- function W = solv(B)
- tweak = rand(43,1);
- W=solverF(B);
- S = mygrade(B,W);
+ function W = solver(board)
- [nr,nc] = size(B);
- [W2,S2] = sunday(B,[1 2],[1 2],4*nr*nc);
- if S > S2
- W = W2;
- S=S2;
- end
+ padSize = 3;
+ % pad board
+ [M,N] = size(board);
+ board_padded = zeros(M+2*padSize, N+2*padSize);
+ board_padded(padSize+1:M+padSize, padSize+1:N+padSize) = board;
+ board = board_padded;
+ M = M + 2*padSize;
+ N = N + 2*padSize;
- X = B(nr:-1:1,:);
- X = X.';
+ % initialize matrix with pins and connections
+ boardMod = board;
- [W2,S2] = sunday(X,[1 2],[1 2],4*nr*nc);
- if S > S2
- W = [nr-W2(:,2)+1 W2(:,1) nr-W2(:,4)+1 W2(:,3)];
- S=S2;
- end
+ % get index of pin positions
+ pinIndex = find(board);
+ pinValues = board(pinIndex); %#ok
- end
+ % get number of pins with a given value
+ pinValuesUnique = unique(pinValues);
+ nrOfSamePins = histc(pinValues, pinValuesUnique);
+ nrOfGroups = length(pinValuesUnique);
+ % decide with which pin value to start
+ pinGroupValues = pinValuesUnique .* nrOfSamePins;
+ [ignore, sortIndex] = sort(pinGroupValues, 1, 'descend'); %#ok
- function [W,S] = sunday(B0,x000,y000,th000)
- [nR,nC]=size(B0);
- Borig= -ones(nR+2,nC+2);
- Borig(2:end-1,2:end-1)=B0;
- Bedit = Borig;
+ % get move codebook
+ [moveCodebook, col] = getmovecodebook__(M);
- maxbridges = 4;
+ % loop over pin values
+ connMatrix = zeros(0,2);
+ for groupNr = 1:nrOfGroups
+ groupPinValue = pinValuesUnique(sortIndex(groupNr));
+ groupPinsIndex = pinIndex(pinValues == groupPinValue);
+ groupSize = length(groupPinsIndex);
+ groupConnect = zeros(groupSize);
+ [groupPinRows, groupPinCols] = ind2sub__(M, groupPinsIndex);
- if size(Bedit,2) > 18
- cutfirst = 4;
- cutsecond = 8;
- cutoff = 18;
- else
- cutfirst = 3;
- cutsecond = 7;
- cutoff = 13;
- end
+ % loop over current group (all pins of current value)
+ for pin1Nr = 1:groupSize-1
+ pin1Index = groupPinsIndex(pin1Nr);
- S = inf;
- X1 = [1 2;2 1];
- X2 = [1 3;3 1];
- Y = [3 2 1;1 2 3];
+ % get vector of move ends
+ moveEnds = pin1Index + moveCodebook(:, col.move);
- % fprintf('\n');
+ % find order for working down pins by distance relation
+ distanceVector = ...
+ abs(groupPinRows(pin1Nr+1:end) - groupPinRows(pin1Nr)) + ...
+ abs(groupPinCols(pin1Nr+1:end) - groupPinCols(pin1Nr));
+
+ % loop over other pins
+ [ignore, sortIndex2] = sort(distanceVector);
+ for pin2Nr = pin1Nr + sortIndex2' % pin1Nr+1:groupSize
+ pin2Index = groupPinsIndex(pin2Nr);
+
+ if groupConnect(pin1Nr, pin2Nr)
+ % pins are already connected indirectly
+ continue
+ end
- for x = x000
- if x == 2
- [U BU] = phase1(Bedit,cutfirst,X1(x,:));
- [UU BUU] = phase3(BU,U,cutsecond,X2(x,:));
- [V BX] = phase3(BUU,UU,cutoff,X2(x,:));
- else
- [U BU] = phase1(Bedit,4,X1(x,:));
- [V BX] = phase3(BU,U,11,X2(x,:));
- end
+ moveIndex = (pin2Index == moveEnds);
- for y = y000
- % if x == 1 && y == 2, continue, end
- %if x == 2 && y == 2 && S > th000, return, end
- W1 = phase2_a(Bedit,BX,V,maxbridges,cutoff,Y(y,:))-1;
- S1 = mygrade(B0,W1);
- % fprintf('x=%d, y=%d, %d', x, y, S1);
- % if isfinite(S), fprintf(' (%4d)\n', S1 - S), else,
- % fprintf('\n'), end
- if S1 <= S
- S = S1;
- W = W1;
- maxbridges = maxbridges - 1;
- end
- end
- end
- end
+ % loop over possible moves
+ for moveNr = find(moveIndex')
- %%
- function score = mygrade(B,W)
- nR=size(B,1);
- B(W(:,1)+(W(:,2)-1)*nR)=0;
- B(W(:,3)+(W(:,4)-1)*nR)=0;
- score=sum(B(:))+size(W,1)+sum(W(:,1)==W(:,3)&W(:,2)==W(:,4))*24;
- end
+ % check if required fields are free
+ nrOfFree = moveCodebook(moveNr, col.free);
+ if nrOfFree > 0
+ freePinIndex = pin1Index + moveCodebook(moveNr, col.ind:(col.ind+nrOfFree-1));
+ boardModTmp = boardMod(freePinIndex);
+ moveValid = ~any(boardModTmp ~= 0 & boardModTmp ~= -groupPinValue);
+ else
+ moveValid = 1;
+ end
- %%
- function [pincount k] = analyzeboard(B,rz)
+ if moveValid
+ % get current moves
+ currConns = pin1Index + getconnections__(moveCodebook(moveNr,:), col);
- % make a sorted list of all pins
- pin = sort(B(B>0),'descend');
- npins = size(pin,1);
- if npins < 1
- pincount = [];
- k = 0;
- return
- end
+ % check if any moves goes outside the original board
+ currMoves = convertConns__(currConns, M);
- uniPins=pin(diff([0;pin])~=0);
- % pin, count, benefit
+ if any(currMoves(:, 1) <= padSize) || ...
+ any(currMoves(:, 1) >= M - padSize + 1) || ...
