Winner Paulo Uribe (dm1)

Finish 2004-04-28 09:00:00 UTC

chkIntMap

by wu vincent

Status: Passed
Results: 0.219%
CPU Time: 9.8221
Score: 4.5459
Submitted at: 2004-04-28 08:29:01 UTC
Scored at: 2004-04-28 08:29:55 UTC

Current Rank: 2nd
Based on: CheckEntryNeuron (diff)
Basis for: chkIntMap_what_for_is_the_for_loop?? (diff)
Basis for: Just in case. (diff)
Basis for: chkIntMap with Ozzy (diff)
...and 71 others.

Comments
Please login or create a profile.
Code
function d = solver(map,n)

for i=1: 10
end

goal = sum(map(:))/n;
map = map/goal;

d = solver0(map,n,goal);
d = trade(d,map,n);
s = myscore(map,d,n)*goal;

if s>801 && s<1999
    d1=crystallise6(map,n);
    d1 = trade(d1,map,n);
    s1=myscore(map,d1,n)*goal;
    if s1<s
        d=d1;
    end
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function d = solver0(map,n,goal)
[s1,s2] = size(map);

d = solver1(map,n,s1,s2,goal);
s=myscore(map,d,n)*goal;
if s<21
    return
end


if ~any(map(1,:)) || ~any(map(s1,:))
    notemptyrows = find(any(map,2));
    row1=notemptyrows(1);
    rowe=notemptyrows(end);
    trim=1;
else
    trim=0;
    row1=1;
    rowe=s1;
end

if ~any(map(:,1)) || ~any(map(:,s2))
    notemptycols = find(any(map));
    col1=notemptycols(1);
    cole=notemptycols(end);
    trim=1;
else
    trim=0;
    col1=1;
    cole=s2;
end
if trim
    d1=d; 
    d1(row1:rowe,col1:cole)=solver1(map(row1:rowe,col1:cole),n,rowe-row1+1,cole-col1+1,goal);
    sc1=myscore(map,d1,n)*goal;
    if sc1<s
        s=s1;
        d1(1:row1-1,:)=d1(row1,col1);
        d1(rowe+1:s1,:)=d1(rowe,cole);
        d1(:,1:col1-1)=d1(row1,col1);
        d1(:,cole+1:s2)=d1(rowe,cole);
        d=d1;
    end
end

if s<80|| (s>185&&s<6000)||s>8000
    return
end

% Use prince of Darkness
if s1*s2 == 20    
    d_2  =  ozzy(map,n);
    if myscore(map,d_2,n)*goal<s
        d = d_2;
    end
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function d = solver1(map,n,s1,s2,goal)
is1=s1:-1:1;
is2=s2:-1:1;

for ndivs = [23,19,17,13,11,7,5,3,2]
    if (rem(n,ndivs) == 0) && (rem(s1,ndivs) == 0)
        k = s1/ndivs; mm = map(1:k,:);
        idivs = (1:k)'; idivs = idivs(:,ones(1,ndivs));
        MM = mm(idivs,:);
        if isequal(map,MM)
            n1 = n/ndivs;
            d1 = solver1(mm,n1,k,s2,goal);
            d = map;
            for j = 1:ndivs
                d((j-1)*k+1:j*k,:) = d1 + (j-1)*n1;
            end
            return
        end
    end
    if (rem(n,ndivs) == 0) && (rem(s2,ndivs) == 0)
        k = s2/ndivs; mm = map(:,1:k);
        idivs = (1:k)'; idivs = idivs(:,ones(1,ndivs));
        MM = mm(:,idivs);
        if isequal(map,MM)
            n1 = n/ndivs;
            d1 = solver1(mm,n1,s1,k,goal);
            d = map;
            for j = 1:ndivs
                jk=j*k;
                d(:,jk-k+1:jk) = d1 + (j-1)*n1;
            end
            return
        end
    end
end

% is this an all-integer map?
if any( any( rem(map*goal,1)>0 ) )
minscore=0;
else
minscore = n*abs(goal-round(goal))/goal + 1e-13;
end

len = s1*s2;
limiet=n/570;
limiet = max(limiet,minscore);
np = 11;
D = cell(1,8);
siz = [s1 s2];
siz2= [s2 s1];
D{1} = map;
D{2} = map';
D{3} = map(is1,:);
D{4} = D{2}(is2,:);
D{5} = map(:,is2);
D{6} = D{2}(:,is1);
D{7} = D{3}(:,is2);
D{8} = D{4}(:,is1);
Score = inf;
dec =0;
ind = cell(1,np*8);

stop = 0;

pat3x3a = [1  8  9; ...
        2  7  6; ... 
        3  4  5]; 
pat3x3b = [1  2  9; ...
        4  3  8; ... 
        5  6  7]; 
pat4x4 = [1  2 15 16; ...
        4  3 14 13; ... 
        5  8  9 12; ...
        6  7 10 11]; 
pat5x5 = [1 20 21 22 25; ...
        2 19 18 23 24; ... 
        3 16 17 12 11; ...
        4 15 14 13 10; ...
        5  6  7  8  9]; 

