max(cell2mat(resultcell(:,3)));
moves = resultcell{best_index,1};
vine = resultcell{best_index,2};
if size(moves,1) < limit
[moves, vine] = use_more_moves(board, moves, vine, limit);
end
if limit > 0 && any(board(:) ~= original(:))
[moves, vine] = robert3(original, moves, vine, limit);
end
end
%% nick
function [moves, vine, scr] = nick(board, limit)
moves = zeros(limit,2);
[m,n] = size(board);
ntot = m*n;
if limit < m-1
scr = -inf;
moves = [];
vine = [];
return;
end;
xg = repmat(1:n,m,1);
yg = repmat((1:m)',1,n);
pos = reshape(1:ntot,m,n);
fitloc = pos;
fitloc(:,2:2:end) = flipud(fitloc(:,2:2:end));
[s,r] = sort(board(:),'descend');
% [s,r] = sort(-board(:)); % is this construct really faster on
% s=-s; % TMW's machine...?
myRank = zeros(m,n);
myRank(r) = pos;
remain = true(1,ntot);
nextfit = 1;
steps = 0;
cboard = board;
for ii = 1:ntot
if remain(ii)
[cy,cx] = find(myRank==ii);
tx = xg(fitloc(nextfit));
ty = yg(fitloc(nextfit));
[cboard,moves,remain,myRank,steps] = oftl2(cx,tx,cy,ty,cboard,myRank,steps,moves,pos,remain,n,m,limit,s,ii);
if steps > limit
break
end
myRank(ty,tx) = ii;
nextfit = nextfit+1;
end
end
moves = moves(1:min(steps,limit),:);
[vine,scr] = real_kurt(cboard);
end
%% michael
% http://www.mathworks.com/matlabcentral/contest/contests/34/submissions/64578
function [moves, vine] = use_more_moves(board, moves, vine, limit)
m = size(board,1);
for i = 1:size(moves,1)
board(moves(i,:)) = [0 board(moves(i,1))];
end
extra_moves = limit - size(moves,1);
%% Uncomment to get this running with TMW's
%% test environment.
%% Comment it out prior to submission. :-/
% tmp = max(board(vine));
% if ~isempty(tmp)
% larger_i = find(board >= tmp);
% larger_i = larger_i( ~ismemberSimpl(larger_i, vine) ); % setdiff( larger_i, vine )
% else
% larger_i = [];
% end
larger_i = find(board >= max(board(vine)));
larger_i = larger_i( ~ismemberSimpl(larger_i, vine) ); % setdiff( larger_i, vine )
if ~isempty(larger_i)
end_row = mod(vine(end)-1,m)+1;
end_col = ceil(vine(end)/m);
larger_rows = mod(larger_i-1,m)+1;
larger_cols = ceil(larger_i/m);
moves_req = abs(end_row - larger_rows) + abs(end_col - larger_cols) - 1;
msk = moves_req < extra_moves;
possible_moves = larger_i( msk );
moves_req = moves_req( msk );
while ~isempty(possible_moves) && extra_moves > 0
[~, sort_i] = sort(moves_req);
possible_moves = possible_moves(sort_i);
test_move = possible_moves(1);
test_row = mod(test_move-1,m)+1;
test_col = ceil(test_move/m);
move_cols = test_col(ones(1, 1+abs(end_row-test_row)));
if end_row > test_row
move_rows = test_row:end_row;
elseif end_row < test_row
move_rows = test_row:-1:end_row;
else
move_rows = [];
move_cols = [];
end
if end_col == test_col
move_rows(end) = [];
move_cols(end) = [];
elseif end_col > test_col
move_cols = [move_cols, test_col+1:end_col-1];
move_rows = [move_rows, end_row(ones(1, end_col-test_col-1))];
else
move_cols = [move_cols, test_col-1:-1:end_col+1];
move_rows = [move_rows, end_row(ones(1, test_col-end_col-1))];
end
add_moves = move_cols(:)*m + move_rows(:) - m;
add_moves = [add_moves(1:end-1), add_moves(2:end)];
if any( ismemberSimpl(add_moves(:),vine) )
possible_moves(1) = [];
moves_req(1) = [];
else
moves = [moves; add_moves];
extra_moves = limit - size(moves,1);
vine = [vine, moves(end,2)];
for i = 1:size(add_moves,1)
board(add_moves(i,:)) = [0 board(add_moves(i,1))];
end
end_row = mod(vine(end)-1,m)+1;
end_col = ceil(vine(end)/m);
larger_i = find(board >= max(board(vine)));
