Winner Ave (More tricks)

Finish 2003-04-08 00:00:00 UTC

Grouped Finers 03

by Yi Cao

Status: Passed
Results: 1701.102K raw score
CPU Time: 89.408
Score: 1713.59
Submitted at: 2003-04-09 08:42:15 UTC
Scored at: 2003-04-09 08:47:33 UTC

Current Rank: 84th
Based on: Grouped Finers 02 (diff)
Basis for: Grouped Finers 04 (diff)
Basis for: Grouped Finers 05 (diff)

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Code
function c = solver(a)

global randfact

xy = (a(:,1)-a(1)) + 1i*(a(:,2)-a(1,2));
d = abs(xy);
if sum(d(a(:,4)>0) <= a(1,4))<=1 % nearest gas too far
    ia = find(d<=a(1,4)/2);
    a = a(ia,:);
    c = [1 1];
    if (size(a,1)>1)
        X = xy(ia,ones(size(ia)));
        X = abs(X.'-X); %dist
        c = addFreight(a,c,X);
        c = ia(c);
    end
    return  
end

randfact=0;

c = subsolver(a);

ft = sum(a(:,3));    
fp = sum(a(c,3));
if fp/ft<.95 && numel(c)>10,
  da=a(:,4)-a(:,3);
  atmp = a;
  pp=find(a(:,3)>0);
  freightMean = sum(a(pp,3))/numel(d);
  highFreight = find(a(:,3)>freightMean*2);
  randfact=7;
  for k=1:5
    atmp(pp,3)=a(pp,3).^(k+1);
    atmp(highFreight,3) = 1.6*atmp(highFreight,3);
    c2 = subsolver(atmp);
    score2 = sum(da(c2(2:end-1)));
    score1 = sum(da(c(2:end-1)));
    if score2<score1,
      c = c2;
      if k<3
        fp = sum(a(c,3));
      end
    end
    if fp/ft>=.95-.15*k
      break
    end
  end
end



function c = subsolver(a)

iworth=find(a(:,3));

mfreight=sum(a(iworth,3))/length(iworth);

ia=find( a(:,4)>a(1,4)*.0714 | a(:,3)>=(mfreight-1.9)*.074);

a=a(ia,:);
xy = (a(:,1)-a(1)) + 1i*(a(:,2)-a(1,2));

n=size(a,1);
da=a(:,4)-a(:,3);
X = xy(:, ones(n,1));
dist = abs(X-X.');
sfr=sum(a(:,3))*.9;
[c,score1]=routefinder(a,dist,xy);
[c,score1]=optim(a,c,score1,dist,da);
[c,score1]=groupfiners(a,c,score1,dist,da);
sfrc=sum(a(c,3));
if sfrc<sfr
    [c2,score2]=findenum(a,dist,da);
    if score2<score1
      [c2,score2]=groupfiners(a,c2,score2,dist,da);
      c = c2;
      score1 = score2;
    end
end
sfrc=sum(a(c,3));
if sfrc<sfr
    c2=diesel2(a,dist);
    score2 = sum(da(c2(2:end-1)));
    c3 = petrol3(a,dist);
    score3 = sum(da(c3(2:end-1)));
    if(score2<score1)
        [c,score1]=optim(a,c2,score2,dist,da);
    end
    if(score3<score1)
        [c,score1]=optim(a,c3,score3,dist,da);
    end
    [c,score1]=groupfiners(a,c,score1,dist,da);
end
[c,score1]=groupfiners(a,c,score1,dist,da);
if da(1)<score1
    % dummy solution is the best(!!)
    c=[1 1];
end
c=ia(c);

function [c,score1]=groupfiners(a,c,score1,dist,da);
da1=da;
da1(c)=0;
if any(da1<0)
    if numel(c)>6
        c=movepoints(a,c,dist);
        c=savegas(a,c,score1,dist,da);
    end
    c = addGas(a(:,4),c,dist);
    c = addFreight(a,c,dist);
    [c,score1]=optim(a,c,score1,dist,da);
end

function c = addGas(a,c,dist)
cont=1;
c=c(:);
while cont
    gasv=a;
    gasv(c)=0;
    fIdx = find(gasv);
    if isempty(fIdx), return; end % NO GAS LEFT TO ADD
    Nc = length(c);
    