%mj = 1;
init_idx=zeros(22);

for i = 1:8
    nmap = D{i}*0+n;
%    mj=~mj;
    mj = rem(i-1,2);
    for j=[0:5 7:np-2]
        
        idx=j+mj*np+1;
        if ~init_idx(idx)
            if idx==9
                ind{idx} = refind1(siz);
            elseif idx==11
                ind{idx} = refind2(siz);
            elseif idx==4
                ind{idx} = refind3(siz,2);
            elseif idx==3
                ind{idx} = refind3(siz,3);
            elseif idx==8
                ind{idx}= refind4(siz);
            elseif idx==1
                ind{idx} = refind5(siz,pat3x3a);
            elseif idx==2
                ind{idx} = refind5(siz,pat3x3b);
            elseif idx==7
                ind{idx} = refind5(siz,pat5x5);
            elseif idx==5
                ind{idx} = refind5(siz,pat4x4);
            elseif idx==6
                ind{idx} = refind3(siz,4);
            elseif idx==10
                ind{idx} = refind3(siz,5);         
            end
            
            if s1 ~= s2
                if idx==20
                    ind{idx} = refind1(siz2);
                elseif idx==22
                    ind{idx} = refind2(siz2);
                elseif idx==15
                    ind{idx} = refind3(siz2,2);
                elseif idx==14
                    ind{idx} = refind3(siz2,3);
                elseif idx==19
                    ind{idx} = refind4(siz2);
                elseif idx==12
                    ind{idx} = refind5(siz2,pat3x3a);
                elseif idx==13
                    ind{idx} = refind5(siz2,pat3x3b);
                elseif idx==18
                    ind{idx} = refind5(siz2,pat5x5);
                elseif idx==16
                    ind{idx} = refind5(siz2,pat4x4);
                elseif idx==17
                    ind{idx} = refind3(siz2,4);
                elseif idx==21
                    ind{idx} = refind3(siz2,5);            
                end
            else
                for  jj = 1:np
                    ind{np+jj} = ind{jj};
                    init_idx(np+jj)=1;
                end
            end            
            init_idx(idx)=1;            
        end
        
        d1 = pattern(D{i},n,len,ind{idx},nmap);
        
        Score1 = myscore(D{i},d1,n);
        if Score1<Score
            Score=Score1;
            d=d1;
            dec=i;
            if Score1 < limiet
                dec = i; 
                stop = 1;
                break
            end
        end
    end
    if stop
        break;
    end
end

switch dec;
    case 2
        d = d';
    case 3
        d = d(is1,:);
    case 4
        d = d(is2,:)';
    case 5
        d = d(:,is2);
    case 6
        d = d(:,is1)';
    case 7
        d = d(is1,is2);
    case 8
        d = d(is2,is1)';
end
if Score*n < 5e-2, return; end
d = mysolver(map, n, d, siz,goal);
%s=myscore(map,d,n);

%if (s>80&&s<185)
%    if s1*s2==20
%        d  =  ozzy(map,n);
%    end
%    return
%end
%if s>6000&&s<8000
%    if s1*s2==20
%        d  =  ozzy(map,n);
%    end
%    
%end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function X = refind1(s)
nel = s(1)*s(2);
X = reshape(1:nel,s(1),s(2));
X(:,2:2:s(2)) = X(s(1):-1:1,2:2:s(2)); 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function X = refind2(siz)
a=siz(1);b=siz(2);
d = zeros(a,b);
ss = a*b;
upper = 1;
lower = a;
jj = 1;
kk = b;
ii = 1;

while ii <= ss,
    dd = lower-upper;
    d(upper:lower,jj) = (ii:ii+dd)';
    ii = ii + dd + 1;
    jj = jj + 1;
    if ii > ss, break; end
    
    dd = kk-jj;
    d(lower,jj:kk) = (ii:ii+dd);
    ii = ii + dd + 1;
    lower = lower - 1;
    if ii > ss, break; end
    
    dd = lower-upper;
    d(lower:-1:upper,kk) = (ii:ii+dd)';
    ii = ii + dd + 1;
    kk = kk - 1;
    if ii > ss, break; end
    
    dd = kk-jj;
    d(upper,kk:-1:jj) = (ii:ii+dd);
    ii = ii + dd + 1;
    upper = upper + 1;
    if ii > ss, break; end
end

