function d = solver(map,n)
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 ccc = 1:ndivs
d((ccc-1)*k+1:ccc*k,:) = d1 + (ccc-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 ccc = 1:ndivs
jk=ccc*k;
d(:,jk-k+1:jk) = d1 + (ccc-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 bbb = 1:8
nmap = D{bbb}*0+n;
% mj=~mj;
mj = rem(bbb-1,2);
for ccc=[0:5 7:np-2]
idx=ccc+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{bbb},n,len,ind{idx},nmap);
Score1 = myscore(D{bbb},d1,n);
if Score1<Score
Score=Score1;
d=d1;
dec=bbb;
if Score1 < limiet
dec = bbb;
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;
bbb = 1;
dir = 1;
row = 1;
col = 1;
c = 1;
if mod(b,2) == 0,
d(:,1) = (a:-1:1)';
bbb = bbb + a;
c = 2;
col = 2;
row = 1;
end
q = mod(a,nr);
while q
if dir > 0
d(row,c:b) = bbb:bbb+b-c;
else
d(row,b:-1:c) = bbb:bbb+b-c;
end
bbb = bbb+b-c+1;
col = col + (b-c)*dir;
dir = -dir;
row = row + 1;
q = q - 1;
end
while bbb <= len,
while bbb <= len
for g = 0:nr-1
d(row+g,col) = bbb+g;
end
bbb = bbb + 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) = bbb+g;
end
bbb = bbb + 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);
bbb = 1;
d = zeros(s1,s2);
r = s1;
c = s2;
x = 1;
y = 1;
while r >= 3 && c >= 2
d(y,x:end) = bbb:bbb+c-1;
bbb = bbb + c;
d(y+1,end:-1:x) = bbb:bbb+c-1;
bbb = bbb + c;
y = y + 2;
r = r - 2;
d(y:end,x) = (bbb:bbb+r-1)';
bbb = bbb + r;
d(end:-1:y,x+1) = (bbb:bbb+r-1)';
bbb = bbb + r;
x = x + 2;
c = c - 2;
end
d(y:end,x:end) = reshape((1:r*c)+bbb-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 bbb = 1:l
Indices(d(bbb)) = bbb;
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);
bbb = 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+(bbb-1);
else
d(r:r+gy-1,c:c+gx-1) = p2+(bbb-1);
end
bbb = bbb + gx*gy;
c = c + dir;
end
c = c - dir*(gx-1)/gx;
if dir < 0
d(r:r+gy-1,c) = (bbb:bbb+gy-1)';
else
d(r:r+gy-1,c+gx-1) = (bbb:bbb+gy-1)';
end
bbb = bbb + gy;
dir = -dir;
r = r + gy;
end
dr = s1 - r + 1;
dc = gx*nx+1;
d(r:end,1:dc) = reshape(bbb:bbb+dr*dc-1,dr,dc);
d(r:end,2:2:dc) = d(end:-1:r,2:2:dc);
if dc < s2
c = dc + 1;
bbb = bbb + dr*dc;
dc = s2 - c + 1;
d(1:end,c:s2) = reshape(bbb:bbb+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 bbb = 1:l
Indices(d(bbb)) = bbb;
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 bbb = 1:l,
ccc = ind(bbb);
m = map(ccc);
if ji<=n-ij || w+w < m ,
if ij == md,
ij = ij + 1;
k = bbb;
break;
end
ij = ij + 1;
w = 1-m;
else
w = w - m;
end
ji = ji-1;
d(ccc) = ij;
end
w = 1;
for bbb = l:-1:k
ccc = ind(bbb);
m = map(ccc);
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(ccc) = ij;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function d = mysolver(map,n,d,siz,goal)
s1=siz(1);s2=siz(2);
rand('state',101);
w = zeros(1,n);
for bbb = 1:s1*s2
w(d(bbb)) = w(d(bbb)) + map(bbb);
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 bbb = 1:numel(ma),
Total(in(bbb)) = Total(in(bbb)) + ma(bbb);
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 bbb=1:n
wi=w(bbb);
nzi=libnz(bbb);
x = xmesh(wi); y = ymesh(wi);
if x>1 && ~d(x-1,y),
nzi=nzi+1;
liberties(bbb,nzi)=wi-1;
end
if x<xn && ~d(x+1,y)
nzi=nzi+1;
liberties(bbb,nzi)=wi+1;
end
if y>1 && ~d(x,y-1)
nzi=nzi+1;
liberties(bbb,nzi)=wi-xn;
end
if y<yn && ~d(x,y+1)
nzi=nzi+1;
liberties(bbb,nzi)=wi+xn;
end
libnz(bbb)=nzi;
end
num=num-n;
while num
if all(groupsize==inf)
break
end
[smallest,bbb]=min(groupsize);
nzi = libnz(bbb);
notzero = (liberties(bbb,1:nzi));
test=~d(notzero);
if ~any(test) || ~nzi
groupsize(bbb)=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(bbb,1:nzi)=notzero;
if ~d(nzm)
x = xmesh(nzm); y = ymesh(nzm);
if x>1 && ~d(x-1,y)
nzi=nzi+1;
liberties(bbb,nzi)=nzm-1;
end
if x<xn && ~d(x+1,y)
nzi=nzi+1;
liberties(bbb,nzi)=nzm+1;
end
if y>1 && ~d(x,y-1)
nzi=nzi+1;
liberties(bbb,nzi)=nzm-xn;
end
if y<yn && ~d(x,y+1)
nzi=nzi+1;
liberties(bbb,nzi)=nzm+xn;
end
num = num - 1;
d(nzm) = bbb;
groupsize(bbb) = groupsize(bbb)+ tmp; %map(nzm);
liberties(bbb,move:nzi-1)=liberties(bbb,move+1:nzi);
libnz(bbb)=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&¬stuck
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 bbb = ndx(end:-1:1)
if traded2(dist1(bbb)) || traded2(dist2(bbb))
continue % One or both districts already traded in this iteration
end
if traded(ndx1(bbb)) % 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(bbb)) = 1;
% Make the trade
d(ndx1(bbb)) = dist2(bbb);
% Check if districts are still contiguous
% if ~isconnected(d,dist1(bbb))
if isNCont(d==dist1(bbb),[r c])
d(ndx1(bbb)) = dist1(bbb); % Undo trade
continue
end
% Update vars
err(dist1(bbb)) = err(dist1(bbb)) - tradevalue(bbb); % the giver
err(dist2(bbb)) = err(dist2(bbb)) + tradevalue(bbb); % the taker
traded2(dist1(bbb)) = 1;
traded2(dist2(bbb)) = 1;
end
if k == length(ndx)
notdone = 0; % All squares have been traded too many times so stop trading
end
end
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