    N = length(fIdx);
    
    % CALCULATE EXCESS GAS AT EACH POINT IN PATH
    d=ones(Nc-1,1);
    for i=1:Nc-1    % faster in Matlab6.5 than sub2ind.. ?
        d(i)=dist(c(i),c(i+1));
    end
    eg = cumsum(a(c(1:Nc-1))-d);
    dispgas=zeros(Nc-1,1);
    dispgas(Nc-1)=eg(Nc-1);
    for counter=Nc-2:-1:1
        dispgas(counter)=min(dispgas(counter+1),eg(counter));
    end
    
    % SORT FREIGHT BY VALUE
    % TRY TO FIT BIGGEST FIRST
    
    ad = dist(c,fIdx);
    h = dispgas(:,ones(1,N)) - (ad(1:Nc-1,:) + ad(2:Nc,:) - d(:,ones(1,N)));
    proximity = max(h);
    [ignore,idx] = sort(-a(fIdx).*proximity(:));
    
    cont=0;
    fIdx = fIdx(idx);
    for n=1:N,
        
        i=fIdx(n);
        % SET OF EXCESS DISTANCES ADDED BY VISITING THIS POINT
        ad = dist(c,i);
        ed = ad(1:Nc-1) + ad(2:Nc) - d;  
        if(any(dispgas>=ed))   
            h=dispgas-ed;
            [ignore,closest] = max(h);     
            
            if ed(closest)<a(fIdx(n))
                if h(closest)>=0
                    cont=1;
                    d1=dist(c(closest),i);
                    d2=dist(i,c(closest+1));
                    d0=dist(c(closest),c(closest+1));
                    c  = [c(1:closest); i; c(closest+1:Nc)];
                    d=[d(1:closest-1);d1;d2;d(closest+1:Nc-1)];
                    eg = cumsum(a(c(1:Nc))-d);
                    dispgas=zeros(Nc,1);
                    dispgas(Nc)=eg(Nc);
                    for counter=Nc-1:-1:1
                        dispgas(counter)=min(dispgas(counter+1),eg(counter));
                    end
                    Nc=Nc+1;
                end
            end
        end    % if any dispgas
    end    % for n
end    % while cont

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% addFreight
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function c = addFreight(a,c,dist)
cont=1;
c=c(:);
a(c,3)=0;
while cont
    Nc = length(c);
    fIdx = find(a(:,3));
    if isempty(fIdx), return; end % NO FREIGHT LEFT TO ADD
    
    N = length(fIdx);
    
    % CALCULATE EXCESS GAS AT EACH POINT IN PATH
    d=ones(Nc-1,1);
    for i=1:Nc-1    % faster in Matlab6.5 than sub2ind.. ?
        d(i)=dist(c(i),c(i+1));
    end
    eg = cumsum(a(c(1:Nc-1),4)-d);
    dispgas=zeros(Nc-1,1);
    dispgas(Nc-1)=eg(Nc-1);
    for counter=Nc-2:-1:1
        dispgas(counter)=min(dispgas(counter+1),eg(counter));
    end
    
    % SORT FREIGHT BY VALUE
    % TRY TO FIT BIGGEST FIRST
    
    ad = dist(c,fIdx);
    h = dispgas(:,ones(1,N)) - (ad(1:Nc-1,:) + ad(2:Nc,:) - d(:,ones(1,N)));
    proximity = max(h);
    [ignore,idx] = sort(-a(fIdx,3).*proximity(:));
    