+ any(currMoves(:, 2) <= padSize) || ...
+ any(currMoves(:, 2) >= N - padSize + 1)
+ moveValid = 0;
+ end
+ end
- pincount = zeros(nnz(uniPins),3);
- thesepins=histc(pin,uniPins(end:-1:1));
- pincount(:,1)=uniPins;
- pincount(:,2)=thesepins(end:-1:1);
- k=nnz(uniPins);
+ if moveValid
+ % save moves
+ connMatrix = [connMatrix; currConns]; %#ok
- if rz < 3, return, end
- % calculate the benefit of a path
- for i = 1:k
- if pincount(i,2) >= 2
- p = pincount(i,1);
- [row col] = find(B == p);
- d = 0;
- N = size(row,1);
- d=sum(abs(diff(row))+abs(diff(col)));
- pincount(i,3) = pincount(i,2)*p - 0.85 * d;
- end
- end
- end
-
- %%
- function [W B] = phase1(B,cutoff,rz)
- % fprintf('-- phase 1 --\n');
-
- W = [];
-
- [pincount k] = analyzeboard(B,rz);
-
- if k < 1
- return
- end
-
- pincount=sortrows(pincount,-rz);
-
- for i = 1:k
- if pincount(i,2) >= 2
- p = pincount(i,1);
- [row col] = find(B == p);
- N = size(row,1);
- % find all pairwise distances
- Npairs = N*(N-1)/2;
- dist = zeros(Npairs,3);
- [I J]=find(tril(ones(N),-1));
- dist(:,1)=J;
- dist(:,2)=I;
- dist(:,3)=abs(col(I)-col(J))+abs(row(I)-row(J));
- % sort by distance
- [d ix] = sort(dist(:,3));
- dist = dist(ix,:);
-
- % try to connect the closest pair possible
- npins = 0;
- for x = 1:Npairs
- if dist(x,3) > cutoff+1
- % fprintf('warning: dist = %2d\n', dist(x,3));
- break
- end
- a = dist(x,1);
- b = dist(x,2);
- % path = simplepath([row(a); row(b)], [col(a); col(b)], -p);
- path = complexpath(B,[row(a); row(b)], [col(a); col(b)], -p, cutoff, 2*p);
- if size(path,1) > 0
- % fprintf('p = %d, connect a=%d, b=%d, dist = %d\n', p, a, b, dist(x,3));
- % fprintf('\nFound path, p = %d, r=%d c=%d, r=%d, c=%d\n', p, row(a), col(a), row(b), col(b));
- W = [W; path];
-
- B = addwirepath(B,path,-p);
-
- % pinlist = [row(a) col(a); row(b) col(b)];
- npins = 2;
- edit = [1:(a-1) (a+1):(b-1) (b+1):N];
- row = [row(a); row(b); row(edit)];
- col = [col(a); col(b); col(edit)];
- break
- else
- % fprintf('p = %d, cannot connect a=%d, b=%d, dist = %d\n', p, a, b, dist(x,3));
- end
- end
-
- if npins < 2
- continue
- end
-
- for j = 3:N
- % find all pins and wires
- [row2 col2] = find(B == -p);
- Npinwires = size(row2,1);
- % fprintf('npins = %d, nwires = %d\n', npins, Npinwires - npins);
-
- % find all pairwise distances
- % a = already connected (pin or wire), b = not yet connected
- Npairs = Npinwires * (N - npins);
-
-
- dist = zeros(Npairs,3);
- x = 0;
- for a = 1:Npinwires
- for b = (npins+1):N
- x = x + 1;
- dist(x,1) = a;
- dist(x,2) = b;
- dist(x,3) = abs(row2(a)-row(b)) + abs(col2(a)-col(b));
- end
- end
- % sort by distance
- [d ix] = sort(dist(:,3));
- dist = dist(ix,:);
-
- % try to connect closest pair possible
- connected = false;
- for x = 1:Npairs
- if dist(x,3) > cutoff+1
- % fprintf('warning: dist = %2d\n', dist(x,3));
- break
- end
- a = dist(x,1);
- b = dist(x,2);
- % path = simplepath([row2(a); row(b)], [col2(a); col(b)], -p);
- path = complexpath(B,[row2(a); row(b)], [col2(a); col(b)], -p, cutoff, p);
- if size(path,1) > 0
- W = [W; path];
+ % mark points as occupied
+ boardMod(currConns(2:end,1)) = -groupPinValue;
- B = addwirepath(B,path,-p);
-
- npins = npins + 1;
- connected = true;
- row([j b]) = row([b j]);
- col([j b]) = col([b j]);
- break
- end
- end
-
- if ~connected
- break
- end
- end
-
- end
- end
- end
+ % mark pins as connected
+ groupConnect(pin1Nr, pin2Nr) = 1;
+ groupConnect(pin2Nr, pin1Nr) = 1;
- %%
- function [W B] = phase2(Borig,B,W,maxbridges,kappa,rz)
+ % update connection matrix
+ groupConnect(:,pin2Nr) = groupConnect(:,pin2Nr) | groupConnect(:,pin1Nr);
+ groupConnect(:,pin1Nr) = groupConnect(:,pin1Nr) | groupConnect(:,pin2Nr);
+ groupConnect(pin2Nr,:) = groupConnect(pin2Nr,:) | groupConnect(pin1Nr,:);
+ groupConnect(pin1Nr,:) = groupConnect(pin1Nr,:) | groupConnect(pin2Nr,:);
- function addbridgewirepath()
- for w = 1:size(path,1);
- if path(w,1) == path(w,3) % horizontal
- BH(path(w,1),path(w,2)) = false;
- BH(path(w,3),path(w,4)) = false;
- if path(w,2) == path(w,4)
- B(path(w,1),path(w,2)) = -9999;
- end
- end
- if path(w,2) == path(w,4) % vertical
- BV(path(w,1),path(w,2)) = false;
