// Search for an augmenting path in the graph graf.
// On success, the path data structure will include a list
// that forms the augmenting path. In this case, the last
// edge in the list is returned as the function value.
// On failure, returns 0.
edge edmonds::findpath() {
vertex u,v,vp,w,wp,x,y; edge e, f;
int t1, t2, t3;
t1 = Util::getTime();
blossoms->clear();
for (u = 1; u <= graf->n(); u++) {
state[u] = even; pEdge[u] = 0; origin[u] = u;
}
for (e = match->first(); e != 0; e = match->next(e)) {
u = graf->left(e); v = graf->right(e);
state[u] = state[v] = unreached;
}
UiList q(graf->m()); // list of edges to be processed in main loop
for (e = 1; e <= graf->m(); e++) {
if (state[graf->left(e)] == even ||
state[graf->right(e)] == even)
q.addLast(e);
}
t2 = Util::getTime();
pathInitTime += (t2-t1);
while (!q.empty()) {
stepCount++;
e = q.first(); q.removeFirst();
v = graf->left(e); vp = origin[blossoms->find(v)];
if (state[vp] != even) {
v = graf->right(e); vp = origin[blossoms->find(v)];
}
w = graf->mate(v,e); wp = origin[blossoms->find(w)];
if (vp == wp) continue; // skip internal edges in a blossom
if (state[wp] == unreached) {
// w is not contained in a blossom and is matched
// so extend tree and add newly eligible edges to q
x = graf->mate(w,mEdge[w]);
state[w] = odd; pEdge[w] = e;
state[x] = even; pEdge[x] = mEdge[w];
for (f = graf->firstAt(x); f != 0;
f = graf->nextAt(x,f)) {
if ((f != mEdge[x]) && !q.member(f))
q.addLast(f);
}
continue;
}
u = nca(vp,wp);
if (state[wp] == even && u == 0) {
// vp, wp are different trees - construct path & return
x = vp;
while (pEdge[x] != 0) {
x = origin[blossoms->find(
graf->mate(x,pEdge[x]))];
}
y = wp;
while (pEdge[y] != 0) {
y = origin[blossoms->find(
graf->mate(y,pEdge[y]))];
}
e = augpath->join(augpath->reverse(path(v,x)),e);
e = augpath->join(e,path(w,y));
t3 = Util::getTime();
pathFindTime += (t3-t2);
return e;
} else if (state[wp] == even) {
// vp and wp are in same tree - collapse blossom
blossomCount++;
x = vp;
int fu = blossoms->find(u);
int fx = blossoms->find(x);
while (fx != fu) {
fu = blossoms->link(fx,fu);
if (state[x] == odd) {
bridge[x].e = e; bridge[x].v = v;
for (f = graf->firstAt(x); f != 0;
f = graf->nextAt(x,f))
if (!q.member(f)) q.addLast(f);
}
x = origin[blossoms->find(
graf->mate(x,pEdge[x]))];
fx = blossoms->find(x);
}
y = wp;
int fy = blossoms->find(y);
while (fy != fu) {
fu = blossoms->link(fy,fu);
if (state[y] == odd) {
bridge[y].e = e; bridge[y].v = w;
for (f = graf->firstAt(y); f != 0;
f = graf->nextAt(y,f))
if (!q.member(f)) q.addLast(f);
}
y = origin[blossoms->find(
graf->mate(y,pEdge[y]))];
fy = blossoms->find(y);
}
origin[fu] = u;
}
}
t3 = Util::getTime();
pathFindTime += (t3-t2);
return 0;
}
int main() {
input();
nca();
//printf("%d",target1_parent[1]);
}