    %[ignore,idx] = sort(-a(fIdx,3));
    fIdx = fIdx(idx);
    cont=0;
    for n=1:N
        
        i=fIdx(n);
        % SET OF EXCESS DISTANCES ADDED BY VISITING THIS POINT
        ad = dist(c,i);
        ed = ad(1:Nc-1) + ad(2:Nc) - d;     
        %%%%%%%%%%%%%%%%%%%  This seems to be quicker than the max...
        if any(dispgas>=ed)
            %%%%%%%%%%%%%%%%%%%
            h=dispgas-ed;
            [ignore,closest] = max(h);     
            
            if h(closest)>=0
                cont=1;
                d1=dist(c(closest),i);
                d2=dist(i,c(closest+1));
                d0=dist(c(closest),c(closest+1));
                a(i,3)=0;
                c  = [c(1:closest); i; c(closest+1:Nc)];
                d=[d(1:closest-1);d1;d2;d(closest+1:Nc-1)];
                eg=[eg(1:closest-1);eg(closest)+d0-d1;eg(closest:Nc-1)-(d1+d2-d0)];
                
                dispgas=zeros(Nc,1);
                dispgas(Nc)=eg(Nc);
                for counter=Nc-1:-1:1
                    dispgas(counter)=min(dispgas(counter+1),eg(counter));
                end;
                Nc=Nc+1;
            end
        end
    end
end

function c = diesel2(a,Dmat)

global randfact;

n=size(a,1);
rand('state',1+randfact);
freightv=a(:,3);
petrolv=a(:,4);

Dmat1=Dmat(:,1);

pos=1;
jdest=1;

totalpetrol=sum(petrolv);
unitpetrol = totalpetrol/(n-1);
petroln=petrolv/totalpetrol;
totalfreight=sum(freightv);
freightn=freightv/totalfreight;


petrol  = petrolv(1);
petrolv(1)=0; freightv(1)=-1;
imax=[0;0];

notbeenthere=logical(ones(n,1));
notbeenthere(1)=0;
c=ones(n+1,1);
notnearlythere=notbeenthere;

while 1
    jdest=jdest+1;
    % is it possible to go anywhere?
    dpos=Dmat(:,pos);
    bpossible=(petrol >= dpos & notbeenthere);
    if ~(bpossible)
        break;    % fuel low, go home if possible
    end
    % is it safe to go there?
    safe = find(bpossible & (petrol + petrolv >= dpos + Dmat1));
    if (isempty(safe))
        possible=find(bpossible);
        % is the next station after this one safe? (Ave)
        safe=zeros(n,1);
        for li=1:length(possible)
            la=possible(li);
            lanotbeenthere=notbeenthere;
            lanotbeenthere(la)=0;
            ladpos=Dmat(la,pos)+Dmat(:,la);
            lapetrol=petrol+petrolv(la);
            lapossible=(lapetrol>=ladpos & lanotbeenthere);
            if any(lapossible & lapetrol+petrolv>=ladpos+Dmat1)
                safe(la)=1;
                break;
            end
        end
        safe=find(safe);
    end
    if isempty(safe)
        break;
    end
    possible=safe;
    
    lm=length(possible);
    
    if (lm>1)
        Dpossible=Dmat(possible,pos);
        metric = ( (petroln(possible) - Dpossible/totalpetrol) * 2*(n-jdest+1)/n*(1+unitpetrol/petrol)^5 ...
            + freightn(possible)) ...
            ./ Dpossible;
        
        
        sm = [-realmax; -realmax];
        for imetric=1:lm
            mi=metric(imetric);
            if(mi>sm(2))
                sm(1)=sm(2);  imax(1)=imax(2);
                sm(2)=mi;     imax(2)=imetric;
            elseif mi>sm(1)
                sm(1)=mi;  imax(1)=imetric;
            end 
        end
        rn=0;
        if sm(1)/sm(2)>.995
            rn=fix(rand+.5);
        end
        next=possible(imax(end-rn));
    else
        next=possible(1);
    end
    
    
    notnearlythere(next)=0;
    r=Dmat(pos,next);
    % find places that are on the way
    ontheway = find( (Dmat(:,next) + Dmat(:, pos) < 1.088*r  & notnearlythere & bpossible)  );
    if(~isempty(ontheway))
        dp = Dmat(ontheway,pos); dn=Dmat(ontheway,next);
        ontheway = ontheway( find ( ...
            dp+dn+Dmat(1,next) <= petrol+petrolv(ontheway)+petrolv(next)  & ...   % can get home from
            ((dp+dn-r)<petrolv(ontheway) | freightv(ontheway)>0 )   ) ...         % net freight or petrol gain
            );
        [maxf,im]=max(freightv(ontheway));
        if (~isempty(ontheway))
            next=ontheway(im(1));
        end
    end
    