larger_i = larger_i( ~ismemberSimpl(larger_i, vine) ); % setdiff( larger_i, vine )
larger_rows = mod(larger_i-1,m)+1;
larger_cols = ceil(larger_i/m);
moves_req = abs(end_row - larger_rows) + abs(end_col - larger_cols) - 1;
msk = moves_req < extra_moves;
possible_moves = larger_i(msk);
moves_req = moves_req(msk);
end
end
end
end
function [cboard,moves,remain,rank,steps]=oftl2(cx,tx,cy,ty,cboard,rank,steps,moves,pos,remain,ncol,nrow,limit,s,i)
while (cx~=tx)||(cy~=ty)
dx = sign(tx-cx);
dy = sign(ty-cy);
if (dx~=0)&&(dy~=0)
correction = cboard(cy,cx+dx)<=cboard(cy+dy,cx);
dy = dy*(1-correction);
dx = dx*correction;
end
if (rank(cy+dy,cx+dx)>0)
vx = cx+dx;
vy = cy+dy;
if (dx==0)
[steps,moves,cboard,rank,remain,breakmarker]=oftl5(steps,limit,moves,pos,vy,vx,cboard,rank,remain,1,0,vx,ncol,cy,dy,cx,dx);
else
[steps,moves,cboard,rank,remain,breakmarker]=oftl5(steps,limit,moves,pos,vy,vx,cboard,rank,remain,0,1,vy,nrow,cy,dy,cx,dx);
end;
if breakmarker
break
end
end;
steps = steps+1;
if (steps > limit)
break
end;
moves(steps,1) = pos(cy,cx);
moves(steps,2) = pos(cy+dy,cx+dx);
cboard(cy+dy,cx+dx) = s(i); %cboard(cy,cx);
cboard(cy,cx) = 0;
rank(cy,cx) = 0;
cx = cx+dx;
cy = cy+dy;
end;
end
function [steps,moves,cboard,rank,remain,breakmarker]=oftl5(steps,limit,moves,pos,vy,vx,cboard,rank,remain,stepx,stepy,v_main,n_main,cy,dy,cx,dx)
if v_main > 1 && cboard(vy,vx)>cboard(vy-(stepy~=0),vx-(stepx~=0)) && ( v_main==n_main || (cboard(vy+(stepy~=0),vx+(stepx~=0))>cboard(vy-(stepy~=0),vx-(stepx~=0))) )
[steps,moves,cboard,rank,remain,breakmarker]=oftl3(steps,limit,moves,pos,vy,vx,cboard,rank,remain,-stepx,-stepy);
elseif (v_main < n_main)&&(cboard(vy,vx)>cboard(vy+(stepy~=0),vx+(stepx~=0)))
[steps,moves,cboard,rank,remain,breakmarker]=oftl3(steps,limit,moves,pos,vy,vx,cboard,rank,remain,stepx,stepy);
else
remain(rank(cy+dy,cx+dx)) = 0;
breakmarker = 0;
end;
end
function [steps,moves,cboard,rank,remain,breakmarker]=oftl3(steps,limit,moves,pos,vy,vx,cboard,rank,remain,stepx,stepy)
steps = steps+1;
if (steps > limit)
breakmarker = 1;
else
breakmarker = 0;
moves(steps,1) = pos(vy,vx);
moves(steps,2) = pos(vy+stepy,vx+stepx);
cboard(vy+stepy,vx+stepx) = cboard(vy,vx);
cboard(vy,vx) = 0;
if (rank(vy+stepy,vx+stepx)>0)
remain(rank(vy+stepy,vx+stepx)) = 0;
end;
rank(vy+stepy,vx+stepx) = rank(vy,vx);
rank(vy,vx) = 0;
end
end
function [moves,vine,scr] = dofilter(board,limit)
[nrow,ncol] = size(board);
ntot = nrow*ncol;
moves = zeros(limit,2);
nmove = 0;
pos = reshape(1:ntot,nrow,ncol);
m1 = median(board,1);
m2 = median(board,2);
if (sum(sign(diff(m1)))>0.67*ncol)||(sum(sign(diff(m2)))>0.67*nrow)||(sum(sign(diff(m2)))<-0.67*nrow)||(sum(sign(diff(m2)))<-0.67*nrow)
d = diff(board,1,2);
mb = median(board,2);
md = median(d,2);
rmb = repmat(mb,1,ncol);
rmd = repmat(md,1,ncol);
guess = rmb+kron(md,-(ncol-1)/2:(ncol-1)/2);
bad = (abs(board-guess)>20*abs(rmd));
for i = nrow:-1:1
[nmove,moves]=oftl6(i,ncol,bad,moves,nmove,limit,pos);
if (nmove>=limit)
break
end;
end;
moves = moves(1:min(nmove,limit),:);
for i = 1:size(moves,1)
board(moves(i,:)) = [0 board(moves(i,1))];
end;
[vine,scr] = SimpleLongestPath(board);
else
scr = -inf;
moves = [];
vine = [];
end
end
function [nmove,moves]=oftl6(i,ncol,bad,moves,nmove,limit,pos)
offset = 0;
for j = ceil(ncol/2):ncol
if bad(i,j)
offset = offset+1;
else
moves(nmove+1:nmove+offset,:) = [pos(i,j:-1:j-offset+1)' pos(i,j-1:-1:j-offset)'];
nmove = nmove+offset;
if (nmove>=limit)
break
end;
end;
end;
offset = 0;
for j = ceil(ncol/2):-1:1
if bad(i,j)
offset = offset+1;