- BV(path(w,3),path(w,4)) = false;
- end
- end
- end
-
- % fprintf('-- phase 2 --\n');
-
- [BH BV] = buildbridges(Borig,B,W);
-
- [pincount k] = analyzeboard(B,rz);
- if k < 1, return, end
-
- pincount=sortrows(pincount,-rz);
-
- for i = 1:k
- p = pincount(i,1);
-
- Npinwires = sum(B == -p);
-
- if Npinwires == 0
- % fprintf('p = %d, no previous pinwires\n', p);
-
- if pincount(i,2) >= 2
- [row col] = find(B == p);
- N = size(row,1);
- % find all pairwise distances
- Npairs = N*(N-1)*.5;
- dist = zeros(Npairs,3);
- x = 0;
- for a = 1:N
- for b = (a+1):N
- x = x + 1;
- dist(x,1) = a;
- dist(x,2) = b;
- dist(x,3) = abs(row(a)-row(b)) + abs(col(a)-col(b));
- end
- end
- % sort by distance
- [d ix] = sort(dist(:,3));
- dist = dist(ix,:);
-
- maxstep = min((maxbridges*25)+kappa,2*p+1);
-
- % try to connect the closest pair possible
- connected = false;
- for x = 1:Npairs
- if dist(x,3) > maxstep+1
- % fprintf('warning: dist = %2d\n', dist(x,3));
+ % leave loop over possible moves
break
end
- a = dist(x,1);
- b = dist(x,2);
- path = bridgepath(B,BH,BV,[row(a); row(b)], [col(a); col(b)], -p, maxbridges, kappa, ceil(1.85*p));
- if size(path,1) > 0
- % fprintf('\nBRIDGE path, p = %d, r=%d c=%d, r=%d, c=%d\n', p, row(a), col(a), row(b), col(b));
- W = [W; path];
-
- B = addwirepath(B,path,-p);
- addbridgewirepath();
-
- connected = true;
- break
- end
- end
- if ~connected
- continue
- end
- end
- end
- [row col] = find(B == p);
- Npins = size(row,1);
-
- maxstep = min((maxbridges*25)+kappa,p+1);
-
- for j = 1:Npins
- [row2 col2] = find(B == -p);
- Npinwires = size(row2,1);
-
- % find all pairwise distances
- % a = already connected (pin or wire), b = not yet connected
- Npairs = Npinwires * (Npins-j+1);
- dist = zeros(Npairs,3);
- x = 0;
- for a = 1:Npinwires
- for b = j:Npins
- x = x + 1;
- dist(x,1) = a;
- dist(x,2) = b;
- dist(x,3) = abs(row2(a)-row(b)) + abs(col2(a)-col(b));
end
end
- % sort by distance
- [d ix] = sort(dist(:,3));
- dist = dist(ix,:);
-
- % try to connect closest pair possible
- connected = false;
- for x = 1:Npairs
- if dist(x,3) > maxstep+1
- % fprintf('warning: dist = %2d\n', dist(x,3));
- break
- end
- a = dist(x,1);
- b = dist(x,2);
- path = bridgepath(B,BH,BV,[row2(a); row(b)], [col2(a); col(b)], -p, maxbridges, kappa, p);
- if size(path,1) > 0
- % fprintf('\nEXTRA BRIDGE path, p = %d, r=%d c=%d, r=%d, c=%d\n', p, row2(a), col2(a), row(b), col(b));
- W = [W; path];
-
- B = addwirepath(B,path,-p);
- addbridgewirepath();
-
- connected = true;
-
- row([j b]) = row([b j]);
- col([j b]) = col([b j]);
- break
- end
- end
-
- if ~connected
- break
- end
end
-
end
- end
+ % remove duplicates
+ connMatrix = unique(connMatrix, 'rows');
- %%
- function [W B] = phase3(B,W,kappa,rz)
+ % convert linear indices to row-column indices
+ W = convertConns__(connMatrix, M);
+ % consider padding
+ W = W - padSize;
- % fprintf('-- phase 3 --\n');
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ function [moveCodebook, col] = getmovecodebook__(M)
- [pincount k] = analyzeboard(B,rz);
- if k < 1, return, end
+ col.move = 1;
+ col.fwd = 2;
+ col.free = 3;
+ col.ind = 4;
- pincount=sortrows(pincount,-rz);
-
- for i = 1:k
- p = pincount(i,1);
+ moveCodebook = [
+ % mv fwd free indices...................
+ 1 1 0 0 0 0 0 0 0; % one down
+ M 1 0 0 0 0 0 0 0; % one right
- Npinwires = sum(B == -p);
+ 2 1 1 1 0 0 0 0 0; % two down
+ 2*M 1 1 M 0 0 0 0 0; % two right
- if Npinwires == 0
- % fprintf('p = %d, no previous pinwires\n', p);
-
- if pincount(i,2) >= 2
- [row col] = find(B == p);
- N = size(row,1);
- % find all pairwise distances
- Npairs = N*(N-1)*.5;
- dist = zeros(Npairs,3);
- x = 0;
- for a = 1:N
- for b = (a+1):N
- x = x + 1;
- dist(x,1) = a;
- dist(x,2) = b;
- dist(x,3) = abs(row(a)-row(b)) + abs(col(a)-col(b));
- end
- end
- % sort by distance
- [d ix] = sort(dist(:,3));
- dist = dist(ix,:);
-
- maxstep = min(kappa,2*p+1);
-
- % try to connect the closest pair possible
- connected = false;
- for x = 1:Npairs
- if dist(x,3) > maxstep+1
- % fprintf('warning: dist = %2d\n', dist(x,3));
- break
- end
- a = dist(x,1);
- b = dist(x,2);
- % path = bridgepath(B,BH,BV,[row(a); row(b)], [col(a); col(b)], -p, maxbridges, kappa, 2*p);