    c(jdest)=next;
    petrol=petrol + petrolv(next) - Dmat(pos,next);
    pos=next;
    notbeenthere(pos)=0;
    notnearlythere=notbeenthere;
end

c(jdest)=1;
c=c(1:jdest);


function c = petrol3(a,Dmat)


n=size(a,1);


freightv=a(:,3);
petrolv=a(:,4);

petrol=0;
freight=0;

pos=1;
jdest=1;

totalpetrol=sum(petrolv);
unitpetrol = totalpetrol/(n-1);
petroln=petrolv/totalpetrol;
totalfreight=sum(freightv);
freightn=freightv/totalfreight;


petrol  = petrol +  petrolv(1);
freight = freight + freightv(1);
petrolv(1)=0; freightv(1)=-1;

notbeenthere=logical(ones(n,1));
notbeenthere(1)=0;
c=ones(1,n+1);
Dp = max(Dmat(:,1) - petrolv,0);

while 1
    jdest=jdest+1;
    pmD = petrol - Dmat(:,pos);
    possible = find(  ...
        (pmD >= Dp)  & ...
        notbeenthere  ...
    );
    
    if isempty(possible)
        break
    end
    
    Dpossible=Dmat(possible,pos);
    metric = ( (petroln(possible) - Dpossible/totalpetrol) * 2*(n-jdest+1)/n*(1+unitpetrol/petrol)^5 ...
        + freightn(possible)) ...
        ./ Dpossible;
    
    imax= 1;maxm = -inf;
    for count = 1:numel(metric)
        if metric(count)>maxm
            imax = count;
            maxm = metric(count);
        end
    end
    %    [maxm,imax]=max(metric);
    
    next=possible(imax);
    c(jdest)=next;
    petrol=petrol + petrolv(next) - Dmat(pos,next);
    freight=freight+freightv(next);
    pos=next;
    notbeenthere(pos)=0;
end
c=c(1:jdest);

function [cbs,fgsbest]=findenum(a,dist,da)
n=size(a,1);

weightfreight=[ones(1,7)*50 zeros(1,n)];
Nstck=n*9;
stck=zeros(Nstck,1);
nstck=1;
c=ones(n+1,1);
cbs=[1 1];    % short-lines
fgsbest=da(1);
avail=logical(ones(n,1));

GAS=c;

gas=a(1,4);
GAS(1)=gas;
stck(2)=1;
nstck=2;

loop=1;
STOP=false;
cnt=0;
opt=1;    % not yet used
while 1
    current=stck(nstck);
    if current
        c(loop)=current;
        avail(current)=0;
        if loop>1
            gas=gas-dist(c(loop-1),current)+a(current,4);
        end
        if dist(current)<=gas    % can return home
            fg=sum(da(c(2:loop)));
            if fgsbest>fg
                cbs=c(1:loop+1);
                cbs(loop+1)=1;
                fgsbest=fg;
            end
        end
        i=find(avail);
        reachable=i(dist(i,current)<=gas);
        if isempty(reachable)
            nstck=nstck-1;
            avail(current)=1;
            cnt=cnt+1;
            if cnt>38
                opt=0;
                STOP=true;
            end
        else
            metric=dist(reachable,current)+a(reachable,3)*weightfreight(loop);
            [dsts,i]=sort(metric);
            stck(nstck)=0;
            if STOP
                stck(nstck+1)=reachable(i(1));
                nstck=nstck+1;
            else
                nn=min(length(reachable),fix(rand+4.5));
                stck(nstck+1:nstck+nn)=reachable(i(nn:-1:1));
                nstck=nstck+nn;
            end
            GAS(loop)=gas;
            loop=loop+1;
        end
    else
        loop=loop-1;
        avail(c(loop))=1;
        if loop==1
            break;
        end
        nstck=nstck-1;
        if STOP
            while loop>5
                while stck(nstck)
                    nstck=nstck-1;
                end
                loop=loop-1;
                nstck=nstck-1;
            end
        end
        gas=GAS(loop-1);
    end
end