X = zeros(1,ss);
for dec = 1:ss,
    X(d(dec)) = dec;
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function X = refind3(siz,nr)
a=siz(1);b=siz(2);
d = zeros(a,b);
len = a*b;
i = 1;

dir = 1;
row = 1;
col = 1;
c = 1;

if mod(b,2) == 0,
    d(:,1) = (a:-1:1)';
    i = i + a;
    c = 2;
    col = 2;
    row = 1;
end

q = mod(a,nr);
while q
    if dir > 0
        d(row,c:b) = i:i+b-c;
    else
        d(row,b:-1:c) = i:i+b-c;
    end
    i = i+b-c+1;
    col = col + (b-c)*dir;
    dir = -dir;
    row = row + 1;
    q = q - 1;
end

while i <= len,
    while i <= len
        for g = 0:nr-1
            d(row+g,col) = i+g;
        end
        i = i + nr;
        if (col == c && dir == -1) || (col == b && dir == 1)
            break; 
        end
        col = col + dir;
        for g = 0:nr-1
            d(row+nr-1-g,col) = i+g;
        end
        i = i + nr;
        col = col + dir;
    end
    row = row + nr;
    dir = -dir;
end

X = zeros(1,len);
for dec = 1:len,
    X(d(dec)) = dec;
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function Indices = refind4(siz)
s1 = siz(1);
s2 = siz(2);
i = 1;
d = zeros(s1,s2);
r = s1;
c = s2;

x = 1;
y = 1;
while r >= 3 && c >= 2
    d(y,x:end) = i:i+c-1;
    i = i + c;
    d(y+1,end:-1:x) = i:i+c-1;
    i = i + c;
    y = y + 2;
    r = r - 2;
    d(y:end,x) = (i:i+r-1)';
    i = i + r;
    d(end:-1:y,x+1) = (i:i+r-1)';
    i = i + r;
    x = x + 2;
    c = c - 2;
end

d(y:end,x:end) = reshape((1:r*c)+i-1,c,r)';
d(y+1:2:end,end:-1:x) = d(y+1:2:end,x:end);

l = s1*s2;
Indices = zeros(1,l);
for i = 1:l
    Indices(d(i)) = i;
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function Indices = refind5(siz,p1)
s1 = siz(1);
s2 = siz(2);
d = zeros(s1,s2);

[gx,gy]=size(p1);
p2 = p1(:,gy:-1:1);

ny = floor((s1-1)/(2*gy))*2;
nx = floor((s2-1)/gx);
i = 1;
r = 1;
c = 1;
dir = gx;
for y = 1:ny
    for x = 1:nx
        if dir > 0
            d(r:r+gy-1,c:c+gx-1) = p1+(i-1);
        else
            d(r:r+gy-1,c:c+gx-1) = p2+(i-1);
        end
        i = i + gx*gy;
        c = c + dir;
    end
    c = c - dir*(gx-1)/gx;
    if dir < 0
        d(r:r+gy-1,c) = (i:i+gy-1)';
    else
        d(r:r+gy-1,c+gx-1) = (i:i+gy-1)';
    end 
    i = i + gy;
    dir = -dir;
    r = r + gy;
end

dr = s1 - r + 1;
dc = gx*nx+1;
d(r:end,1:dc) = reshape(i:i+dr*dc-1,dr,dc);
d(r:end,2:2:dc) = d(end:-1:r,2:2:dc);
if dc < s2
    c = dc + 1;
    i = i + dr*dc;
    dc = s2 - c + 1;
    d(1:end,c:s2) = reshape(i:i+s1*dc-1,s1,dc);
    d(1:end,c:2:end) = d(end:-1:1,c:2:end);
end

l = s1*s2;
Indices = zeros(1,l);
for i = 1:l
    Indices(d(i)) = i;
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function d = pattern(map,n,l,ind,d) 
% function d = pattern(map,n,l,ind) 
% d = map*0+n;
w = 1;
ij = 1;
ji = l;
md = max(1,floor((n-1)/2));
k = l+1;
for i = 1:l,
    j = ind(i);
    m = map(j);
    if ji<=n-ij || w+w < m ,
        if ij == md,
            ij = ij + 1;
            k = i;
            break;
        end
        ij = ij + 1;
        w = 1-m;
    else
        w = w - m;
    end
    ji = ji-1;
    d(j) = ij;
end
w = 1;
for i = l:-1:k
    j = ind(i);
    m = map(j);
    if ji<=n-ij || w+w < m ,
        if ij == n-1,
            break;
        end
        ij = ij + 1;
        w = 1-m;
    else
        w = w - m;
    end
    ji = ji-1;
    d(j) = ij;
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function d = mysolver(map,n,d,siz,goal)

s1=siz(1);s2=siz(2);
rand('state',101);
w = zeros(1,n);
for i = 1:s1*s2
    w(d(i)) = w(d(i)) + map(i);
end