else
moves(nmove+1:nmove+offset,:) = [pos(i,j:1:j+offset-1)' pos(i,j+1:1:j+offset)'];
nmove = nmove+offset;
if (nmove>=limit)
break
end;
end;
end;
end
%% alfi
function [moves, vine, gain] = alfi(board, limit)
moves=[];
ab=accumarray(1+board(:),1);
cab=flipud(cumsum(flipud(ab)))-ab(end);
m = size(board,1) + 2;
n = size(board,2) + 2;
board2 = zeros( m, n );
board2(2:end-1,2:end-1) = board;
board = board2;
board2 = [];
boardab=cab(1+board);
if max(ab(2:end))>1,
% compute same-valued clusters
[BoardCluster,ClusterValue,IdxList,IdxSegments,Nclusters] = connected(board);
ClusterSize = diff(IdxSegments);
ClusterNeighb = neighb(BoardCluster,board,Nclusters);
% search between-clusters
ClustersOrder = bellman(ClusterNeighb,ClusterValue(:).*sqrt(ClusterSize(:)));
% search within-clusters
iC=bellman_postprocess(ClustersOrder,IdxList,IdxSegments,BoardCluster);
else
% search between-pixels
% iC = bellman_pixel(board,limit,boardab);
iC = SimpleLongestPath( board );
iC = fliplr(iC);
iC = iC(board(iC)>0);
end
% post-processing moves
if limit>0
[board,iC,moves,limit] = postprocess(board,iC,moves,limit,boardab);
% [iC1,iC2]=ind2sub([m,n],moves);
iC1=rem(moves-1,m)+1;
iC2=(moves-iC1)/m+1;
% moves=sub2ind([m-2,n-2],iC1-1,iC2-1);
moves=iC1-1+(m-2)*(iC2-2);
end
%[iC1,iC2]=ind2sub([m,n],iC);
iC1=rem(iC-1,m)+1;
iC2=(iC-iC1)/m+1;
%vine=sub2ind([m-2,n-2],iC1-1,iC2-1);
vine=iC1-1+(m-2)*(iC2-2);
vine=fliplr(vine);
board=board(2:end-1,2:end-1);
gain=sum(board(vine));
end
function [board,tiC,moves,limit] = postprocess(board,tiC,moves,limit,boardab)
[m,n]=size(board);
nC=numel(tiC);
tP=board>0;
maxIter = 1e2;
if nC>1&&limit>0, %%%
% grow laterally
d=abs(diff(tiC))==1;
E=[m*~d+d; m*d+~d];
BorderUp={repmat(1+(0:n-1)*m,[m,1]),repmat((1:m)',[1,n])};
BorderDown={repmat(m+(0:n-1)*m,[m,1]),repmat(m*(n-1)+(1:m)',[1,n])};
% tP=board>0;
tP(tiC)=false;
for n1=1:maxIter
[board,moves,tiC,tP,E,limit,ok]=postprocess_lateral(board,moves,tiC,tP,E,limit,BorderDown,BorderUp,m);
if ~ok, break; end
end
end
if limit>0
% grow end-points
% tP=board>0;
tP(tiC)=false;
for n1=1:maxIter
[board,moves,tiC,tP,limit,ok]=postprocess_endpoint(board,moves,tiC,tP,limit,1,m,n);
if ~ok, break; end
end
for n1=1:10*maxIter
[board,moves,tiC,tP,limit,ok]=postprocess_endpoint(board,moves,tiC,tP,limit,2,m,n);
if ~ok, break; end
end
end
end
function [board,moves,tiC,tP,E,limit,ok]=postprocess_lateral(board,moves,tiC,tP,E,limit,BorderDown,BorderUp,m)
ok=0;
for ndir=1:4
offset = ndir>2.5;
coeff = (2*mod(ndir,2)-1);
K=size(tiC,2);
idx1=find(tP(tiC((1+offset):2:K-1)+coeff*E(2,(1+offset):2:K-1))&tP(tiC((2+offset):2:K)+coeff*E(2,(1+offset):2:K-1)));
for n2=numel(idx1):-1:1, %%%
switch(ndir)
case {1,3}
tempA=tiC(2*idx1(n2)-1+offset)+E(2,2*idx1(n2)-1+offset):E(2,2*idx1(n2)-1+offset):BorderDown{1+(E(2,2*idx1(n2)-1+offset)==m)}(tiC(2*idx1(n2)-1+offset));
tempB=tiC(2*idx1(n2)+offset)+E(2,2*idx1(n2)-1+offset):E(2,2*idx1(n2)-1+offset):BorderDown{1+(E(2,2*idx1(n2)-1+offset)==m)}(tiC(2*idx1(n2)+offset));
case {2,4}
tempA=tiC(2*idx1(n2)-1+offset)-E(2,2*idx1(n2)-1+offset):-E(2,2*idx1(n2)-1+offset):BorderUp{1+(E(2,2*idx1(n2)-1+offset)==m)}(tiC(2*idx1(n2)-1+offset));
tempB=tiC(2*idx1(n2)+offset)-E(2,2*idx1(n2)-1+offset):-E(2,2*idx1(n2)-1+offset):BorderUp{1+(E(2,2*idx1(n2)-1+offset)==m)}(tiC(2*idx1(n2)+offset));
end
idxZ=find(~tP(tempA),1,'first');
[nill,idxA]=max((1./(abs(board(tiC(2*idx1(n2)-1+offset))-board(tempA))+1)).*(board(tiC(2*idx1(n2)-1+offset))>=board(tempA)&board(tempA)>=board(tiC(2*idx1(n2)+offset))));