function [c,s]=optim(a,c,s,dist,da)
n = length(c);
if n<4
    return
end
mi=1; 
d = zeros(n-1,1);
eg = d;
while mi~=0 % while removed a point 
    n = length(c);
    n1=n-1;
    d(1) = dist(c(2));
    eg(1) = a(1,4)-d(1);
    for i=2:n1 
        d(i)=dist(c(i),c(i+1));
        eg(i) = eg(i-1) + a(c(i),4)-d(i);
    end
    %   xy = a(:,1)+1i*a(:,2);
    %e = cumsum(a(c(1:end-1),4)-abs(diff(xy(c))));
    %all(abs(e-eg(1:n1))<1e-9)
    mg = eg(n1); % min spare gas
    mx = 0; % max improvement
    mi = 0; 
    for i = n1:-1:2
        if(mg>eg(i))
            mg = eg(i);
        end
        g = da(c(i));
        if g >=0
            delta = -d(i-1)-d(i)+dist(c(i-1),c(i+1))+g;
            if delta<=0
                c(i) = [];
                d(i-1) = dist(c(i-1),c(i));
                s = s - g;
                mi = -1;
                mg = 0; %mg-delta; % increases spare gas
            elseif (delta<=mg) && (g>mx) % possible max adjustment
                mx = g;
                mi = i;
            end
        end
    end
    if mi>0
        c(mi) = [];
        s = s - mx;
    end
end

function c=savegas(a,c,score,dist,da)

% more iterations takes too much time but there may be a smarter way
n = numel(c);
m=n-1;
d=zeros(m,1);
eg = d;
for outer = [12:-2:2 3:2:11 10:-2:2 3:2:9 2 2 2 2 2]
    d(1) = dist(c(2));
    eg(1) = a(1,4)-d(1);
    for i=2:m 
        d(i)=dist(c(i),c(i+1));
        eg(i) = eg(i-1) + a(c(i),4)-d(i);
    end
    
    for point = n-outer:-1:2
        ia = c(point-1);
        ib = c(point);
        ic = c(point+outer-1);
        id = c(point+outer);
        % The JIT is a strange beast
        d1 = dist(ia,ib)+dist(ic,id);
        d2 = dist(ia,ic)+dist(ib,id);
        if d1>d2
            
            g = eg(point-1)+dist(ia,ib)-dist(ia,ic);
            
            for i = point+outer-1:-1:point+1
                if g<0 
                    break;
                end
                g = g + a(c(i),4)-dist(c(i),c(i-1));
            end
            if g<0 
                continue;
            end
            g = g + a(ib,4)-dist(ib,id);
            c(point:point+outer-1) = c(point+outer-1:-1:point);
            g = eg(point-1)+dist(ia,ib)-dist(ia,ic);
            for ii=point-1:point+outer-1
                eg(ii) = g; 
                g = g + a(c(ii),4) - dist(c(ii),c(ii+1));
            end
        end
    end
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [c,s]=routefinder(a,mD,xY)

aN = size(a,1);                          % Constant section
onesN = ones(aN,1);