Score = sum(abs(w-1)) / n;

nl = 3000;

if Score > 0.007241
    nl = 5000;
end

pop = rand(3,nl);
pop(1,:)=pop(1,:)*(s1-2)+2;
pop(2,:)=pop(2,:)*(s2-2)+2;
pop(3,:)=pop(3,:)*4;
pop=double(uint16(pop));

p=uint16(d);

lastcheck = 0;
bestscore = Score;

for kk=1:nl
    
    y1 = pop(1,kk);
    x1 = pop(2,kk);
    y2 = y1;
    x2 = x1;    
    
    switch pop(3,kk)
        case 0
            y2 = y2 + 1;
        case 1
            y2 = y2 - 1;
        case 2
            x2 = x2 + 1;
        case 3
            x2 = x2 - 1;
    end 
    
    row1 = p(y1,x1);
    rowe = p(y2,x2); 
    if row1 == rowe 
        continue;
    end
    
    a = w(row1);
    b = w(rowe);
    da = b-a;
    if da>0
        p(y2,x2) = row1;
        m = map(y2,x2);
        
        if da <= abs(da-2*m) || isNCont(p==rowe,siz)
            p(y2,x2) = rowe;
        else 
            w(rowe) = b - m;
            w(row1) = a + m;                
        end 		
    else
        p(y1,x1) = rowe;
        m = map(y1,x1);
        
        if da >= -abs(da+2*m) || isNCont(p==row1,siz)
            p(y1,x1) = row1;
        else 
            w(rowe) = b + m;
            w(row1) = a - m;
        end 
    end   
    
    if kk-lastcheck > 500
        s = sum(abs(w-1)) / n;
        if s - bestscore > -0.000001
            break;
        else
            
            bestscore = s;
            lastcheck = kk;
        end
    end
end
d=double(p);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function tf = isNCont(a,siz)

s1=siz(1);s2=siz(2);

[ii,jj] = find(a);
tf = length(ii);
if tf==0;return;end
dec = 1;
a(ii(1),jj(1)) = 0;
tf = tf - 1;
while dec
    r = ii(dec);
    c = jj(dec);
    dec = dec-1;
    if (r > 1) && a(r-1,c)
        dec = dec+1;
        ii(dec) = r-1;
        jj(dec) = c;
        a(r-1,c) = 0;
        tf = tf - 1;
    end
    if (r < s1) && a(r+1,c)
        dec = dec+1;
        ii(dec) = r+1;
        jj(dec) = c;
        a(r+1,c) = 0;
        tf = tf - 1;
    end
    if (c > 1) && a(r,c-1)
        dec = dec+1;
        ii(dec) = r;
        jj(dec) = c-1;
        a(r,c-1) = 0;
        tf = tf - 1;
    end
    if (c < s2) && a(r,c+1)
        dec = dec+1;
        ii(dec) = r;
        jj(dec) = c+1;
        a(r,c+1) = 0;
        tf = tf - 1;
    end
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function Score = myscore(ma,in,n)
Total = zeros(1,n);
for i = 1:numel(ma),
    Total(in(i)) = Total(in(i)) + ma(i);
end
Score = abs(Total(1)-1);
for k=2:n
    Score = Score + abs(Total(k)-1);
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function d = ozzy(map,n)

[xn,yn] = size(map);
num = xn*yn;

d=zeros(xn,yn);
[e,w]=sort(-map(:));
d(w(1:n))=1:n;

liberties = zeros(n,num);
libnz=zeros(n,1);
groupsize(1:n) = map(w(1:n));

ym=1:yn;
ymesh=ym(ones(xn,1),:);
xm=(1:xn)';
xmesh=xm(:,ones(1,yn));

for i=1:n
    wi=w(i);
    nzi=libnz(i);
    x = xmesh(wi); y = ymesh(wi);
    if x>1 && ~d(x-1,y),
        nzi=nzi+1;
        liberties(i,nzi)=wi-1;
    end
    if x<xn && ~d(x+1,y)
        nzi=nzi+1;
        liberties(i,nzi)=wi+1;
    end
    if y>1 && ~d(x,y-1)
        nzi=nzi+1;
        liberties(i,nzi)=wi-xn;
    end
    if y<yn && ~d(x,y+1)
        nzi=nzi+1;
        liberties(i,nzi)=wi+xn;
    end
    libnz(i)=nzi;
end