if ~nill,idxA=[]; end
if ~isempty(idxA)&&idxA<idxZ
idxZ=find(~tP(tempB),1,'first');
idxB=find(board(tempA(idxA))>=board(tempB)&board(tempB)>=board(tiC(2*idx1(n2)+offset)),1,'first');
if ~isempty(idxB)&&idxB<idxZ&&idxA+idxB-2<=limit
ok=1;
tiC=[tiC(1:2*idx1(n2)-1+offset),tiC(2*idx1(n2)-1+offset)+coeff*E(2,2*idx1(n2)-1+offset), tiC(2*idx1(n2)+offset)+coeff*E(2,2*idx1(n2)-1+offset), tiC((2*idx1(n2)+offset):end)];
E=[E(:,1:2*idx1(n2)-2),E([2,1],2*idx1(n2)-1), E([1,2],2*idx1(n2)-1), E([2,1],2*idx1(n2)-1), E(:,2*idx1(n2):end)];
tP(tiC)=false;
newmoveA=[tempA(2:idxA)',tempA(1:idxA-1)'];
newmoveB=[tempB(2:idxB)',tempB(1:idxB-1)'];
board(newmoveA(:,2))=board(tempA(idxA));
board(newmoveB(:,2))=board(tempB(idxB));
board(newmoveA(:,1))=0;
board(newmoveB(:,1))=0;
moves=[moves;flipud(newmoveA);flipud(newmoveB)];
limit=limit-size(newmoveA,1)-size(newmoveB,1);
end
end
end
end
end
function [board,moves,tiC,tP,limit,ok]=postprocess_endpoint(board,moves,tiC,tP,limit,type,m,n)
%[m,n]=size(board);
ok=1;
switch(type)
case 1
mask=tP&board<2*board(tiC(1));
D=Dijkstra(mask,tiC(1),m,n);
idx1=find(mask&D-1<=limit&board>=board(tiC(1)));
if isempty(idx1),
mask=tP;
D=Dijkstra(mask,tiC(1),m,n);
idx1=find(mask&D-1<=limit&board>=board(tiC(1)));
if isempty(idx1),ok=0;end
end
if ok
if limit>150
[~,idx2]=min(board(idx1)+1e-3*D(idx1)); %%%t3
else
[~,idx2]=min(board(idx1).*(D(idx1)/limit).^0.2); %%%t3
end
idx0=idx1(idx2);
limit=limit-(D(idx0)-1);
for n2=D(idx0)-1:-1:1
tidx0 = idx0 + (D(idx0+1)==n2) + (~(D(idx0+1)==n2))*(-(D(idx0-1)==n2)+(~(D(idx0-1)==n2))*(m*(D(idx0+m)==n2)+(~(D(idx0+m)==n2))*(-m*(D(idx0-m)==n2))));
moves=[moves; idx0, tidx0];
board(tidx0)=board(idx0);
board(idx0)=0;
idx0=tidx0;
end
tiC=[idx0,tiC];
tP(idx0)=false;
end
case 2
mask=tP;
D=Dijkstra(mask,tiC(end),m,n);
idx1=find(mask&D-1<=limit&board<=board(tiC(end))&board>0);
if isempty(idx1),ok=0;end
if ok
if limit>300
[~,idx2]=min(-board(idx1)+1e-3*D(idx1)); %%%t3
else
[~,idx2]=min(-board(idx1).*(limit./D(idx1)).^0.085); %%%t3
end
idx0=idx1(idx2);
limit=limit-(D(idx0)-1);
for n2=D(idx0)-1:-1:1
tidx0 = idx0 + (D(idx0+1)==n2) + (~(D(idx0+1)==n2))*(-(D(idx0-1)==n2)+(~(D(idx0-1)==n2))*(m*(D(idx0+m)==n2)+(~(D(idx0+m)==n2))*(-m*(D(idx0-m)==n2))));
moves=[moves; idx0, tidx0];
board(tidx0)=board(idx0);
board(idx0)=0;
idx0=tidx0;
end
tiC=[tiC,idx0];
tP(idx0)=false;
end
end
end
function iC = bellman(C,D)
N=size(C,1);
c=cell(1,N); for n1=1:N,c{n1}=find(C(:,n1)); end
%C=full(C);
IDX=zeros(N,1);
cD=D;
touched=true(1,N);
while any(touched)
for touch=find(touched),
touched(touch) = false;
idx = c{touch};
cDnew = D(idx) + cD(touch);
idx2 = (cD(idx)<cDnew);
if any(idx2(:))
idx = idx(idx2);
cD(idx) = cDnew(idx2);
touched(idx) = true;
IDX(idx) = touch;
end
end
end
[~,idx]=max(cD);
iC=zeros(N,1);
for n1=1:N,
if idx>0
iC(n1)=idx;
idx=IDX(idx);
else
break
end
end
iC=iC(1:n1-1);
end
function iC = bellman_postprocess(ClustersOrder,IdxList,IdxSegments,BoardCluster)
[m,n]=size(BoardCluster);
iC=[];
false1N = false(1,n);
falseM1 = false(m,1);
falseMN = false(m,n);
for n1=1:numel(ClustersOrder)
idx=IdxList(IdxSegments(ClustersOrder(n1)):IdxSegments(ClustersOrder(n1)+1)-1);
if numel(idx)==1
iC=[iC,idx(1)];
else
% longest shortest-path
ThisCluster=falseMN;
ThisCluster(idx)=true;
D=Dijkstra(ThisCluster,iC,m,n);
if n1==numel(ClustersOrder)
temp=D(ThisCluster);
else
temp=D(ThisCluster).*(BoardCluster([false1N;ThisCluster(1:m-1,:)])==ClustersOrder(n1+1)|BoardCluster([ThisCluster(2:m,:);false1N])==ClustersOrder(n1+1)|BoardCluster([falseM1,ThisCluster(:,1:n-1)])==ClustersOrder(n1+1)|BoardCluster([ThisCluster(:,2:n),falseM1])==ClustersOrder(n1+1));