- path = complexpath(B,[row(a); row(b)], [col(a); col(b)], -p, kappa, 2*p);
- if size(path,1) > 0
- % fprintf('\nBRIDGE path, p = %d, r=%d c=%d, r=%d, c=%d\n', p, row(a), col(a), row(b), col(b));
- W = [W; path];
-
- B = addwirepath(B,path,-p);
- % [B BH BV] = addbridgewirepath(B,BH,BV,path,-p);
-
- connected = true;
- break
- end
- end
- if ~connected
- continue
- end
- end
- end
+ M-1 1 1 -1 0 0 0 0 0; % one up, one right
+ M-1 1 1 M 0 0 0 0 0; % one right, one up
- [row col] = find(B == p);
- Npins = size(row,1);
+ M+1 1 1 1 0 0 0 0 0; % one down, one right
+ M+1 1 1 M 0 0 0 0 0; % one right, one down
- maxstep = min(kappa,p+1);
+ 3 1 2 1 2 0 0 0 0; % three down
+ 3*M 1 2 M 2*M 0 0 0 0; % three right
+
+ 2*M+1 1 2 M 2*M 0 0 0 0; % two right, one down (1)
+ 2*M+1 1 2 M M+1 0 0 0 0; % two right, one down (2)
+ 2*M+1 1 2 1 M+1 0 0 0 0; % two right, one down (3)
- for j = 1:Npins
- [row2 col2] = find(B == -p);
- Npinwires = size(row2,1);
-
- % find all pairwise distances
- % a = already connected (pin or wire), b = not yet connected
- Npairs = Npinwires * (Npins-j+1);
- dist = zeros(Npairs,3);
- x = 0;
- for a = 1:Npinwires
- for b = j:Npins
- x = x + 1;
- dist(x,1) = a;
- dist(x,2) = b;
- dist(x,3) = abs(row2(a)-row(b)) + abs(col2(a)-col(b));
- end
- end
- % sort by distance
- [d ix] = sort(dist(:,3));
- dist = dist(ix,:);
-
- % try to connect closest pair possible
- connected = false;
- for x = 1:Npairs
- if dist(x,3) > maxstep+1
- % fprintf('warning: dist = %2d\n', dist(x,3));
- break
- end
- a = dist(x,1);
- b = dist(x,2);
- % path = bridgepath(B,BH,BV,[row2(a); row(b)], [col2(a); col(b)], -p, maxbridges, kappa, p);
- path = complexpath(B,[row2(a); row(b)], [col2(a); col(b)], -p, kappa, 2*p);
- if size(path,1) > 0
- % fprintf('\nEXTRA BRIDGE path, p = %d, r=%d c=%d, r=%d, c=%d\n', p, row2(a), col2(a), row(b), col(b));
- W = [W; path];
-
- B = addwirepath(B,path,-p);
- % [B BH BV] = addbridgewirepath(B,BH,BV,path,-p);
-
- connected = true;
- row([j b]) = row([b j]);
- col([j b]) = col([b j]);
- break
- end
- end
+ M+2 1 2 1 2 0 0 0 0; % one right, two down (1)
+ M+2 1 2 1 M+1 0 0 0 0; % one right, two down (2)
+ M+2 1 2 M M+1 0 0 0 0; % one right, two down (3)
- if ~connected
- break
- end
- end
+ 4 1 3 1 2 3 0 0 0; % four down
+ 4*M 1 3 M 2*M 3*M 0 0 0; % four right
- end
+ 2*M 1 3 -1 M-1 2*M-1 0 0 0; % two right with a loop (1)
+ 2*M 1 3 1 M+1 2*M+1 0 0 0; % two right with a loop (2)
- end
+ 2 1 3 M M+1 M+2 0 0 0; % two down with a loop (1)
+ 2 1 3 -M -M+1 -M+2 0 0 0; % two down with a loop (2)
- %%
- function [BH BV] = buildbridges(Borig,B,path)
- [NR NC] = size(B);
- BH = Borig == 0;
- BV = BH;
- BH(:,[1 NC]) = false;
- BV([1 NR],:) = false;
- for i = 1:size(path,1)
- if path(i,1) == path(i,3) % horizontal
- BH(path(i,1),path(i,2)) = false;
- BH(path(i,3),path(i,4)) = false;
- end
- if path(i,2) == path(i,4) % vertical
- BV(path(i,1),path(i,2)) = false;
- BV(path(i,3),path(i,4)) = false;
- end
- end
- end
+ 2*M-2 1 3 M 2*M 2*M-1 0 0 0; % two right, two up (1)
+ 2*M-2 1 3 M M-1 2*M-1 0 0 0; % two right, two up (2)
+ 2*M-2 1 3 M M-1 M-2 0 0 0; % two right, two up (3)
+ 2*M-2 1 3 -1 M-1 2*M-1 0 0 0; % two right, two up (4)
+ 2*M-2 1 3 -1 -2 M-2 0 0 0; % two right, two up (5)
+
+ 2*M+2 1 3 M 2*M 2*M+1 0 0 0; % two right, two down (1)
+ 2*M+2 1 3 M M+1 2*M+1 0 0 0; % two right, two down (2)
+ 2*M+2 1 3 M M+1 M+2 0 0 0; % two right, two down (3)
+ 2*M+2 1 3 1 M+1 2*M+1 0 0 0; % two right, two down (4)
+ 2*M+2 1 3 1 2 M+2 0 0 0; % two right, two down (5)
- %%
- function B = addwirepath(B,path,label)
- B(path(1,1),path(1,2)) = label;
- for i = 1:size(path,1);
- B(path(i,3),path(i,4)) = label;
- end
- end
+ 5 1 4 1 2 3 4 0 0; % five down
+ 5*M 1 4 M 2*M 3*M 4*M 0 0; % five right
+ ];
- %%
- function path = traceback(z,PZ,NR,t)
- path = zeros(t,4);
- dr = mod(z,NR);
- dc = ceil(z/NR);
- for j = 1:t
- path(j,1:2) = [dr dc];
- z = PZ(z);
- dr = mod(z,NR);
- dc = ceil(z/NR);
- path(j,3:4) = [dr dc];
- end
- end
+ moveCodebook = addmirrors__(moveCodebook, col);
+ % compute forward index
+ moveCodebook(:, col.fwd) = moveCodebook(:, col.move) > 0;
