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struct edge_t { int to, cap, rev; };
int maximum_flow_destructive(int s, int t, vector<vector<edge_t> > & g) { // ford fulkerson, O(EF)
int n = g.size();
vector<bool> used(n);
function<int (int, int)> dfs = [&](int i, int f) {
if (i == t) return f;
used[i] = true;
for (edge_t & e : g[i]) {
if (used[e.to] or e.cap <= 0) continue;
int nf = dfs(e.to, min(f, e.cap));
if (nf > 0) {
e.cap -= nf;
g[e.to][e.rev].cap += nf;
return nf;
}
}
return 0;
};
int result = 0;
while (true) {
used.clear(); used.resize(n);
int f = dfs(s, numeric_limits<int>::max());
if (f == 0) break;
result += f;
}
return result;
}
void add_edge(vector<vector<edge_t> > & g, int from, int to, int cap) {
g[from].push_back((edge_t) { to, cap, int(g[ to].size() ) });
g[ to].push_back((edge_t) { from, 0, int(g[from].size() - 1) });
}
int maximum_flow(int s, int t, vector<vector<edge_t> > g /* adjacency list */) { // ford fulkerson, O(FE)
return maximum_flow_destructive(s, t, g);
}
vector<pair<int,int> > perfect_bipartite_matching(set<int> const & a, set<int> const & b, vector<vector<int> > const & g /* adjacency list */) { // O(V + FE)
assert (a.size() + b.size() <= g.size());
int n = g.size();
int src = n;
int dst = n + 1;
vector<vector<edge_t> > h(n + 2);
auto add_edge = [&](int from, int to, int cap) {
h[from].push_back((edge_t) { to, cap, int(h[ to].size() ) });
h[ to].push_back((edge_t) { from, 0, int(h[from].size() - 1) });
};
repeat (i,n) {
if (a.count(i)) {
add_edge(src, i, 1);
for (int j : g[i]) if (b.count(j)) {
add_edge(i, j, 1); // collect edges e : a -> b, from g
}
}
if (b.count(i)) {
add_edge(i, dst, 1);
}
}
maximum_flow_destructive(src, dst, h);
vector<pair<int,int> > ans;
for (int from : a) {
for (edge_t e : h[from]) if (b.count(e.to) and e.cap == 0) {
ans.emplace_back(from, e.to);
}
}
return ans;
}
#line 1 "old/ford-fulkerson.inc.cpp"
struct edge_t { int to, cap, rev; };
int maximum_flow_destructive(int s, int t, vector<vector<edge_t> > & g) { // ford fulkerson, O(EF)
int n = g.size();
vector<bool> used(n);
function<int (int, int)> dfs = [&](int i, int f) {
if (i == t) return f;
used[i] = true;
for (edge_t & e : g[i]) {
if (used[e.to] or e.cap <= 0) continue;
int nf = dfs(e.to, min(f, e.cap));
if (nf > 0) {
e.cap -= nf;
g[e.to][e.rev].cap += nf;
return nf;
}
}
return 0;
};
int result = 0;
while (true) {
used.clear(); used.resize(n);
int f = dfs(s, numeric_limits<int>::max());
if (f == 0) break;
result += f;
}
return result;
}
void add_edge(vector<vector<edge_t> > & g, int from, int to, int cap) {
g[from].push_back((edge_t) { to, cap, int(g[ to].size() ) });
g[ to].push_back((edge_t) { from, 0, int(g[from].size() - 1) });
}
int maximum_flow(int s, int t, vector<vector<edge_t> > g /* adjacency list */) { // ford fulkerson, O(FE)
return maximum_flow_destructive(s, t, g);
}
vector<pair<int,int> > perfect_bipartite_matching(set<int> const & a, set<int> const & b, vector<vector<int> > const & g /* adjacency list */) { // O(V + FE)
assert (a.size() + b.size() <= g.size());
int n = g.size();
int src = n;
int dst = n + 1;
vector<vector<edge_t> > h(n + 2);
auto add_edge = [&](int from, int to, int cap) {
h[from].push_back((edge_t) { to, cap, int(h[ to].size() ) });
h[ to].push_back((edge_t) { from, 0, int(h[from].size() - 1) });
};
repeat (i,n) {
if (a.count(i)) {
add_edge(src, i, 1);
for (int j : g[i]) if (b.count(j)) {
add_edge(i, j, 1); // collect edges e : a -> b, from g
}
}
if (b.count(i)) {
add_edge(i, dst, 1);
}
}
maximum_flow_destructive(src, dst, h);
vector<pair<int,int> > ans;
for (int from : a) {
for (edge_t e : h[from]) if (b.count(e.to) and e.cap == 0) {
ans.emplace_back(from, e.to);
}
}
return ans;
}