static void addOrthEdge(GraphVertex u, GraphVertex v,
const std::vector<Primitive*>& vecPrimitive,
std::vector<GraphVertex>& vecPredecessor,
double angleThreshold,
Graph& g)
{
u = g[u].getParent();
v = g[v].getParent();
// check if edge exists
if (edge(u, v, g).second) {
return;
}
if (!willProduceLoop(vecPredecessor, v, u, g)) {
add_edge(u, v, EdgeProp(RelationEdge::RET_ORTHOGONAL), g);
}
else {
add_edge(u, v, EdgeProp(RelationEdge::RET_ORTHOGONAL), g);
// there is a path between u and v, and we added edge(u, v), so there will be loop
std::vector<GraphVertex> vecLoop;
GraphVertex current = u;
vecLoop.push_back(current);
while (vecPredecessor[current] != current) {
current = vecPredecessor[current];
vecLoop.push_back(current);
}
int nLoopSize = vecLoop.size();
if (nLoopSize == 3) {
GraphVertex opposite2 = 0;
GraphVertex opposite0 = 0;
bool bShare01 = findBridge(vecLoop[0], vecLoop[1], g, opposite2);
bool bShare12 = findBridge(vecLoop[1], vecLoop[2], g, opposite0);
if (bShare01) {
addParaEdge(opposite2, vecLoop[2], vecPrimitive, vecPredecessor, angleThreshold, g);
}
if (bShare12) {
addParaEdge(opposite0, vecLoop[0], vecPrimitive, vecPredecessor, angleThreshold, g);
}
} else {
std::pair<GraphVertex, GraphVertex> para = findParalell(vecLoop, vecPrimitive, (nLoopSize == 4), angleThreshold);
if (para.first != para.second) {
addParaEdge(para.first, para.second, vecPrimitive, vecPredecessor, angleThreshold, g);
}
}
}
return;
}
int main() {
int test, cs, n, m, i, u, v;
scanf("%d", &test);
for(cs = 1; cs <= test; cs++) {
scanf("%d %d", &n, &m);
memset(fin, -1, sizeof(int)*n);
memset(used, 0, sizeof(int)*n);
for(i = nEdge = 0; i < m; i++) {
scanf("%d %d", &u, &v);
addEdge(u, v);
}
dfsTime = nComp = 0;
findBridge(0, -1);
memset(used, 0, sizeof(int)*n);
for(i = 0; i < n; i++) {
if(!used[i]) {
traverse(i);
nComp++;
}
}
memset(deg, 0, sizeof(int)*nComp);
for(i = 0; i < nEdge; i+=2) {
if(bridge[i]) {
deg[compo[from[i]]]++;
deg[compo[to[i]]]++;
}
}
for(i = m = 0; i < nComp; i++) m += (deg[i] == 1);
printf("Case %d: %d\n", cs, (m + 1)>>1);
}
return 0;
}
void findBridge(int u, int par) {
int i, v;
used[u] = 1;
vis[u] = low[u] = ++dfsTime;
for(i = fin[u]; i >= 0; i = next[i]) {
v = to[i];
if(v == par) continue;
if(used[v]) low[u] = min(low[u], vis[v]);
else {
findBridge(v, u);
low[u] = min(low[u], low[v]);
if(low[v] > vis[u]) bridge[i] = bridge[i^1] = 1;
}
}
}