- function path = complexpath(B,row,col,label,cutoff,maxpathlen)
-
- % - complexpath -
- [NR NC] = size(B);
- PZ = zeros(NR,NC);
- C = -ones(NR,NC);
- C(row(2),col(2)) = 0; % source
-
- % tag the targets
- C(row(1),col(1)) = -2;
- C( B == label ) = -2;
-
- znext = zeros(NR*NC,1);
- znext(1) = row(2) + (col(2)-1)*NR;
- count = 1;
- dZ = [-1 1 -NR NR];
-
- [ign, ir] = sort(rand(1,4));
- for step = 0:min(cutoff,maxpathlen)
- if count < 1, break, end
- N = count;
- z = znext;
- count = 0;
- for i = 1:N
- zi = z(i);
- for s=1:4
- Z = zi + dZ(ir(s));
- tag = C(Z);
- if tag == -2
- PZ(Z) = zi;
- path = traceback(Z,PZ,NR,step+1);
- return
- end
- if tag == -1 && B(Z) == 0
- C(Z) = step+1;
- PZ(Z) = zi;
- count = count + 1;
- znext(count) = Z;
- end
- end
- end
+ if 0
+ plotcodebook(moveCodebook, col, M);
end
- path = [];
- end
- %%
- function path = bridgepath(B,BH,BV,row,col,label,maxbridges,kappa,maxpathlen)
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ function moveCodebook = addmirrors__(moveCodebook, col)
- % - bridgepath -
- % fprintf('bridgepath ...\n');
- [NR NC] = size(B);
- BRIDGE = false(NR,NC);
- PZ = zeros(NR,NC);
- C = -ones(NR,NC);
- % C(row(2),col(2)) = 0; % source
+ [nOfRows, nOfCols] = size(moveCodebook);
- % tag targets
- C(row(1),col(1)) = -2;
- C( B == label ) = -2;
+ colIndex = [col.move, col.ind:nOfCols];
+ rowIndex = nOfRows+1:2*nOfRows;
- maxstep = min((maxbridges*27)+kappa,maxpathlen+1);
- nextstep = zeros(maxstep+28,1);
- nextstep(1) = row(2) + (col(2)-1)*NR;
- dZ = [-NR NR -1 1];
+ moveCodebook = [moveCodebook; moveCodebook];
+ moveCodebook(rowIndex, colIndex) = -moveCodebook(rowIndex, colIndex);
- for step = 1:maxstep
- while nextstep(step)>0
- zi = nextstep(step);
- nextstep(step)=C(zi);
- for s = 1:4
- Z = zi + dZ(s);
- tag = C(Z);
- if tag==-1
- if B(Z) == 0
- C(Z) = nextstep(step+1);
- nextstep(step+1) = Z;
- PZ(Z) = zi;
- elseif (BH(Z)&&(s<3)) || (BV(Z)&&(s>2))
- C(Z) = nextstep(step+26);
- nextstep(step+26) = Z;
- PZ(Z) = zi;
- BRIDGE(Z) = true;
- end
- end
- if tag==-2
- step=step+1;
- PZ(Z) = zi;
- dr=mod(Z,NR);
- dc=ceil(Z/NR);
- path = zeros(step,4);
- j = 0;
- while dr ~= row(2) || dc ~= col(2)
- j = j + 1;
- path(j,1:2) = [dr dc];
- Z = dr + (dc-1)*NR;
- pz = PZ(Z);
- pr=mod(pz,NR);
- pc=ceil(pz/NR);
- path(j,3:4) = [pr pc];
- dr = pr;
- dc = pc;
- if BRIDGE(dr,dc)
- j = j + 1;
- path(j,:) = [dr dc dr dc];
- end
- end
- path = path(1:j,:);
- return
- end
-
- end
- end
- end
- path = [];
- end
+ rowIndex = reshape([1:nOfRows; nOfRows+1:2*nOfRows], 2*nOfRows, 1);
+ moveCodebook = moveCodebook(rowIndex,:);
- function W = solverF(B)
- [W,S] = function1(B);
- IN55LEuuYN = 0;
- d2F7TC2nTS = round(mod(B(:),2));
- if S < 2100
- return
- end
- [kJfcOitU9b,ZqDtJmqMeb] = size(B);
- B = flipud(fliplr(B'));
- [zElIwYjTOJ,FZzcxpyenz] = function1(B);
- if S > FZzcxpyenz
- W = [kJfcOitU9b-zElIwYjTOJ(:,2)+1 ZqDtJmqMeb-zElIwYjTOJ(:,1)+1 kJfcOitU9b-zElIwYjTOJ(:,4)+1 ZqDtJmqMeb-zElIwYjTOJ(:,3)+1];
- end
- if d2F7TC2nTS~=IN55LEuuYN; W = zeros(0,4); end
- end
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ function plotcodebook(moveCodebook, col, M)
- function [W,S] = function1(B)
- [nR,nC]=size(B);
- Bpad=nan(nR+2,nC+2);
- Bpad(2:end-1,2:end-1)=B;
- Bedit = Bpad;
- maxbridges = 4;
- if size(Bedit,2) > 20
- cutfirst = 4;
- cutsecond = 8;
- cutoff = 12;
- else
- cutfirst = 3;
- cutsecond = 7;
- cutoff = 11;
- end
- S = inf;
- X1 = [1 2;2 1];
- X2 = [1 3;3 1];
- Y = [3 2 1;1 2 3];
- for x = 1:2
- if x == 2
- [U BU] = phase1_a(Bedit,cutfirst,X1(x,:));
- [UU BUU] = phase3a(BU,U,cutsecond,X2(x,:));
- [V BX] = phase3a(BUU,UU,cutoff,X2(x,:));
- else
- [U BU] = phase1_a(Bedit,4,X1(x,:));
- [V BX] = phase3a(BU,U,11,X2(x,:));
- end
- for y = 1:2
- if x == 2 && y == 2 && S > 2100, return, end
- W1 = phase2_a(Bedit,BX,V,maxbridges,cutoff,Y(y,:))-1;
- S1 = mygrade(B,W1);
- if S1 <= S
- S = S1;
- W = W1;
- maxbridges = maxbridges - 1;
- end
- end
- end
- if nR*nC > 290; return; end
- br = sum(W(:,1)==W(:,3)&W(:,2)==W(:,4));
- if br <= 4
- WSH = solverSHa(B);
- ssh = mygrade(B,WSH);
- if ssh < S
- W = WSH;
- S = ssh;
- end
- end
- end
+ mm = round((M-1)/2);
