//
// minimum spanning tree, Kruskal
// start from the smallest weight edge, and join vertices in a tree,
// as long as there is no cycle (ie both terminals in the same tree)
// to achieve that we need a set indicating each subtree, and merge
// the two corresponding sets when extracting an edge that joins two vertices.
// the union find mechanism works well and performs almost constant
float MST(const graphtp & g, pqtp & pq)
{
vi uf(g.size()); //union find structure
int visited = 0;
float totpath = 0.0;
//for each vertex need a set
for(int n = 0; n < g.size(); n++)
uf[n] = n;
pqtp::iterator it = pq.begin();
while(it != pq.end() && visited < g.size()) {
edge e = *it; //extract min
pq.erase(it++);
//unionfind will return false if they are in the same tree
if(false == unionfind(uf,e.to,e.from))
continue;
//process this edge
printf ("%d - %d (%f)\n", e.from, e.to, e.weight);
totpath += e.weight;
visited++;
}
return totpath;
}
int main(void){
int m, n;
for(RI(n), RI(m); (m || n); RI(n), RI(m)){
int a, ans = 0, b, maxppa = MINPPA, ppa;
FOR(i, n) cnt[i] = 0, p[i] = i;
FOR(i, n) FORI(j, i + 1, n) adj[i][j] = MINPPA;
FOR(i, m){
RI(a), RI(b), RI(ppa);
--a; --b;
if(a > b) swap(a, b);
if(ppa > adj[a][b]){
adj[a][b] = ppa;
maxppa = max(maxppa, ppa);
}
}
FOR(i, n) FORI(j, i + 1, n) if(adj[i][j] == maxppa) unionfind(i, j);
FOR(i, n) ans = max(ans, ++cnt[findroot(i)]);
printf("%d\n", ans);
}
int main(void) {
memset(dad,sizeof(dad),0);
/* lets union some prime numbers */
unionfind(2,7,1);
unionfind(3,11,1);
unionfind(13,7,1);
unionfind(5,7,1);
unionfind(2,11,1);
/* and some non prime */
unionfind(8,1,1);
unionfind(6,20,1);
unionfind(1,6,1);
printf("%d %d, %d\n", 2,7,unionfind(2,7,0));
printf("%d %d, %d\n", 5,11,unionfind(5,11,0));
printf("%d %d, %d\n", 5,8,unionfind(5,8,0));
printf("%d %d, %d\n", 20,1,unionfind(20,1,0));
return 0;
}
