Finish 2011-11-09 12:00:00 UTC

Some say that he is the real reason for the NBA lockout

by Magnus S

Status: Passed
Results: 65573693 (cyc: 10, node: 8659)
CPU Time: 71.372
Score: 655850.0
Submitted at: 2011-11-09 15:07:34 UTC
Scored at: 2011-11-09 15:10:13 UTC

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Code
function [moves, vine] = solver(board, limit)

[m,n] = size(board);
largestValue = max(board(:));
original=board;

if limit > 0
    % Gwendolyn's neat board-tuning
    board(board<median(board(:))/114)=0;
end

%Allocate result cell
resultcell(:,3) = num2cell(-inf(9,1));

id = reshape( 1:m*n, m, n);

if limit < 14000
    [resultcell{1,1}, resultcell{1,2}, resultcell{1,3}] = alfi(board, limit);
end

if largestValue > 220
    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{5,3}] = robert(flipud(board),limit);
        idtemp = flipud(id);
        resultcell{5,1} = idtemp(movestemp);
        resultcell{5,2} = 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
    
    [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 resultcell{5,3} < 2 * max(cell2mat(resultcell([1 2 3 4 5 9],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};

[moves,vine]=oftl10(moves,limit,board,vine,original);

end

function [moves,vine]=oftl10(moves,limit,board,vine,original)
if size(moves,1) < limit
    [moves, vine] = use_more_moves(board, moves, vine, limit);
end
if limit > 0 && ~all(board(:)==original(:))
    [moves, vine] = robert3(original, moves, vine);
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 = [];
else
    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
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)];
        
        possible_moves(1) = [];
        moves_req(1) = [];
        
    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);
    cboard(cy,cx) = 0;
    rank(cy,cx) = 0;
    cx = cx+dx;
    cy = cy+dy;
    moves(steps,2) = pos(cy,cx);
    cboard(cy,cx) = s(i);
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);

m = size(board,1) + 2;
n = size(board,2) + 2;

board2 = zeros( m, n );
board2(2:end-1,2:end-1) = board;
board = board2;

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] = postprocess(board,iC,moves,limit);
    %    [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)
[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=[]; 
        elseif 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
            idx2=oftl11(type,limit,board,idx1,D);
            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
            idx2=oftl11(type,limit,board,idx1,D);
            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 idx2=oftl11(type,limit,board,idx1,D)
            if limit>150*type
                [~,idx2]=min((3-2*type)*board(idx1)+1e-3*D(idx1)); %%%t3
            else
                [~,idx2]=min((3-2*type)*board(idx1).*(D(idx1)./limit).^((3-2*type)*(.315-.115*type))); %%%t3
            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);
    
    [B,C,updated] = oftl12(flag1, flag2, flag3, flag4, idxStart, A,B,C,updated,m);
    
    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] = oftl12(flag1, flag2, flag3, flag4, idxStart, A,B,C,updated,m)
    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
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
            [moves,board]=oftl13(moveFromCol,moveToCol,moves,limit,row,rows,board,0);
        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
            [moves,board]=oftl13(moveToCol,moveFromCol,moves,limit,row,rows,board,1);
        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]=oftl13(moveFromCol,moveToCol,moves,limit,row,rows,board,offset)
for j = moveFromCol:moveToCol-1
    if size(moves,1) < limit
        moves = [moves; [row+rows*(j-1+offset), row+rows*(j-offset)]];
        board(row,j+1-offset) = board(row,j+offset);
        board(row,j+offset) = 0;
    else
        break   % Used up all moves
    end
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 = size(boardin,1);
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
        for step = stepvec;
            targ = test + step;
            [score,dir]=oftl14(targ,boardsize,step,rows,test,board,score,dir);
        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 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

function [moves,vine] = robert3(board, moves, vine)
% 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>=last)=NaN;
board(board==0)=NaN;
board(vine(1))=last;

dir = zeros(size(board));   % points way down vine, 0 at root
rows = size(board,1);
boardsize   = numel(board);
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

stepvec = [-rows,-1,1,rows];

for i = 1:boardsize;
    test = ind(i);
    if isnan(board(test))
        break;
    end
    for step = stepvec;
        targ = test + step;
        [score,dir]=oftl14(targ,boardsize,step,rows,test,board,score,dir);
    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 [score,dir]=oftl14(targ,boardsize,step,rows,test,board,score,dir)
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