function h = treehij(A,C,T,i,j)
% bounds hh(i,j) for a tree

% find j0, where
% j0 is the minimum descendant of i s.t. j0>=j

[n,n] = size(T);

global LEVELS
LEVELS = repmat({[]},n,1);

Ti = getSubt(T,i);

jj = Ti(Ti>=j);
if isempty(jj)
  h = 0;
  return
end


j0 = min(jj);
dpath = parentseq(T,j0,i);
getLevels(T,1,0);
h = 1;
for k=2:length(dpath)
  u = dpath(k);
  LEVu = getLevu(u);
  S = 0;
  thlev = [];
  for li = 1:length(LEVu)
    u1 = LEVu(li);
    v = find(T(:,u1));
    Avu = getAij(A,v,u1);
    th = getTH(Avu);
    %S = max(S,th);
    %S = S + th;
    thlev(end+1) = th;
  end
  S = inclexcl(thlev);
  h = h * S;
end
return


function h = getTH(A)
[n,n] = size(A);
h = 0;
for i=1:n
  for j=i+1:n
    x = A(:,i);
    y = A(:,j);
    d = TV(x-y);
    h = max(h,d);
  end
end
return


function LEVu = getLevu(u)
global LEVELS
for ell=1:length(LEVELS)
  if ismember(u,LEVELS{ell})
    LEVu = LEVELS{ell};
    return
  end
end
return



function getLevels(T,u,ell)
global LEVELS
ell = ell+1;
LEVELS{ell}(end+1) = u;
ukids = find(T(u,:));
for vi=1:length(ukids)
  v = ukids(vi);
  getLevels(T,v,ell);
end

return


function pseq = parentseq(T,u,r)
v = u;
el = 0;
pseq = [u];
while v~=r
  el = el+1;
  rents = find(T(:,v));
  v = rents;
  pseq = [v pseq];
end
return



function sT = getSubt(T,v)
% a list of v's descendents in T
% includes v itself
global SUBT
SUBT = [];
Pi(T,v);
sT = SUBT;
return

function Pi(T,v)
global SUBT
SUBT(end+1) = v;
vkids = find(T(v,:));
for vi=1:length(vkids)
  v1 = vkids(vi);
  Pi(T,v1);
end