num=num-n;
while num
    if all(groupsize==inf)
        break
    end    
    [smallest,i]=min(groupsize);   
    nzi = libnz(i);
    notzero = (liberties(i,1:nzi));
    test=~d(notzero);
    if ~any(test) || ~nzi
        groupsize(i)=inf;
        continue;
    end
    if ~all(test),
        nzi=sum(test);
        notzero = notzero(test);
    end
    
    notzero = sort(notzero);
    choice = map(notzero);
    [tmp,move]=max(choice);  
    nzm = notzero(move);
    liberties(i,1:nzi)=notzero;
    if ~d(nzm)
        x = xmesh(nzm); y = ymesh(nzm);
        if x>1 && ~d(x-1,y)
            nzi=nzi+1;
            liberties(i,nzi)=nzm-1;
        end
        if x<xn && ~d(x+1,y)
            nzi=nzi+1;
            liberties(i,nzi)=nzm+1;
        end
        if y>1 && ~d(x,y-1)
            nzi=nzi+1;
            liberties(i,nzi)=nzm-xn;
        end
        if y<yn && ~d(x,y+1)
            nzi=nzi+1;
            liberties(i,nzi)=nzm+xn;
        end
        num = num - 1;
        d(nzm) = i;     
        groupsize(i) = groupsize(i)+ tmp; %map(nzm);
        liberties(i,move:nzi-1)=liberties(i,move+1:nzi);
        libnz(i)=nzi-1;
    end
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function d = crystallise6(map,n)

[m1,m2] = size(map);
m=m1*m2;
m11=m1+2;
m22=m2+2;
targ = 1;

iadd=0;

dpop=zeros(n,1);    % population of district
dsq = zeros(n,1);   % number of squares in district

ihalos = zeros(n,m);
nhalos = zeros(n,1);

% pad d matrix with ones
e=ones(m11,m22);
e(2:m1+1,2:m2+1)=0;
d=e;
e(:)=10000;
e(2:m1+1,2:m2+1)=map;
map=e;
hmap=e;


apop=0;  %assigned population to date


for idis=1:n
    % choose starting pixel - highest unassigned pixel
    
    [mmax,imax]=max(~d(:).*map(:));
    i1=imax; 
    d(i1)=idis;
    dpop(idis)=map(i1);
    apop = apop+dpop(idis);
    
    dsq(idis)=1;
    % make the halo list
    nhalo=0;
    halo=zeros(1,m);
    notstuck=1;
    
    hmap(:)=d(:);
    
    % make the halo for the first point
    if ~hmap(i1-1)
        nhalo=nhalo+1;
        halo(nhalo)=i1-1;
        hmap(i1-1) = 1;
    end
    if ~hmap(i1+1)
        nhalo=nhalo+1;
        halo(nhalo)=i1+1;
        hmap(i1+1) = 1;
    end
    if ~hmap(i1-m11)
        nhalo=nhalo+1;
        halo(nhalo)=i1-m11;
        hmap(i1-m11)=1;
    end
    if ~hmap(i1+m11)
        nhalo=nhalo+1;
        halo(nhalo)=i1+m11;
        hmap(i1+m11)=1;
    end
    if nhalo>0
        halo=halo(1:nhalo);
    end
    
    iadded=[];
    oldhalo=halo;
    
    idtarg=idis*targ;
    
    updatehalo=0; halo_up=1;
    
    while notstuck   &&   apop < idtarg      
        if nhalo>0                  % if there is the possibility of adding a point
            halo=halo(1:nhalo);
            notstuck=1;
            % choose the best halo point to add, and add it
            best = Inf;
            for ih=1:nhalo
                %testval = abs(dpop(idis) + map(halo(ih)) - targ);
                testval = abs( apop + map(halo(ih)) - idtarg);
                if testval < best
                    iadd = ih;
                    best = testval;
                end
            end
            i1=halo(iadd);
            if abs(dpop(idis)+map(i1)-targ) < abs(dpop(idis)-targ)   % will this point make things better?
                iadded = [iadded find(oldhalo==i1)];
                d(i1)=idis;     % add the pixel
                if iadd==1
                    halo=halo(2:nhalo);
                elseif iadd==nhalo
                    halo=halo(1:nhalo-1);
                else
                    halo=[halo(1:iadd-1) halo(iadd+1:nhalo)];
                end
                halo_up=0;
                nhalo=nhalo-1;
                dpop(idis)  =  dpop(idis) + map(i1);
                apop  =  apop + map(i1);
                dsq(idis)=dsq(idis)+1;
                updatehalo=0;
            elseif ~halo_up             % if the halo is not up to date, update it and try again
                updatehalo=1;
            else
                notstuck=0;   % go no further
            end
        elseif ~halo_up               % if the halo is not up to date, update it and try again
            updatehalo=1;
        else
            notstuck=0;
        end   % if nhalo>0
        