end
[~,idx0]=max(temp(:));
idx0=idx(idx0);
E=zeros(2,D(idx0)-1);
tiC=zeros(1,D(idx0));
tiC(end)=idx0;
[E, tiC]=oftl8(D, idx0, E, m,tiC);
% now grow it
tP=ThisCluster;
tP(tiC)=false;
ok=1;
while ok
ok=0;
K=size(tiC,2);
idx1=find(tP(tiC(1:2:K-1)+E(2,1:2:K-1))&tP(tiC(2:2:K)+E(2,1:2:K-1)));
for n2=numel(idx1):-1:1
ok=1;
tiC=[tiC(1:2*idx1(n2)-1),tiC(2*idx1(n2)-1)+E(2,2*idx1(n2)-1), tiC(2*idx1(n2))+E(2,2*idx1(n2)-1), tiC(2*idx1(n2):end)];
E=[E(:,1:2*idx1(n2)-2),E([2,1],2*idx1(n2)-1), E([1,2],2*idx1(n2)-1), E([2,1],2*idx1(n2)-1), E(:,2*idx1(n2):end)];
tP(tiC)=false;
end
K=size(tiC,2);
idx1=find(tP(tiC(1:2:K-1)-E(2,1:2:K-1))&tP(tiC(2:2:K)-E(2,1:2:K-1)));
for n2=numel(idx1):-1:1
ok=1;
tiC=[tiC(1:2*idx1(n2)-1),tiC(2*idx1(n2)-1)-E(2,2*idx1(n2)-1), tiC(2*idx1(n2))-E(2,2*idx1(n2)-1), tiC(2*idx1(n2):end)];
E=[E(:,1:2*idx1(n2)-2),E([2,1],2*idx1(n2)-1), E([1,2],2*idx1(n2)-1), E([2,1],2*idx1(n2)-1), E(:,2*idx1(n2):end)];
tP(tiC)=false;
end
K=size(tiC,2);
idx1=find(tP(tiC(2:2:K-1)+E(2,2:2:K-1))&tP(tiC(3:2:K)+E(2,2:2:K-1)));
for n2=numel(idx1):-1:1
ok=1;
tiC=[tiC(1:2*idx1(n2)),tiC(2*idx1(n2))+E(2,2*idx1(n2)), tiC(2*idx1(n2)+1)+E(2,2*idx1(n2)), tiC(2*idx1(n2)+1:end)];
E=[E(:,1:2*idx1(n2)-1),E([2,1],2*idx1(n2)), E([1,2],2*idx1(n2)), E([2,1],2*idx1(n2)), E(:,2*idx1(n2)+1:end)];
tP(tiC)=false;
end
K=size(tiC,2);
idx1=find(tP(tiC(2:2:K-1)-E(2,2:2:K-1))&tP(tiC(3:2:K)-E(2,2:2:K-1)));
for n2=numel(idx1):-1:1
ok=1;
tiC=[tiC(1:2*idx1(n2)),tiC(2*idx1(n2))-E(2,2*idx1(n2)), tiC(2*idx1(n2)+1)-E(2,2*idx1(n2)), tiC(2*idx1(n2)+1:end)];
E=[E(:,1:2*idx1(n2)-1),E([2,1],2*idx1(n2)), E([1,2],2*idx1(n2)), E([2,1],2*idx1(n2)), E(:,2*idx1(n2)+1:end)];
tP(tiC)=false;
end
end
iC=[iC,tiC];
end
end
end
function B = neighb(A,V,nA)
[m,n] = size(A);
B=sparse(A(:,1:n-1),A(:,2:n),double(V(:,1:n-1)>V(:,2:n)),nA,nA)+sparse(A(:,2:n),A(:,1:n-1),double(V(:,2:n)>V(:,1:n-1)),nA,nA)+sparse(A(1:m-1,:),A(2:m,:),double(V(1:m-1,:)>V(2:m,:)),nA,nA)+sparse(A(2:m,:),A(1:m-1,:),double(V(2:m,:)>V(1:m-1,:)),nA,nA);
B=B>0;
end
function [E, tiC]=oftl8(D, idx0, E, m,tiC)
for n2=D(idx0)-1:-1:1
if D(idx0+1)==n2, idx0=idx0+1; E(1,n2)=1;E(2,n2)=m;
elseif D(idx0-1)==n2, idx0=idx0-1; E(1,n2)=1;E(2,n2)=m;
elseif D(idx0+m)==n2, idx0=idx0+m; E(1,n2)=m;E(2,n2)=1;
elseif D(idx0-m)==n2, idx0=idx0-m; E(1,n2)=m;E(2,n2)=1;
end
tiC(n2)=idx0;
end
end
function [B,C,p,r,nc] = connected(A)
[m,n] = size(A);
N = m*n ;
K = reshape (1:N, m, n) ;
V = A(:,1:n-1) == A(:,2:n);
H = A(1:m-1,:) == A(2:m,:);
G = sparse(K([V,false(m,1)]),K([false(m,1),V]),1,N,N) + sparse(K([H; false(1,n)]),K([false(1,n); H]),1,N,N);
G = G + G' + speye(N);
[p, ~, r] = dmperm(G);
nc = numel(r) - 1;
C = A(p(r(1:nc)));
B = ones(m, n);
for a = 2:nc
B(p(r(a):r(a+1)-1)) = a;
end
end
function D = Dijkstra(A,i1,m,n)
D=inf(m,n);
D(~A)=0;
falseMN = false( m*n, 1);
if isempty(i1),
i1=find(A,1,'first');
mode=0;
else
i1=i1(end);
mode=1;
end
D(i1)=1;
for n1=2:m*n,
X = falseMN;
X(i1(isinf(D(i1+1)))+1) = true;
X(i1(isinf(D(i1-1)))-1) = true;
X(i1(isinf(D(i1+m)))+m) = true;
X(i1(isinf(D(i1-m)))-m) = true;
%i1=unique([i1(idx1)+1,i1(idx2)-1,i1(idx3)+m,i1(idx4)-m]);
i1=find(X);
if isempty(i1), break; end
D(i1)=n1;
end
if mode
msk = D>0;
D(msk)=D(msk)-1;
end
end
%% kurt
function [vine, bestsom] = real_kurt(A)
[m,n]=size(A);
Asort = sort(A(:));
content = unique(Asort);
cumS = cumsum(Asort);
tttt = cumS( diff(Asort) ~= 0 ); % tttt is to find non-plateaus...?
