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

The art of mergers

by Fel

Status: Passed
Results: 1374 (cyc: 6, node: 1263)
CPU Time: 52.048
Score: 1444.68
Submitted at: 2012-11-03 21:46:18 UTC
Scored at: 2012-11-03 21:53:06 UTC

Current Rank: 1165th (Highest: 84th )
Based on: The art of mergers (diff)
Basis for: The art of mergers (diff)
Basis for: The art of mergers (diff)
Basis for: The art of mergers (diff)

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Code
function xyOut = solver(a, xyIn, wts)

% Place nodes in radial pattern
xy{1}       = solver_alfonso  (a, xyIn, wts);
xy{2}       = solver_hannes   (a, xyIn);
xy{3}       = solver_pavan(a, xyIn);
N(1)        = gradeIt(a,xyIn,xy{1},wts);
N(2)        = gradeIt(a,xyIn,xy{2},wts);
N(3)        = gradeIt(a,xyIn,xy{3},wts);
[~,best]    = min(N);
xyOut       = xy{best};

end

function xyOut = solver_alfonso(a, xyIn, wts)

randn('seed',2);

N=length(wts);
    
    deg=diag(sum(a));
    [V,~]=eig(deg-a,deg);
    xyOut=V(:,2:3);

for ncut=1:2
    Mbeta=(0.9*eye(N)+0.1*bsxfun(@rdivide,a+eye(N),sum(a,2)+1))^10;
    for n1=1:119
        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>0.009); 
    dd=sum((xyOut(i,:)-xyOut(j,:)).^2,2);
    k=find(dd>3.35*mean(dd));
    if isempty(k), break; end
    a(i(k)+N*(j(k)-1))=0.009;
end

xyOut0=sqrt(N)*detrend(xyOut,'constant')*diag(1./std(xyOut,1,1));
k=5;
[sxyOut0,idxequal]=sortrows(round(15*xyOut0)/15);
idxequal=idxequal(all(~diff(sxyOut0,1,1),2));
xyOut=round(xyOut0);
while size(unique(xyOut,'rows'),1)~=N
    k=k*1.1;
    xyOut=xyOut0*k;
    xyOut(idxequal,:)=(xyOut0(idxequal,:)+randn(numel(idxequal),2)/10)*k;
    xyOut=round(xyOut);
end
if N<35 % small map knot lines
 xyOut=3*xyOut+randi([-1,1],N,2);
end

xyOut = bsxfun(@minus,xyOut,round(wts*(xyOut-xyIn)./sum(wts))); % AV's
end

function xyOut = solver_hannes(a, xyIn)
% Entry 67561: 2503 (cyc: 2, node: 166) CPU Time: 1.536 Score: 2505.98

sz      = size(a,1);
deg     = diag(sum(a));
L       = deg-a;
[V,~]   = eig(L,deg);
xyOut   = 0;
outdiam = norm(max(V(:,2:3)) - min(V(:,2:3)));
indiam  = norm(max(xyIn)     - min(xyIn));
mult    = indiam/outdiam;

while size(unique(xyOut,'rows'),1) < sz
    
    xyOut      = round(V(:,2:3)*mult);
    [~,i]      = unique(xyOut,'rows');
    m          = setdiff(1:sz,i);
    xyOut(m,:) = xyOut(m,:) + round(rand(length(m),2))*2 - 1;
    mult       = mult*1.5;
    
end

end

function xyOut = solver_pavan(a, xyIn)
% Entry 67362: 10567 (cyc: 2, node: 225) CPU Time: 38.203 Score: 10575.5

s = 100;
zmax = 50;
tweakdir = [1 0; 0 -1];
orig_mean = mean(xyIn, 1);
len = length(xyIn);

xyIn = (xyIn - repmat(orig_mean, len, 1)).*s + repmat(orig_mean, len, 1);
for z = 1:zmax
   xyIn = round(cell2mat(cellfun(@(a_row) mean(xyIn(a_row==1, :), 1), num2cell(a, 1), 'uni', false)'));
   tweak_overlap
   xyIn = (xyIn - repmat(orig_mean, len, 1)).*1.05 + repmat(orig_mean, len, 1);
end

xyOut = xyIn;
%shift mean back
xyOut = round(xyOut + repmat(orig_mean - mean(xyOut, 1), length(xyIn), 1));
tweak_overlap;

    function tweak_overlap
        [u I J] = unique(xyIn, 'rows');
        n = size(xyIn, 1) - size(u, 1);
        while(n>0)
            xyIn(setdiff(1:length(xyIn), I), :) = xyIn(setdiff(1:length(xyIn), I), :) + ones(n, 2) * tweakdir;
            [u I J] = unique(xyIn, 'rows');
            n = size(xyIn, 1) - size(u, 1);
        end
    end


end

function S = gradeIt(a,XYold,XYnew,wts)

A         = triu(a,1);
nLines    = nnz(A);
[p1i,p2i] = find(A);
pick      = tril(true(nLines),-1);
x1        = pickCoordinates(XYnew(p1i,1) ,1,nLines,pick);
x3        = pickCoordinates(XYnew(p1i,1)',nLines,1,pick);
y1        = pickCoordinates(XYnew(p1i,2) ,1,nLines,pick);
y3        = pickCoordinates(XYnew(p1i,2)',nLines,1,pick);
x2        = pickCoordinates(XYnew(p2i,1) ,1,nLines,pick);
x4        = pickCoordinates(XYnew(p2i,1)',nLines,1,pick);
y2        = pickCoordinates(XYnew(p2i,2) ,1,nLines,pick);
y4        = pickCoordinates(XYnew(p2i,2)',nLines,1,pick);

N         = sum(areIntersecting(x1,y1,x2,y2,x3,y3,x4,y4));
d         = sqrt(sum((XYnew-XYold).^2,2));
A         = bsxfun(@minus,XYold',mean(XYold',2));
S         = full(dot(A,A,1));
D         = bsxfun(@plus,S,S')-full(2*(A'*A));
D         = sqrt(max(max(D)));
S         = N + sum(d.*wts')/D/sum(wts);

end

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

function bool = areIntersecting(x1,y1,x2,y2,x3,y3,x4,y4)


Px_n = (x1.*y2 - y1.*x2).*(x3 - x4) - (x1 - x2).*(x3.*y4 - y3.*x4);
Px_d = (x1 - x2).*(y3 - y4) - (y1 - y2).*(x3 - x4);

Py_n = (x1.*y2 - y1.*x2).*(y3 - y4) - (y1 - y2).*(x3.*y4 - y3.*x4);
Py_d = (x1 - x2).*(y3 - y4) - (y1 - y2).*(x3 - x4);


bool = (isPointBetween(x1, x2, Px_n, Px_d) & ...
        isPointBetween(y1, y2, Py_n, Py_d) & ...
        isPointBetween(x3, x4, Px_n, Px_d) & ...
        isPointBetween(y3, y4, Py_n, Py_d));

end

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

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