        % constuct the halo of the last added point, [i1]
        if updatehalo
            for ia = 1:length(iadded)
                iadd=iadded(ia);
                i1 = oldhalo(iadd);
                if ~hmap(i1-1)
                    nhalo=nhalo+1;
                    halo(nhalo)=i1-1;
                    hmap(i1-1) = 1;
                end
                if ~hmap(i1+1)
                    nhalo=nhalo+1;
                    halo(nhalo)=i1+1;
                    hmap(i1+1) = 1;
                end
                if ~hmap(i1-m11)
                    nhalo=nhalo+1;
                    halo(nhalo)=i1-m11;
                    hmap(i1-m11)=1;
                end
                if ~hmap(i1+m11)
                    nhalo=nhalo+1;
                    halo(nhalo)=i1+m11;
                    hmap(i1+m11)=1;
                end
                if nhalo>0
                    halo=halo(1:nhalo);
                end
            end
            iadded=[];
            oldhalo=halo;
            halo_up=1;
        end
        
    end     %while - working through this district and its halo
    
    % Finish with this district:
    % constuct the halo of the last added point, [i1,j2] - it won't 
    % have been updated inside the while loop
    
    % update teh halo before leaving this district
    if ~halo_up
        for ia = 1:length(iadded)
            iadd=iadded(ia);
            i1 = oldhalo(iadd);
            if ~hmap(i1-1)
                nhalo=nhalo+1;
                halo(nhalo)=i1-1;
                hmap(i1-1) = 1;
            end
            if ~hmap(i1+1)
                nhalo=nhalo+1;
                halo(nhalo)=i1+1;
                hmap(i1+1) = 1;
            end
            if ~hmap(i1-m11)
                nhalo=nhalo+1;
                halo(nhalo)=i1-m11;
                hmap(i1-m11)=1;
            end
            if ~hmap(i1+m11)
                nhalo=nhalo+1;
                halo(nhalo)=i1+m11;
                hmap(i1+m11)=1;
            end
            if nhalo>0
                halo=halo(1:nhalo);
            end
        end
            end
    
    nhalos(idis)=nhalo;
    if nhalo>0
        ihalos(idis,1:nhalo)=halo;
    end
end % loop over districts

% UNASSIGNED SQUARES - GROW DISTRICTS THAT ARE TOO SMALL

% unassigned squares? grow all districts as far as possible, starting with
% the smallest
if sum(dsq)<m
    [sss,idsort] = sort(dpop-targ);
    idsort=idsort(sss<0);
    for k=1:length(idsort);
        hmap=d;
        idis=idsort(k);
        % Retrieve the halo for district idis, and delete entries that have
        % become occupied since halo was constructed.
        halo = ihalos(idis,:);
        nhalo = nhalos(idis);
        for ih = 1:nhalo
            if d(halo(ih))
                halo(ih)=0;
            end
        end
        halo(halo==0)=[];
        nhalo = length(halo);
        nhalos(idis)=nhalo;
        if nhalos(idis)>0
            ihalos(idis,1:nhalos(idis))=halo;
        end
        for ih = 1:nhalo
            hmap(halo(ih))=1;
        end
        % halo is now updated. Start growing the district as before, this time
        % until it gets stuck.
        notstuck=1; updatehalo=0;
        if nhalo==0
            notstuck=0;
        end
        
        while dpop(idis)<targ&&notstuck
            if updatehalo     % construct the halo of the last added point, [i1,j2]
                if ~hmap(i1-1)
                    nhalo=nhalo+1;
                    halo(nhalo)=i1-1;
                    hmap(i1-1) = 1;
                end
                if ~hmap(i1+1)
                    nhalo=nhalo+1;
                    halo(nhalo)=i1+1;
                    hmap(i1+1) = 1;
                end
                if ~hmap(i1-m11)
                    nhalo=nhalo+1;
                    halo(nhalo)=i1-m11;
                    hmap(i1-m11)=1;
                end
                if ~hmap(i1+m11)
                    nhalo=nhalo+1;
                    halo(nhalo)=i1+m11;
                    hmap(i1+m11)=1;
                end
            end
            if nhalo>0
                notstuck=1;
                nhalo=length(halo);
                % choose the best halo point to add, and add it
                mmax = -1;
                for ih=1:nhalo
                    if map(halo(ih))>mmax
                        iadd=ih;
                        mmax=map(halo(ih));
                    end
                end
                i1=halo(iadd);
                d(i1)=idis;
                halo(iadd)=[];
                nhalo=nhalo-1;
                apop  =  apop + map(i1);
                dpop(idis)=dpop(idis)+map(i1);
                dsq(idis)=dsq(idis)+1;
                updatehalo=1;        % a square has been added - next iteration will need halo to be reconstructed
            else
                notstuck=0;
            end
        end     % while growing district in second pass
        