t2 = zeros(size(content,1),1);
t2(content+1) = [0; tttt];
H = t2(A+1);
if size(H,1) ~= m
H=H';
end
C = num2cell(reshape(1:m*n, m, n));
updated = true(size(A));
G = A+H;
[maxG,idxStart] = max(G(:));
B=A;
while (maxG > max(B(:))) && maxG
ii = mod(idxStart-1,m)+1;
jj = ceil(idxStart/m);
flag1 = ii > 1 && A(idxStart - 1) <= A(idxStart);
flag2 = ii < m && A(idxStart + 1) <= A(idxStart);
flag3 = jj < n && A(idxStart + m) <= A(idxStart);
flag4 = jj > 1 && A(idxStart - m) <= A(idxStart);
if flag1
[B,C,updated] = oftl4( idxStart-1, idxStart,A,B,C,updated );
end
if flag2
[B,C,updated] = oftl4( idxStart+1, idxStart,A,B,C,updated );
end
if flag3
[B,C,updated] = oftl4( idxStart+m, idxStart,A,B,C,updated );
end
if flag4
[B,C,updated] = oftl4( idxStart-m, idxStart,A,B,C,updated );
end
updated(idxStart) = false;
G=(B+H).*updated;
[maxG,idxStart] = max(G(:));
end
[bestsom,index]=max(B(:));
vine = fliplr(C{index});
end
function [B,C,updated]=oftl4(verplaatsindex,currIdx,A,B,C,updated )
if (B(currIdx)+A(verplaatsindex) > B(verplaatsindex)) && ~sum(verplaatsindex==C{currIdx}) % Gwendothanks
B(verplaatsindex) = B(currIdx) + A(verplaatsindex);
updated(verplaatsindex)=true;
C{verplaatsindex} = [C{currIdx} verplaatsindex];
end
end
function [vine, bestScore] = SimpleLongestPath( board )
% Treats the board as a directed-acyclic-graph and finds the best
% possible solution. Upper-left wins to break cycles in the graph
% (when adjacent squares have the same value).
%
% This is basically a completely rewritten version of the sebastian()
% function, and is about 15 times faster than sebastian() on the contest
% machine.
%
% This function is only called 8 times presently on the sample set so it
% doesn't make much difference. I optimised it so extremely expecting to use it as
% a candidate-scoring/fitness function as part of some sort of larger algorithm.
%
% - Wesley
[m, n] = size( board );
count = m * n;
sentinel = count + 1;
board = board(:);
score = [board; 0];
nOnes = ones( 1,n );
mOnes = ones( m,1 );
seq = reshape( 1:count, m, n );
north = reshape( [sentinel(nOnes); seq(1:end-1,:)], [], 1);
north(board<score(north)) = sentinel;
south = reshape( [seq(2:end,:); sentinel(nOnes)], [], 1);
south(board<score(south)) = sentinel;
west = [sentinel(mOnes); (1:count-m)'];
west(board<score(west)) = sentinel;
east = [(m+1:count)'; sentinel(mOnes)];
east(board<score(east)) = sentinel;
prev = zeros( sentinel, 1 );
[~, order] = sort( board );
for ii = seq(:).'
curr = order(ii);
% Yes, this fixed size (4) sorting network really
% is faster than using max() for some reason.
northNeighbour = north(curr);
northScore = score(northNeighbour);
southNeighbour = south(curr);
southScore = score(southNeighbour);
if northScore >= southScore
scoreNS = northScore;
neighbourNS = northNeighbour;
else
scoreNS = southScore;
neighbourNS = southNeighbour;
end
westNeighbour = west(curr);
westScore = score(westNeighbour);
eastNeighbour = east(curr);
eastScore = score(eastNeighbour);
if westScore >= eastScore
scoreEW = westScore;
neighbourEW = westNeighbour;
else
scoreEW = eastScore;
neighbourEW = eastNeighbour;
end
if scoreEW >= scoreNS
prev(curr) = neighbourEW;
score(curr) = score(curr) + scoreEW;
else
prev(curr) = neighbourNS;
score(curr) = score(curr) + scoreNS;
end
end
[bestScore, c] = max( score );
for ii = 1:count
seq(ii) = c;
c = prev(c);
if c == sentinel
break
end
end
vine = seq(ii:-1:1);
end
% robert
function [moves, vine, score] = robert(board, limit)
% The Fragrant Honeysuckle gives up on moving and just tries to produce
% some prettier vines 8-)
% Faster to use isconnected logic, or to embed in a zeros(m+1,n+1) and guard?
% Grow a simple vine on given board
%[vine, score, dirsimple, moves] = robert2(board);
% Try constructing a boardwalk down left side
[movesb, boardb] = robert1(board, limit);
[vineb, vscoreb, dirsimple] = robert2(boardb); % Rerun vine code on modified board
% Improve score on board 47 and similar that feature a steady slope and speckle
IsMonotonous = ~(any(dirsimple(vineb) == 1) && any(dirsimple(vineb) == -1));
if IsMonotonous
% Only bother if I have a decent score already and vine goes
% solely up or solely down.
[movesm, boardm] = monotonous(board, vineb, dirsimple, limit);
[vinem, vscorem] = SimpleLongestPath(boardm); % Rerun vine code on modified board
end
% Pick best
if IsMonotonous && vscorem > vscoreb
vine = vinem;
moves = movesm;
score = vscorem;
else
vine = vineb;
moves = movesb;
score = vscoreb;
end
end % solver function
function [moves, board] = monotonous(boardin, vine, dir, limit)
% Focus n high-scoring vines with strong vertical orientation and high limit,
% and aim to shuffle blocking values out of high-scoring rows.
