matlab实现基于DFS的Ford_Fulkerson最大流最小割算法

function [F, maxf, V, S] = Ford_Fulkerson(C, src, sink)

n = size(C, 1);

F = zeros(n);
maxf = 0;
V = [];
S = [];

while true
% in: ResNet.
ResNet = C - F + F';   % residual network.
% out: pre, Df
pre = ones(1, n) * NaN;
Df = ones(1, n) * inf;
% DFS to find augmenting path.
stk = [ src ];
unvisited = setdiff(1:n, src);
while ~isempty(stk)
if stk(1) == sink
break;
end
% pop
from = stk(1);
stk(1) = [];

% fot v in adj(u)
[~, to] = find(ResNet(from, unvisited) > 0);
tovisit = unvisited(unique(to));
% visit
pre(tovisit) = from;
Df(tovisit) = min(Df(from), ResNet(from, tovisit));

% push
stk = [tovisit, stk];
unvisited = setdiff(unvisited, tovisit);
end
% DFS end.

if isempty(stk)
% not found. max flow get.
S = setdiff(1:n, unvisited);
V = unvisited;
break;

else
% Augmenting path found.
%in: pre, Df
maxf = maxf + Df(sink);
%update arc.
t = sink;
while t ~= src
% pre(t)-t
if C(pre(t), t) ~= 0
% forward arc.
F(pre(t), t) = F(pre(t), t) + Df(sink);
else
% backward arc.
F(t, pre(t)) = F(t, pre(t)) - Df(sink);
end

t = pre(t);
end
end

end

end