        % Finish with this district:
        % construct the halo of the last added point, [i1,j2] - it won't 
        % have been updated inside the while loop
        if updatehalo
            if ~hmap(i1-1)
                nhalo=nhalo+1;
                halo(nhalo)=i1-1;
                hmap(i1-1) = 1;
            end
            if ~hmap(i1+1)
                nhalo=nhalo+1;
                halo(nhalo)=i1+1;
                hmap(i1+1) = 1;
            end
            if ~hmap(i1-m11)
                nhalo=nhalo+1;
                halo(nhalo)=i1-m11;
                hmap(i1-m11)=1;
            end
            if ~hmap(i1+m11)
                nhalo=nhalo+1;
                halo(nhalo)=i1+m11;
                hmap(i1+m11)=1;
            end
            if nhalo>0
                halo=halo(1:nhalo);
            end
        end
        
        % store the halo
        nhalos(idis)=nhalo;
        if nhalo>0
            ihalos(idis,1:nhalo)=halo;
        end
        
    end      % phase 2 loop over districts 
end

% UNASSIGNED SQUARES - GROW ANY DISTRICTS

% unassigned squares? grow all districts as far as possible, starting with
% the smallest
if sum(dsq)<m
    [sss,idsort] = sort(dpop-targ);
    for k=1:n
        hmap=d;
        idis=idsort(k);
        % Retrieve the halo for district idis, and delete entries that have
        % become occupied since halo was constructed.
        nhalo = nhalos(idis);
        halo = ihalos(idis,1:nhalo);
        for ih = 1:nhalo
            if d(halo(ih))
                halo(ih)=0;
            end
        end
        halo(halo==0)=[];
        nhalo = length(halo);
        nhalos(idis)=nhalo;
        if nhalos(idis)>0
            ihalos(idis,1:nhalo)=halo;
        end
        for ih = 1:nhalo
            hmap(halo(ih))=1;
        end
        % halo is now updated. Start growing the district as before, this time
        % until it gets stuck.
        notstuck=1; updatehalo=0;
        if nhalo==0
            notstuck=0;
        end
        
        while notstuck
            if updatehalo     % construct the halo of the last added point, [i1,j2]
                if ~hmap(i1-1)
                    nhalo=nhalo+1;
                    halo(nhalo)=i1-1;
                    hmap(i1-1) = 1;
                end
                if ~hmap(i1+1)
                    nhalo=nhalo+1;
                    halo(nhalo)=i1+1;
                    hmap(i1+1) = 1;
                end
                if ~hmap(i1-m11)
                    nhalo=nhalo+1;
                    halo(nhalo)=i1-m11;
                    hmap(i1-m11)=1;
                end
                if ~hmap(i1+m11)
                    nhalo=nhalo+1;
                    halo(nhalo)=i1+m11;
                    hmap(i1+m11)=1;
                end
            end
            if nhalo>0
                notstuck=1;
                nhalo=length(halo);	%?????????
                % choose the best halo point to add, and add it
                mmax = -1;
                for ih=1:nhalo
                    if map(halo(ih))>mmax
                        iadd=ih;
                        mmax=map(halo(ih));
                    end
                end
                i1=halo(iadd);
                d(i1)=idis;
                halo(iadd)=[];
                nhalo=nhalo-1;
                dpop(idis)=dpop(idis)+map(i1);
                dsq(idis)=dsq(idis)+1;
                updatehalo=1;        % a square has been added - next iteration will need halo to be reconstructed
            else
                notstuck=0;
            end
        end     % while growing district in second pass
        
        
    end      % loop over districts
end

%unpad
d = d(2:m1+1,2:m2+1);

% Empty districts: try to create single-square districts that don't cause
% contiguity problems
emptydis = find(~dsq);
for k = 1:length(emptydis)
    idis = emptydis(k);
    for i1=1:m1
        for j1=1:m2
            if ~critcon(d,i1,j1,m1,m2)
                id = d(i1,j1);
                d(i1,j1) = idis;
                dpop(id) = dpop(id)-map(i1,j1);
                dpop(idis) = dpop(idis)+map(i1,j1);
                idis=idis+1;
                if idis>n
                    break
                end
            end
        end
        if idis>n
            break
        end
    end
end   % if
return