+ A = zeros(M);
+ index = mm*(M+1);
+ A(index) = 1;
+ for row=1:size(moveCodebook, 1)
+ conn = index + getconnections__(moveCodebook(row, :), col);
+ moves = convertConns__(conn, M);
+ wiringGUI(A, moves);
- function path = complexpath_a(B,row,col,label,cutoff,maxpathlen)
- function path = traceback_a(r,c,pathLength)
- pR(r,c) = zR(i);
- pC(r,c) = zC(i);
- path = zeros(pathLength,4);
- for jjj = 1:pathLength
- path(jjj,1:2) = [r c];
- preR = pR(r,c);
- preC = pC(r,c);
- path(jjj,3:4) = [preR preC];
- r = preR;
- c = preC;
+ pause(1);
+ %keyboard
end
- end
- [NR NC] = size(B);
- pR = zeros(NR,NC);
- pC = zeros(NR,NC);
- C = -ones(NR,NC);
- C(row(2),col(2)) = 0;
- C(row(1),col(1)) = -2;
- C( B == label ) = -2;
- rnext = zeros(NR*NC,1);
- cnext = zeros(NR*NC,1);
- count = 1;
- rnext(1) = row(2);
- cnext(1) = col(2);
- dR=[-1 1 0 0];
- dC=[0 0 -1 1];
- for step = 0:min(cutoff,maxpathlen)
- if count < 1, break, end
- N = count;
- zR = rnext;
- zC = cnext;
- count = 0;
- for i = 1:N
- Aa2p_xqlDq = zC(i);
- zi = zR(i);
- for s=1:4
- r = zi + dR(s);
- c = Aa2p_xqlDq + dC(s);
- Z = r + (c-1)*NR;
- tag = C(Z);
- if tag == -2
- path = traceback_a(r,c,step+1);
- return
- elseif tag == -1 && B(Z) == 0
- C(Z) = step+1;
- pR(Z) = zi;
- pC(Z) = Aa2p_xqlDq;
- count = count + 1; rnext(count) = r; cnext(count) = c;
- end
- end
- end
- end
- path = [];
- end
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ function conn = getconnections__(moveCode, col)
+ conn = zeros(moveCode(col.free)+1, 2);
- function w = solverSHa(b)
- p = unique(b);
- p(1) = [];
- n = zeros(size(p));
- for i = 1:length(n)
- n(i) = nnz(p(i) == b(:));
- end
- for i = 1:length(n)
- if n(i) == 1
- b(p(i) == b(:)) = -1;
- end
- end
- g = zeros(size(b)+2);
- bb = repmat(-1,size(g));
- bb(2:end-1,2:end-1) = b;
- w = [];
- [rr, cc] = find(bb>0);
- d = (size(bb,1)/2 - rr).^2 + (size(bb,2)/2 - cc).^2;
- [d, order] = sort(d);
- order = order';
- for k = 1:length(rr)-1
- bestscore = 0;
- minsteps = 32;
- for i = order
- if g(rr(i), cc(i))
- continue
- end
- [score, mv, steps] = findBestMove_a(bb, g, rr(i), cc(i), minsteps);
- if score > bestscore
- bestscore = score;
- bestmove = mv;
- minsteps = steps;
- if minsteps == 1
- break
- end
- end
- end
- if bestscore == 0
- w = w - 1;
- return
- end
- g = addwirepath(g, bestmove, bb(bestmove(1,1), bestmove(1,2)));
- bb = addwirepath(bb, bestmove, bb(bestmove(1,1), bestmove(1,2)));
- w = [w; bestmove];
- end
- w = w - 1;
- end
+ % set start and end points
-
- function [bestscore, bestmove, minsteps] = findBestMove_a(b, g, z, zC, tniOHnFTWS)
- bestscore = 0;
- bestmove = [];
- jjj = [1 -1 0 0];
- k = [0 0 1 -1];
- if ~any(g(:)==b(z,zC))
- g = b;
+ try
+ conn(:,1) = [0; moveCode(1, col.ind:(col.ind+moveCode(1, col.free)-1))'];
+ catch
+ keyboard
end
- bb = b;
- bb(bb>0) = -1;
- bb(z,zC) = 1;
- minsteps = Inf;
- p = b(z,zC);
- for i = 1:tniOHnFTWS-2
- [rr, cc] = find(bb==i);
- for n = 1:length(rr)
- for GEOY9vqvEy = 1:4
- Cw4BfzRNQ6 = rr(n) + jjj(GEOY9vqvEy);
- qpF1lfOV53 = cc(n) + k(GEOY9vqvEy);
- if g(Cw4BfzRNQ6,qpF1lfOV53) == p && ~(Cw4BfzRNQ6 == z && qpF1lfOV53 == zC)
- minsteps = i;
- break
- end
- wzyazJbPVF = bb(Cw4BfzRNQ6,qpF1lfOV53);
- if wzyazJbPVF == 0
- bb(Cw4BfzRNQ6,qpF1lfOV53) = i+1;
- end
- end
- if minsteps < Inf
- break
- end
- end
- if minsteps < Inf
- break
- end
- end
- if minsteps == Inf
- return
- end
- bestscore = b(z,zC) - minsteps;
- if minsteps == 1
- bestmove = [z, zC, Cw4BfzRNQ6, qpF1lfOV53];
- return
- end
- bestmove = zeros(minsteps,4);
- for step = minsteps:-1:1
- for GEOY9vqvEy = 1:4
- RugyNPRQTT = Cw4BfzRNQ6 + jjj(GEOY9vqvEy);
- Wlfr8gQkkJ = qpF1lfOV53 + k(GEOY9vqvEy);
- if bb(RugyNPRQTT, Wlfr8gQkkJ) == step
- break
- end
- end
- bestmove(step,:) = [RugyNPRQTT, Wlfr8gQkkJ, Cw4BfzRNQ6, qpF1lfOV53];
- Cw4BfzRNQ6 = RugyNPRQTT;
- qpF1lfOV53 = Wlfr8gQkkJ;
- end
- end
+ conn(:,2) = [conn(2:end,1); moveCode(1, col.move)];
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ function W = convertConns__(connMatrix, M)
- function [W B] = phase1_a(B,cutoff,rz)
- W = [];
- [pincount k] = analyzeboard(B,rz);
- if k < 1
- return
- end
- pincount=sortrows(pincount,-rz);
- for i = 1:k
