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function [mpe, clpot, seppot] = find_max_config(engine, clpot, seppot, evidence)
% FIND_MAX_CONFIG Backwards pass of Viterbi fro jtree
% function [mpe, clpot, seppot] = find_max_config(engine, clpot, seppot, evidence)
% See Cowell99 p98
bnet = bnet_from_engine(engine);
nnodes = length(bnet.dag);
mpe = cell(1, nnodes);
maximize = 1;
c = engine.root_clq;
pot = struct(clpot{c}); % violate object privacy
dom = pot.domain;
[indices, clpot{c}] = find_most_prob_entry(clpot{c});
mpe(dom) = num2cell(indices);
for n=engine.preorder
for c=engine.preorder_children{n}
clpot{c} = divide_by_pot(clpot{c}, seppot{n,c});
seppot{n,c} = marginalize_pot(clpot{n}, engine.separator{n,c}, maximize);
clpot{c} = multiply_by_pot(clpot{c}, seppot{n,c});
pot = struct(clpot{c}); % violate object privacy
dom = pot.domain;
[indices, clpot{c}] = find_most_prob_entry(clpot{c});
mpe(dom) = num2cell(indices);
end
end
obs_nodes = find(~isemptycell(evidence));
% indices for observed nodes will be 1 - need to overwrite these
mpe(obs_nodes) = evidence(obs_nodes);
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