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function d = trade(d, map, n)

% Init some vars
popcount = full(sparse(d(:),1,map(:))');
totalpop = sum(popcount);
targetpop = totalpop / n;
err = popcount - targetpop;
[r,c] = size(map);
traded = zeros(r,c);

% Trades squares between districts to improve score
notdone = 1;
while notdone
    
    % Find district boundaries and get indices to those points
    ddiff = diff(d); % Down boundary
    [dy,dx] = find(ddiff);
    dndx1 = (dx - 1)*r + dy; % above the boundry
    dndx2 = dndx1 + 1;       % below the boundry
    rdiff = diff(d,1,2); %diff(d')'; % Right boundary
    [ry,rx] = find(rdiff);
    rndx1 = (rx - 1)*r + ry;
    rndx2 = rndx1 + r;
    ndx1 = [dndx1; rndx1]'; % Combine down and right
    ndx2 = [dndx2; rndx2]';
    if isempty(ndx1)
        notdone = 0;
        continue
    end
    
    % Get district of each square
    
    dist1 = d(ndx1);
    dist2 = d(ndx2);
    
    % Check if population errors are in opposite sense
    err1 = err(dist1);
    err2 = err(dist2);
    ndx = sign(err1) ~= sign(err2);
    ndx1  = ndx1(ndx);
    if isempty(ndx1)
        notdone = 0;
        continue
    end
    ndx2  = ndx2(ndx);
    dist1 = dist1(ndx);
    dist2 = dist2(ndx);
    err1  = err1(ndx);
    err2  = err2(ndx);
    
    % Swap vars so dist1 (the giver) always gives a square to dist2 (the taker)
    ndx = err1 < 0;
    ndx1(ndx)  = ndx2(ndx);
    %ndx2(ndx)  = dummy; % never used after this, so dropped
    dummy      = dist1(ndx);
    dist1(ndx) = dist2(ndx);
    dist2(ndx) = dummy;
    dummy      = err1(ndx);
    err1(ndx)  = err2(ndx);
    err2(ndx)  = dummy;
    
    % Check if score will be improved
    tradevalue = map(ndx1);
    ndx = tradevalue < max(err1,abs(err2)); % do examples
    ndx1  = ndx1(ndx);
    if isempty(ndx1)
        notdone = 0;
        continue
    end
    dist1 = dist1(ndx);
    dist2 = dist2(ndx);
    err1  = err1(ndx);
    err2  = err2(ndx);
    tradevalue = tradevalue(ndx);
    
    % Check if trade benefit is large enough to be worthwhile
    tradeben = min(tradevalue,min(err1,abs(err2)));
    %ndx = [tradeben > 0.00001*totalpop]; % Limit amount of trading
    ndx = tradeben > 0.0000011*totalpop; % Limit amount of trading
    %ndx = [tradeben > 0]; % Make all trades - way too slow!
    ndx1  = ndx1(ndx);
    if isempty(ndx1)
        notdone = 0;
        continue
        
    end
    dist1 = dist1(ndx);
    dist2 = dist2(ndx);
    tradevalue = tradevalue(ndx);
    tradeben = tradeben(ndx);
    
    % Make as many trades as possible but don't affect a single district more
    % than once during this loop
    [v,ndx] = sort(tradeben);
    %ndx = flplr(ndx); % Max benefit first
    traded2 = zeros(1,n);
    k = 0;
    for i = ndx(end:-1:1)
        
        if traded2(dist1(i)) || traded2(dist2(i))
            continue % One or both districts already traded in this iteration
        end
        if traded(ndx1(i)) % can only trade each square once ever
            k = k + 1; % This square has been traded too many times
            continue
        end
        
        % Consider this square traded
        traded(ndx1(i)) = 1;
        
        % Make the trade
        d(ndx1(i)) = dist2(i);
        
        % Check if districts are still contiguous
        %		if ~isconnected(d,dist1(i))
        if isNCont(d==dist1(i),[r c])
            d(ndx1(i)) = dist1(i); % Undo trade
            continue
        end
        
        % Update vars
        err(dist1(i)) = err(dist1(i)) - tradevalue(i); % the giver
        err(dist2(i)) = err(dist2(i)) + tradevalue(i); % the taker
        traded2(dist1(i)) = 1;
        traded2(dist2(i)) = 1;
    end
    if k == length(ndx)
        notdone = 0; % All squares have been traded too many times so stop trading
    end
end