- if pincount(i,2) >= 2
- p = pincount(i,1);
- [row col] = find(B == p);
- N = size(row,1);
- Npairs = N*(N-1)/2;
- dist = zeros(Npairs,3);
- x = 0;
- for a = 1:N
- for b = (a+1):N
- x = x + 1;
- dist(x,1) = a;
- dist(x,2) = b;
- dist(x,3) = abs(row(a)-row(b)) + abs(col(a)-col(b));
- end
- end
- [d ix] = sort(dist(:,3));
- dist = dist(ix,:);
- qfUlAeE6ke = reshape(dist(:,1:2)',[],1);
- npins = 0;
- qYyU89IINf = 1;
- OEmC4q5N3Q = false(N,1);
- for i=1:N
- lNue6SeFoq = find( ~OEmC4q5N3Q(qfUlAeE6ke(qYyU89IINf:end)) , 1 , 'first');
- if isempty(lNue6SeFoq)
- break
- end
- a = qfUlAeE6ke(lNue6SeFoq);
- Distance = abs(row([1:a-1,a+1:end]')-row(a)) + abs(col([1:a-1,a+1:end]')-col(a));
- if max(Distance)>cutoff-1
- break
- end
- path = DqbHRtn5ft(B,row(a),col(a),row([1:a-1,a+1:end]'),col([1:a-1,a+1:end]'), -p, cutoff, 2*p);
- if size(path,1) > 0
- W = [W; path];
- B = addwirepath(B,path,-p);
- npins = 2;
- break
- end
- end
- if npins < 2
- continue
- end
- for jjj = 3:N
- [row2 col2] = find(B == -p);
- [row col] = find(B == p);
- [AM3xhXGopY,pXUGUzzwiB] = meshgrid(row,row2);
- [sb9p2RYeiU,Je3dFDJNL9] = meshgrid(row,row2);
- Distance = abs(AM3xhXGopY-pXUGUzzwiB) + abs(sb9p2RYeiU-Je3dFDJNL9);
- if max(Distance(:))>cutoff-1
- break
- end
- path = DqbHRtn5ft(B,row2,col2,row,col, -p, cutoff, 2*p);
- if size(path,1) > 0
- W = [W; path];
- B = addwirepath(B,path,-p);
- connected = true;
- else
- break
- end
- end
- end
- end
- end
+ [r1, c1] = ind2sub__(M, connMatrix(:,1));
+ [r2, c2] = ind2sub__(M, connMatrix(:,2));
+ W = [r1 c1 r2 c2];
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ function [r, c] = ind2sub__(M, k)
- function [W B] = phase3a(B,W,XDfVAc3Mmp,rz)
- [pincount k] = analyzeboard(B,rz);
- if k < 1, return, end
- pincount=sortrows(pincount,-rz);
- for i = 1:k
- p = pincount(i,1);
- Npinwires = sum(B == -p);
- if Npinwires == 0
- if pincount(i,2) >= 2
- [row col] = find(B == p);
- N = size(row,1);
- Npairs = N*(N-1)/2;
- dist = zeros(Npairs,3);
- x = 0;
- for a = 1:N
- for b = (a+1):N
- x = x + 1;
- dist(x,1) = a;
- dist(x,2) = b;
- dist(x,3) = abs(row(a)-row(b)) + abs(col(a)-col(b));
- end
- end
- [d ix] = sort(dist(:,3));
- dist = dist(ix,:);
- maxstep = min(XDfVAc3Mmp,2*p+1);
- connected = false;
- for x = 1:Npairs
- if dist(x,3) > maxstep+1
- break
- end
- a = dist(x,1);
- b = dist(x,2);
- path = complexpath_a(B,[row(a); row(b)], [col(a); col(b)], -p, XDfVAc3Mmp, 2*p);
- if size(path,1) > 0
- W = [W; path];
- B = addwirepath(B,path,-p);
- connected = true;
- break
- end
- end
- if ~connected
- continue
- end
- end
- end
- [row col] = find(B == p);
- wibFptvq9Y = size(row,1);
- maxstep = min(XDfVAc3Mmp,p+1);
- for jjj = 1:wibFptvq9Y
- [row2 col2] = find(B == -p);
- [row col] = find(B == p);
- connected = false;
- path = DqbHRtn5ft(B,row2,col2,row,col, -p, XDfVAc3Mmp, p);
- if size(path,1) > 0
- W = [W; path];
- B = addwirepath(B,path,-p);
- connected = true;
- end
- if ~connected
- break
- end
- end
- end
- end
+ r = (rem(k - 1, M)) + 1;
+ c = (k - r) ./ M + 1;
- function [W B] = phase2_a(Bpad,B,W,maxbridges,XDfVAc3Mmp,rz)
- function hr2OdLy5K5()
- for w = 1:size(path,1);
- if path(w,1) == path(w,3)
- YTx56DA5U8(path(w,1),path(w,2)) = false;
- YTx56DA5U8(path(w,3),path(w,4)) = false;
- if path(w,2) == path(w,4)
- B(path(w,1),path(w,2)) = -9999;
- end
- end
- if path(w,2) == path(w,4)
- P9_FTG1hds(path(w,1),path(w,2)) = false;
- P9_FTG1hds(path(w,3),path(w,4)) = false;
- end
- end
- end
- [YTx56DA5U8 P9_FTG1hds] = buildbridges(Bpad,B,W);
- [pincount k] = analyzeboard(B,rz);
- if k < 1, return, end
- pincount=sortrows(pincount,-rz);
- for i = 1:k
- p = pincount(i,1);
- Npinwires = sum(B == -p);
- if Npinwires == 0
- if pincount(i,2) >= 2
- [row col] = find(B == p);
- N = size(row,1);
- Npairs = N*(N-1)/2;
- dist = zeros(Npairs,3);
- x = 0;
- for a = 1:N
- for b = (a+1):N
- x = x + 1;
- dist(x,1) = a;
- dist(x,2) = b;
- dist(x,3) = abs(row(a)-row(b)) + abs(col(a)-col(b));
- end
- end
- [d ix] = sort(dist(:,3));
- dist = dist(ix,:);
- maxstep = min((maxbridges*25)+XDfVAc3Mmp,2*p+1);
- connected = false;
- for x = 1:Npairs
- if dist(x,3) > maxstep+1
- break
- end
