Greedier 0000

function xyOut = solver(a, xyIn, wts)
deg=diag(sum(a));
[V,~]=eig(deg-a,deg);
N = length(a);
[p1i,p2i] = find( triu(a,1));
[pickr,pickc] = find(tril(true(nnz(triu(a,1))),-1));

for ss=1:3
    [xy{ss} xy{ss+3}] = solver_alfonsoz (a, ss+1, N, V+rand(size(V))/25); % (Biswas)
end
%[xy{7} xy{8}] = solver_alfonsoz (a, 1, N, V);
xy{7} = solver_hannes(xyIn, N, V(:,2:3),0);

parfor ss=1:7
 NN(ss)=gradeIt(p1i,p2i,pickr,pickc,xy{ss})
end

[ZBest,best] = min(NN);
xyOut = xy{best};

xyOut = bsxfun(@minus,xyOut,round(wts*(xyOut-xyIn)./sum(wts)));

sprev = rng(0,'twister');

for ii=1:2
for jiggle=1:40
 xyOutZ=xyOut+randi([-ii ii],N,2);
 grade=gradeIt(p1i,p2i,pickr,pickc,xyOutZ);
 if grade<ZBest && size(unique(xyOutZ,'rows'),1)==N
  xyOut=xyOutZ;
  ZBest=grade;
 end
end
end

rng(sprev);

for jiggle=2:min(20,N)
 xyOutJ=xyOut;
 idx=jiggle:jiggle:2*N;
 
 xyOutJ(idx)=xyOut(idx)+1;
 grade=gradeIt(p1i,p2i,pickr,pickc,xyOutJ);
 if grade<ZBest && size(unique(xyOutJ,'rows'),1)==N
  xyOut=xyOutJ; % Use jiggle enhanced for more jiggling
  %break % Greedy
  ZBest=grade;
 end
 
 xyOutJ(idx)=xyOut(idx)-1;
 grade=gradeIt(p1i,p2i,pickr,pickc,xyOutJ);
 if grade<ZBest && size(unique(xyOutJ,'rows'),1)==N
  xyOut=xyOutJ; % Use jiggle enhanced for more jiggling
  %break % Greedy
  ZBest=grade;
 end
 
end






end

function [xyOut xyOut1] = solver_alfonsoz(a, ss, N, V)
randn('seed',ss);
xyOut=V(:,2:3);
sN=sqrt(N);
for ncut=1:2
    Mbeta=((1-ss/15)*eye(N)+(ss/15)*bsxfun(@rdivide,a+eye(N),sum(a,2)+1))^10;
    for n1=1:(117+ss)
        xyOut=Mbeta*xyOut;
        xc = bsxfun(@minus,xyOut,sum(xyOut)/N);
        [c1,D]=svd(xc');
        xyOut=xc*c1*diag(sN./(.1+D([1 4])))*c1';
    end
    [i,j]=find(a>0.00075+ss*5.1e-4);
    dd=sum((xyOut(i,:)-xyOut(j,:)).^2,2);
    k=find(dd>(3.15 + ss*0.102)*mean(dd));
    if isempty(k), break; end
    a(i(k)+N*(j(k)-1))=0.00075+ss*5.1e-4;
end

xyOutH=xyOut;
single_idx = find(sum(a)==1);
[singles_link, ~] = find(a(:,single_idx)==1);
xyOut(single_idx,:)=xyOut(singles_link,:);

for zsingle=1:2  
    xyOut0=sqrt(N)*detrend(xyOut,'constant')*diag(1./std(xyOut,1,1));
    k=5;
    [sxyOut0,idxequal]=sortrows(round(15*xyOut0));
    idxequal=idxequal(all(~diff(sxyOut0,1,1),2));
    xyOut=round(xyOut0);
    while size(unique(xyOut,'rows'),1)~=N
        k=k*(1.0+ss*0.055);
        xyOut=xyOut0*k;
        xyOut(idxequal,:)=(xyOut0(idxequal,:)+randn(numel(idxequal),2)/(9+ss))*k;
        xyOut=round(xyOut);
    end
    if zsingle==1
        xyOut1=xyOut;
        xyOut=xyOutH;
    end
end 
end

function xyOut = solver_hannes(xyIn, N, V,xyOut)
mult    = norm(max(xyIn)-min(xyIn))/norm(max(V)-min(V));
%xyOut   = [];
while size(unique(xyOut,'rows'),1)<N
    xyOut       = round(V*mult);
    [~,i]       = unique(xyOut,'rows');
    m           = setdiff(1:N,i);
    xyOut(m,:)  = xyOut(m,:) + round(rand(length(m),2))*2 - 1;
    mult        = mult*1.5;
end
end

function ans = gradeIt(p1i,p2i,pickr,pickc,XYnew)

X = [XYnew(p1i,:) XYnew(p2i,:)];
x1 = X(pickr,:);
x3 = X(pickc,:);
sum(areIntersecting(x1(:,1),x1(:,2),x1(:,3),x1(:,4),x3(:,1),x3(:,2),x3(:,3),x3(:,4)));
end

function ans = areIntersecting(x1,y1,x2,y2,x3,y3,x4,y4)
a = x1.*y2 - y1.*x2;
b = x3.*y4 - y3.*x4;
Px_n = a.*(x3 - x4) - b.*(x1 - x2);
Py_n = a.*(y3 - y4) - b.*(y1 - y2);
Pxy_d = (x1 - x2).*(y3 - y4) - (y1 - y2).*(x3 - x4);
isPointBetween(x1, x2, Px_n, Pxy_d) & ...
    isPointBetween(y1, y2, Py_n, Pxy_d) & ...
    isPointBetween(x3, x4, Px_n, Pxy_d) & ...
    isPointBetween(y3, y4, Py_n, Pxy_d);
end

function ans = isPointBetween(pt1, pt2, num, den)
(pt1.*den - num).*(num - pt2.*den) >= 0;
end