Finish 2012-11-07 16:00:00 UTC

Sunday Brunch

by AMITAVA BISWAS

Status: Passed
Results: 1318 (cyc: 7, node: 1014)
CPU Time: 40.82
Score: 1359.42
Submitted at: 2012-11-04 15:48:51 UTC
Scored at: 2012-11-04 16:00:21 UTC

Current Rank: 817th (Highest: 1st )
Basis for: try83 (diff)
Basis for: try84 (diff)
Basis for: SB2 No H (diff)
...and 13 others.

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Code
function xyOut = solver(a, xyIn, wts)
deg=diag(sum(a));
[V,~]=eig(deg-a,deg);
N = length(a);
A = triu(a,1);
for ss=1:3
    [xy{ss} xy{ss+3}] = solver_alfonsoz (a, xyIn , wts, ss+1, N, V+rand(size(V))/30); % (Biswas)
    NN(ss) = gradeIt(A,xy{ss});
    NN(ss+3) = gradeIt(A,xy{ss+3});
end
xy{7} = solver_hannes(xyIn, N, V);
NN(7) = gradeIt(A,xy{7});
[xy{8} xy{9}] = solver_alfonsoz (a, xyIn , wts, 1, N, V);
NN(8) = gradeIt(A,xy{8});
NN(9) = gradeIt(A,xy{9});
[~,best] = min(NN);
xyOut = xy{best};

end

function [xyOut xyOut1] = solver_alfonsoz(a, xyIn, wts, ss, N, V)
randn('seed',ss);
xyOut=V(:,2:3);

for ncut=1:2
    Mbeta=((1-ss/10)*eye(N)+(ss/10)*bsxfun(@rdivide,a+eye(N),sum(a,2)+1))^10;
    for n1=1:(117+ss)
        xyOut=Mbeta*xyOut;
        [c1,D]=svd(cov(xyOut,1));
        xyOut=(bsxfun(@minus,xyOut,mean(xyOut)))*c1*diag(1./sqrt(.1+diag(D)))*c1';
    end
    [i,j]=find(a>0.0075+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))=0.0075+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)/(15)); % (Biswas)
    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
    xyOut = bsxfun(@minus,xyOut,round(wts*(xyOut-xyIn)./sum(wts))); 
    if zsingle==1
        xyOut1=xyOut;
        xyOut=xyOutH;
    end
end 
end

function xyOut = solver_hannes(xyIn, N, V)
outdiam=sqrt(sum((max(V(:,2:3))-min(V(:,2:3))).^2));
indiam=sqrt(sum((max(xyIn)-min(xyIn)).^2));
mult=indiam/outdiam;
while mult==indiam/outdiam || size(unique(xyOut,'rows'),1)<N
    xyOut=round(V(:,2:3)*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 S = gradeIt(A,XYnew)
nLines = nnz(A);
[p1i,p2i] = find(A);
pick = tril(true(nLines),-1);
for nt=1:2
    x1{nt} = pickCoordinates(XYnew(p1i,nt) ,1,nLines,pick);
    x3{nt} = pickCoordinates(XYnew(p1i,nt)',nLines,1,pick);
    x2{nt} = pickCoordinates(XYnew(p2i,nt) ,1,nLines,pick);
    x4{nt} = pickCoordinates(XYnew(p2i,nt)',nLines,1,pick);
end
S = sum(areIntersecting(x1{1},x1{2},x2{1},x2{2},x3{1},x3{2},x4{1},x4{2}));
end

function bool = 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);
bool = (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 x = pickCoordinates(xy,n,m,pick)
x = repmat(xy,n,m);
x = x(pick);
end

function bool = isPointBetween(pt1, pt2, num, den)

bool = ((pt1.*den <= num) & (num <= pt2.*den)) | ...
    ((pt1.*den >= num) & (num >= pt2.*den));
end