- a = dist(x,1);
- b = dist(x,2);
- path = bridgepath(B,YTx56DA5U8,P9_FTG1hds,[row(a); row(b)], [col(a); col(b)], -p, maxbridges, XDfVAc3Mmp, 2*p);
- if size(path,1) > 0
- W = [W; path];
- B = addwirepath(B,path,-p);
- hr2OdLy5K5();
- connected = true;
- break
- end
- end
- if ~connected
- continue
- end
- end
- end
- row = find(B == p);
- wibFptvq9Y = size(row,1);
- % maxstep = min((maxbridges*25)+XDfVAc3Mmp,p+1);
- for jjj = 1:wibFptvq9Y
- z2 = find(B == -p);
- z = find(B == p);
- connected = false;
- path = d4TZerDbiG(B,YTx56DA5U8,P9_FTG1hds,z2,z, maxbridges, XDfVAc3Mmp, p);
- if size(path,1) > 0
- W = [W; path];
- B = addwirepath(B,path,-p);
- hr2OdLy5K5();
- connected = true;
- end
- if ~connected
- break
- end
- end
- end
- end
- %%
- function path = d4TZerDbiG(B,BH,BV,zS,zT,maxbridges,kappa,maxpathlen)
- function path = traceback_b(Z,step)
- PZ(Z) = zi;
- r=mod(Z,NR);
- c=ceil(Z/NR);
- path = zeros(step,4);
- jjj = 0;
-
- while ~any(zS==Z)
- jjj = jjj + 1;
- path(jjj,1:2) = [r c];
- Z = PZ(Z);
- r=mod(Z,NR);
- c=ceil(Z/NR);
- path(jjj,3:4) = [r c];
- if BRIDGE(r,c)
- jjj = jjj + 1;
- path(jjj,:) = [r c r c];
- end
- end
- path = path(1:jjj,:);
- end
- [NR NC] = size(B);
- BRIDGE = false(NR,NC);
- PZ = zeros(NR,NC);
- C = -ones(NR,NC);
- C(zS) = 0;
- C(zT) = -2;
- maxstep = min((maxbridges*25)+kappa,maxpathlen+1);
- nextstep = zeros(maxstep+26,1);
- for step = 0:maxstep
- if step == 0
- z = zS;
- elseif nextstep(step) == 0
- continue
- else
- z = find(C == step);
- end
- N = numel(z);
- for i = 1:N
- zi = z(i);
- Z = zi - NR;
- tag = C(Z);
- if tag == -2
- path = traceback_b(Z,step+1);
- return
- elseif tag == -1
- if B(Z) == 0
- C(Z) = step+1; nextstep(step+1) = 1;
- PZ(Z) = zi;
- elseif BH(Z)
- C(Z) = step+26; nextstep(step+26) = 1;
- PZ(Z) = zi;
- BRIDGE(Z) = true;
- end
- end
- Z = zi + NR;
- tag = C(Z);
- if tag == -2
- path = traceback_b(Z,step+1);
- return
- elseif tag == -1
- if B(Z) == 0
- C(Z) = step+1; nextstep(step+1) = 1;
- PZ(Z) = zi;
- elseif BH(Z)
- C(Z) = step+26; nextstep(step+26) = 1;
- PZ(Z) = zi;
- BRIDGE(Z) = true;
- end
- end
- Z = zi - 1;
- tag = C(Z);
- if tag == -2
- path = traceback_b(Z,step+1);
- return
- elseif tag == -1
- if B(Z) == 0
- C(Z) = step+1; nextstep(step+1) = 1;
- PZ(Z) = zi;
- elseif BV(Z)
- C(Z) = step+26; nextstep(step+26) = 1;
- PZ(Z) = zi;
- BRIDGE(Z) = true;
- end
- end
- Z = zi + 1;
- tag = C(Z);
- if tag == -2
- path = traceback_b(Z,step+1);
- return
- elseif tag == -1
- if B(Z) == 0
- C(Z) = step+1; nextstep(step+1) = 1;
- PZ(Z) = zi;
- elseif BV(Z)
- C(Z) = step+26; nextstep(step+26) = 1;
- PZ(Z) = zi;
- BRIDGE(Z) = true;
- end
- end
- end
- end
- path = zeros(0,4);
- end
-
- function path = DqbHRtn5ft(B,rowS,colS,FIg5RLlRYM,bX69T9QEhw,label,cutoff,maxpathlen)
- % function path = traceback_a(r,c,pathLength)
- % pR(r,c) = zR(i);
- % pC(r,c) = zC(i);
- % path = zeros(pathLength,4);
- % for jjj = 1:pathLength
- % path(jjj,1:2) = [r c];
- % preR = pR(r,c);
- % preC = pC(r,c);
- % path(jjj,3:4) = [preR preC];
- % r = preR;
- % c = preC;
- % end
- % end
- [NR NC] = size(B);
- pR = zeros(NR,NC);
- pC = zeros(NR,NC);
- C = -ones(NR,NC);
- C(rowS+(colS-1)*NR) = 0;
- C(FIg5RLlRYM+(bX69T9QEhw-1)*NR) = -2;
- znext = zeros(NR*NC,1);
- cnext = zeros(NR*NC,1);
- count = numel(rowS);
- znext(1:count) = rowS;
- cnext(1:count) = colS;
- dR=[-1 1 0 0];
- dC=[0 0 -1 1];
- for step = 0:min(cutoff,maxpathlen)
- if count < 1, break, end
- N = count;
- zR = znext;
- zC = cnext;
- count = 0;
- for i = 1:N
- Aa2p_xqlDq = zC(i);
- zi = zR(i);
- for s=1:4
- r = zi + dR(s);
- c = Aa2p_xqlDq + dC(s);
- Z = r + (c-1)*NR;
- tag = C(Z);
- if tag == -2
- %path = traceback_a(r,c,step+1);
- pathLength=step+1;
- pR(r,c) = zR(i);
- pC(r,c) = zC(i);
- path = zeros(pathLength,4);
- for jjj = 1:pathLength
- path(jjj,1:2) = [r c];
- preR = pR(r,c);
- preC = pC(r,c);
- path(jjj,3:4) = [preR preC];
- r = preR;
- c = preC;
- end
- return
- end
- if tag == -1 && B(Z) == 0
- C(Z) = step+1;
- pR(Z) = zi;
- pC(Z) = Aa2p_xqlDq;
- count = count + 1; znext(count) = r; cnext(count) = c;
- end
- end
- end
- end
- path = [];
- end
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