aF = a(:,3);
aG = a(:,4);
tF = sum(aF);
da = aG - aF;
vD = mD(:,1);
tL = 5;
C=ones(tL,aN+1);
K=ones(tL,1);
S=zeros(tL,1);
eps10=10*eps;
for L=1:tL,
    I=1;
    c=C(L,:);
    g=0;
    f=aF;
    rf=tF;
    for k=2:aN
        g=g+aG(I);    
        d=g-mD(:,I);
        d(c(1:k-1))=-inf;
        rf=rf-f(I);
        f(I)=0;
        if rf<eps10 && g >= mD(I,1),
            k=k-1;
            break;
        end
        if L==2,
            [Y,I]=max(d);
        elseif L==5
            [Y,I]=max(d+sign(d).*aG);
        elseif L==4
            if k > max(0.04*aN,5),
                [Y,I]=max(d);
            else
                [Y,I]=max(0.4*d+sign(d).*aG);
            end    
        elseif L==3
            xy=abs(xY-sum(xY.*f)/(aN-k+1)/(rf+eps))+eps;
            [Y,I]=max(d+0.17*sign(d).*aG./xy);
        else
            p=d>0;
            af=f.*p;
            cf=sum(af);
            if cf > eps10,
                xy=abs(xY-sum(af.*xY)/sum(p)/(cf+eps))+eps;
                [Y,I]=max(d+sign(d).*af./xy);
            else
                xy=abs(xY-sum(xY.*f)/(aN-k+1)/(rf+eps))+eps;
                [Y,I]=max(d);
            end
        end
        if Y<0,
            k=k-1;
            break;
        end
        g=d(I);
        c(k) = I;
    end
    C(L,:)=c;
    K(L)=k;
    if k/aN > 0.9,
        break;
    end
end
for L=1:tL,
    k=K(L);
    c=C(L,1:k+1);
    if k<2, 
        c=[1 1];
        i2=2;
        g1=aG(1);
    else,
        vG=aG(c);
        d=diag(mD(c,c),1);
        g1 = [aG(1);cumsum(vG(1:k-1))-cumsum(d(1:k-1))+vG(2:k)-mD(c(2:k),1)];
        i1 = find(g1>=0);
        i2 = i1(end) + 1;
        c = c(1:i2);
        c(i2) = 1;
        S(L)=sum(da(c(2:i2-1)));
    end
    K(L)=i2;
    C(L,1:i2)=c;
end
[s,L]=min(S);
c=C(L,1:K(L));

function c=movepoints(a,c,dist)
if length(c)<4
    return
end
c=c(:);
n=length(c);
opt=1;
nopt=1;
while opt && nopt<4
    opt=0;
    g0=ones(n-1,1);
    g0(1)=a(1,4)-dist(c(2));
    f=a(c,4);
    dxy=zeros(n-1,1);
    d2xy=zeros(n-2,1);
    dxy(1)=dist(c(2));
    for i=2:n-1
        dxy(i)=dist(c(i),c(i+1));
        d2xy(i-1)=dist(c(i-1),c(i+1));
        g0(i)=g0(i-1)+f(i)-dxy(i);
    end
    lim=sum(dxy)/(n-1)*2;
    ddxy=dxy(1:end-1)+dxy(2:end)-d2xy;
    icorn=find(ddxy>lim);
    if isempty(icorn)
        break;
    end
    [dum,i]=sort(-ddxy(icorn));
    icorn=icorn(i);
    for i=1:length(icorn)
        k=icorn(i)+1;
        ddxy2=dist(c(1:end-1),c(k))+dist(c(2:end),c(k))-dxy;
        ddxy2(k)=NaN;
        ddxy2(k-1)=NaN;
        [mn,l]=min(ddxy2);
        if mn<ddxy(k-1)
            opt=0;
            if k<l
                if ddxy(k-1)>=a(c(k),4)
                    opt=1;    % you gain more then what you loose, so no problem
                elseif g0(k+1:l)>=a(c(k),4)-ddxy(k-1)
                    opt=1;
                end
                if opt
                    c0=c;
                    c=[c(1:k-1);c(k+1:l);c(k);c(l+1:n)];
                end
            else
                if l==1
                    g01=a(1,4)-dist(c(k));
                else
                    g01=g0(l-1)+a(c(l),4)-dist(c(l),c(k));
                end
                if g01>=0
                    dg0=dxy(l)-dist(c(k),c(l))-dist(c(k),c(l+1))+a(c(k),4);
                    if all(g0(l:k-1)+dg0>=0)
                        opt=1;
                    end
                end
                if opt
                    c0=c;
                    c=[c(1:l);c(k);c(l+1:k-1);c(k+1:n)];
                end
            end
            if opt
                break;    % currently just one correction/loop
                nopt=nopt+1;
            end
        end
    end
end