% Should never damage a unidirectional vine but ineffective unless the
% board has the structure of board 47
moves = [];
board = boardin;
[rows,cols] = size(board);
boardsize = numel(board);
lastdir = dir(vine(end)); % initialise with vine top
for i = size(vine,1)-1:-1:2 % walk down vine to polish high scores first
if abs(dir(vine(i))) == 1 % found a vertical step
valmin = board(vine(i)+dir(vine(i)));
valmax = board(vine(i)); % range of non-blocking values
% [row,col] = ind2sub([rows,cols],vine(i));
row=rem(vine(i)-1,rows)+1;
col=(vine(i)-row)/rows+1;
if lastdir > 0 && vine(i)+lastdir <= boardsize-cols
% a right edge in mid board
moveToCol = col+1;
[board,moves]=oftl(board,moves,limit,row,moveToCol,valmin,valmax,cols,rows);
row = row - 1;
if row > 0 % Needed?
moveToCol = col+1;
[board,moves]=oftl(board,moves,limit,row,moveToCol,valmin,valmax,cols,rows);
end % if second row > 0
end % if we have a midboard right edge
% Now repeat whole thing for left edges. Should be a minor pickup
% from having more moves in high-scoring areas.
% Check lastedge logic when I make 2 upward moves in a row
if lastdir == -cols && vine(i) > cols
% a left edge in mid board. Check logic.
moveToCol = col-1;
[board,moves]=oftl7(board,moves,limit,row,moveToCol,valmin,valmax,rows);
end % if we have a midboard left edge
end % vertical step
lastdir = dir(vine(i));
end % for each leaf of vine
% Have now modified board, hopefully improved it in a few high-scoring cases
end % function monotonous
function [board,moves] = oftl7(board,moves,limit,row,moveToCol,valmin,valmax,rows)
while size(moves,1) < limit % loop through all blockages (if any)
while ( board(row,moveToCol) >= valmin && ...
board(row,moveToCol) <= valmax ) && moveToCol > 1
moveToCol = moveToCol - 1;
end
if moveToCol > 1 % Found a blockage I'd like to replace
moveFromCol = moveToCol-1;
while moveFromCol > 0 && ...
( board(row,moveFromCol) < valmin || ...
board(row,moveFromCol) > valmax )
moveFromCol = moveFromCol - 1;
end
if moveFromCol > 0
% Something to replace it with exists, so do slide
for j = moveFromCol:moveToCol-1
if size(moves,1) < limit
moves = [moves; [row+rows*(j-1), row+rows*j]];
board(row,j+1) = board(row,j);
board(row,j) = 0;
else
break % Used up all moves
end
end
else
break % no more nonblocks to use so row finished
end
else
break % no blocks so row finished
end % (needed in case block is in other row...?)
end % First row while loop. Break out when complete and apply
% same logic to second row
end
function [board,moves]=oftl(board,moves,limit,row,moveToCol,valmin,valmax,cols,rows)
while size(moves,1) < limit % loop through all blockages (if any)
while ( board(row,moveToCol) >= valmin && ...
board(row,moveToCol) <= valmax ) && moveToCol <= cols-1
moveToCol = moveToCol + 1;
end
if moveToCol < cols % Found a blockage I'd like to replace
moveFromCol = moveToCol+1;
while moveFromCol <= cols && ...
( board(row,moveFromCol) < valmin || ...
board(row,moveFromCol) > valmax )
moveFromCol = moveFromCol + 1;
end
if moveFromCol <= cols
% Something to replace it with exists, so do slide
for j = moveToCol:moveFromCol-1
if size(moves,1) < limit
moves = [moves; [(row+rows*j), (row+rows*(j-1))]];
board(row,j) = board(row,j+1);
board(row,j+1) = 0;
else
break % Used up all moves
end
end
else
break % no more nonblocks to use so row finished
end
else
break % no blocks so row finished
end % (needed in case block is in other row...?)
end
end
function [moves, board] = robert1(boardin, limit)
% Focus n high-score boards like 8 where there is a high limit but no structure.
% Aim to construct a path from scratch. To keep the movement choices simple do
% this along an edge; a spiral in centre would require far fewer moves on
% average but would require more complex pathfinding
% Minor bug with equal values, which may upset vine constructor so add a small
% amount of noise.
moves = zeros(limit,2); mv=0;
[rows,cols] = size(boardin);
boardsize = numel(boardin);
board = boardin - reshape(1:boardsize,size(boardin))*1e-4;
Target = 1; % Pick a corner, any corner
[Biggest,BlockAt] = max(board(:)); % Move biggest
while mv < limit && Biggest > 0 % Find another block to move
Vt=rem(Target-1,rows)+1;
Ut=(Target-Vt)/rows+1;
% First move onto a channel that will be cleared of blocks
Vb=rem(BlockAt-1,rows)+1;
Ub=(BlockAt-Vb)/rows+1;
if Ub-Ut > 1 % Only if not next to target column
Nudge = 1-mod(Vb-1,3); % [+1,0,-1,...]
if (Nudge ~= 0) && ~(Vb==rows && Nudge==1)
mv=mv+1; moves(mv,1:2) = [BlockAt,BlockAt+Nudge];
board(BlockAt+Nudge) = board(BlockAt);
board(BlockAt) = 0;
BlockAt = BlockAt+Nudge;
end
end
% Now move towards target
Vb = rem(BlockAt-1,rows)+1;
U = Ut-(BlockAt-Vb)/rows-1;
V = Vt-Vb; % Horiz and Vert moves required
[mv,moves,board]=oftl9(U, V, mv, limit, moves, BlockAt, rows, board);
board(Target) = -board(Target); % Ignore moved blocks
Target=Target+(mod(Ut,2))*(Vt<rows)-(~mod(Ut,2))*(Vt>1)+rows*(mod(Ut,2))*(~(Vt<rows))+rows*(~mod(Ut,2))*(~(Vt>1));
[Biggest,BlockAt] = max(board(:)); % Move biggest
end % Finding blocks to slide
board = abs(board);
moves=moves(1:mv,:);
end % function boardwalk
function [mv,moves,board]=oftl9(U, V, mv, limit, moves, BlockAt, rows, board)
while (U~=0 || V~=0) && mv<limit
if U<-1 || V==0
mv=mv+1; moves(mv,1:2) = [BlockAt,BlockAt-rows];
board(BlockAt-rows) = board(BlockAt);
board(BlockAt) = 0;
BlockAt = BlockAt-rows;
U = U+1;
elseif V>0 % Just ignore erases until I get it working
mv=mv+1; moves(mv,1:2) = [BlockAt,BlockAt+1];
board(BlockAt+1) = board(BlockAt);
board(BlockAt) = 0;
BlockAt = BlockAt+1;
V=V-1;
else
mv=mv+1; moves(mv,1:2) = [BlockAt,BlockAt-1];
board(BlockAt-1) = board(BlockAt);
board(BlockAt) = 0;
BlockAt = BlockAt-1;
V=V+1;
end
end % Sliding this block
end
function [vine, vscore, dir, moves] = robert2(board)
% Test each square on the board from low to high values to find whether vine
% can grow upwards onto an adjacent target square.
% To handle plateaux I superimpose a faint watermark on flat areas to nudge vine
% towards a space-covering pattern. On each plateau I track 4 orientations
% separately, but whenever looking up to a higher level I can pick the best.
% Quite pretty, but as all plateaux problems in testset are low-scoring I don't
% think it makes much difference.
%
dir = zeros(size(board)); % points way down vine, 0 at root
% done = false(size(board)); % have already examined this one
[rows,cols] = size(board);
boardsize = numel(board);
watermark = reshape(1:boardsize,size(board)) * 1e-6;
watermark(:,2:2:cols) = flipud(watermark(:,2:2:cols));
board = board + watermark .* (mod(board,2)-0.5);
% superimpose a faint watermark on flat areas. Direction should change
% between adjacent levels (but will fail if steps are even)
score = board; % score for a vine starting and ending here
[~, ind] = sort(board(:));
% Loop through board from low to high values to find the score associated
% with the best vine growing down from each square
% Needs more care on equal values, for now just weave up and down
% -- Could try 4 weaves and pick best, or proper handling of plateaux
stepvec = [-rows,-1,1,rows];
for i = 1:boardsize;
test = ind(i);
if board(test) < .1
continue
end
for step = stepvec;
targ = test + step;
if targ > 0 && targ <= boardsize && ...
(abs(step)==rows || mod(min(test,targ), rows))
% consider only adjacent squares on board
if (board(targ) > board(test)) && (board(targ)+score(test) > score(targ))
% Targ can grow from me (and has nothing better yet)
score(targ) = score(test) + board(targ);
% add test vine to targ score
dir(targ) = -step;
% and note where it came from
end
end
end
end
% Assemble vine from top down
[~,leaf] = max(score(:));
vine = [];
while dir(leaf)~=0
vine = [vine;leaf];
leaf = leaf+dir(leaf);
end
vine = flipud([vine;leaf]); % return it in correct order
vscore = score(vine(end));
moves = [];
end % growvine
function [moves,vine] = robert3(board, moves, vine, limit)
% modified version of robert2 to finish off an incomplete vine
% Perform moves on the board:
for i = 1:size(moves,1)
board(moves(i,:)) = [0 board(moves(i,1))];
end
% clear out unneeded parts of board
last = board(vine(1));
board(~board)=NaN;
board(board>last)=NaN;
board(vine(1))=last;
dir = zeros(size(board)); % points way down vine, 0 at root
[rows,cols] = size(board);
boardsize = numel(board);
score = board; % score for a vine starting and ending here
[ign, ind] = sort(board(:));
% Loop through board from low to high values to find the score associated
% with the best vine growing down from each square
stepvec = [-rows,-1,1,rows];
for i = 1:boardsize;
test = ind(i);
if isnan(board(test))
break;
end
for step = stepvec;
targ = test + step;
if targ > 0 && targ <= boardsize && ...
(abs(step)==rows || mod(min(test,targ), rows))
% consider only adjacent squares on board
if (board(targ) > board(test)) && (board(targ)+score(test) > score(targ))
% Targ can grow from me (and has nothing better yet)
score(targ) = score(test) + board(targ);
% add test vine to targ score
dir(targ) = -step;
% and note where it came from
end
end
end
end
% Assemble vine from top down
leaf = vine(1);
tip = [];
while dir(leaf)~=0
leaf = leaf+dir(leaf);
tip = [tip leaf];
end
vine = [fliplr(tip) vine];
end
function tf = ismemberSimpl( a, s )
% behaves like ismember(a,s) for typical input and one output,
% but has no error checking and is faster
% MiVö
[m,n] = size(a);
tf = false(m,n);
for ii = 1:m*n
tf(ii) = any(a(ii)==s(:));
end
end
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