#include #ifndef LOCAL_TEST #pragma GCC target ("avx") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native") #endif // LOCAL_TEST using namespace std; using ll = long long; using pii = pair; using pll = pair; using vi = vector; using vvi = vector; using vvvi = vector; using vl = vector; using vvl = vector; using vvvl = vector; using vb = vector; using vvb = vector; using vvvb = vector; using vc = vector; using vvc = vector; using vvvc = vector; using vd = vector; using vvd = vector; using vvvd = vector; using vs = vector; using vvs = vector>; using vvvs = vector>>; template using priority_queue_min = priority_queue, greater>; const double PI = acos(-1.0); int INF = 100100111; ll INFL = 3300300300300300491LL; double EPS = 1e-8; double EPSL = 1e-16; constexpr int MODINT998244353 = 998244353; constexpr int MODINT1000000007 = 1000000007; struct fast_io { fast_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } fastIOtmp; #define all(a) (a).begin(), (a).end() #define sz(x) ((int)(x).size()) #define lbpos(a, x) (int)distance((a).begin(), std::lower_bound(all(a), x)) #define ubpos(a, x) (int)distance((a).begin(), std::upper_bound(all(a), x)) #define rep(i, n) for(ll i = 0, i##_len = ll(n); i < i##_len; ++i) // 0 から n-1 まで昇順 #define repi(i, s, t) for(ll i = ll(s), i##_end = ll(t); i < i##_end; ++i) // s から t まで昇順 #define repis(i, s, t, step) for(ll i = ll(s), i##_end = ll(t); i < i##_end; i+=step) // s から t まで stepずつ #define repir(i, s, t, step) for(ll i = ll(s), i##_end = ll(t); i > i##_end; i+=step) // s から t まで stepずつ #define repe(a, v) for(auto& a : (v)) // v の全要素(変更可能) #define repea(a, v) for(const auto& a : (v)) // v の全要素(変更不可能) #define smod(n, m) ((((n) % (m)) + (m)) % (m)) // 非負mod #define sdiv(n, m) (((n) - smod(n, m)) / (m)) // 非負div #define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} // 重複除去 #define EXIT(a) {cout << (a) << endl; exit(0);} // 強制終了 void Yes(bool b) { cout << (b ? "Yes\n" : "No\n"); return; } ll powm(ll a, ll n, ll mod=INFL) { ll res = 1; while (n > 0) { if (n & 1) res = (res * a) % mod; a = (a * a) % mod; n >>= 1; } return res; } template inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // 最大値を更新(更新されたら true を返す) template inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // 最小値を更新(更新されたら true を返す) int digit(ll x, int d=10) { int rev=0; while (x > 0) { rev++; x /= d;}; return rev; } // xのd進数桁数 #include #include #include namespace atcoder { struct dsu { public: dsu() : _n(0) {} explicit dsu(int n) : _n(n), parent_or_size(n, -1) {} int merge(int a, int b) { assert(0 <= a && a < _n); assert(0 <= b && b < _n); int x = leader(a), y = leader(b); if (x == y) return x; if (-parent_or_size[x] < -parent_or_size[y]) std::swap(x, y); parent_or_size[x] += parent_or_size[y]; parent_or_size[y] = x; return x; } bool same(int a, int b) { assert(0 <= a && a < _n); assert(0 <= b && b < _n); return leader(a) == leader(b); } int leader(int a) { assert(0 <= a && a < _n); if (parent_or_size[a] < 0) return a; return parent_or_size[a] = leader(parent_or_size[a]); } int size(int a) { assert(0 <= a && a < _n); return -parent_or_size[leader(a)]; } std::vector> groups() { std::vector leader_buf(_n), group_size(_n); for (int i = 0; i < _n; i++) { leader_buf[i] = leader(i); group_size[leader_buf[i]]++; } std::vector> result(_n); for (int i = 0; i < _n; i++) { result[i].reserve(group_size[i]); } for (int i = 0; i < _n; i++) { result[leader_buf[i]].push_back(i); } result.erase( std::remove_if(result.begin(), result.end(), [&](const std::vector& v) { return v.empty(); }), result.end()); return result; } private: int _n; std::vector parent_or_size; }; } // namespace atcoder template struct Graph{ public: struct Edge { int to; Cost cost; Edge() {}; Edge(int _to, Cost _cost) : to(_to), cost(_cost) {}; }; struct AdjacencyListRange{ using iterator = typename std::vector::const_iterator; iterator begi, endi; iterator begin() const { return begi; } iterator end() const { return endi; } int size() const { return (int)distance(begi, endi); } const Edge& operator[](int i) const { return begi[i]; } }; private: public: vector E; vector I; int n; Graph() : n(0) {} Graph(int _n) : n(_n) {} Graph(int _n, const vector& from, vector& to, vector& cost, bool rev = false) : n(_n) { vector buf(n+1, 0); for(int i=0; i<(int)from.size(); i++){ ++buf[from[i]]; if (rev) ++buf[to[i]]; } for(int i=1; i<=_n; i++) buf[i] += buf[i-1]; E.resize(buf[n]); for(int i=(int)from.size()-1; i>=0; i--){ int u = from[i]; int v = to[i]; Cost c = cost[i]; E[--buf[u]] = Edge(v, c); if(rev) E[--buf[v]] = Edge(u, c); } I = move(buf); } AdjacencyListRange operator[](int u) const { return AdjacencyListRange{ E.begin() + I[u], E.begin() + I[u+1] }; } int num_vertices() const { return n; } int size() const { return num_vertices(); } int num_edges() const { return E.size(); } }; template ostream& operator<<(ostream& os, Graph g) { bool first = true; rep(i, g.n) repe(e, g[i]) { if (first) first = false; else os << endl; os << i << "->" << e.to << ": " << e.cost; } return os; } template Graph kruskal(const Graph& G){ atcoder::dsu uf(G.n); priority_queue, vector>, greater>> que; rep(i, G.n) repe(e, G[i]) { que.emplace(e.cost, i, e.to); } int count = 0; vi from,to; vector cost; while(que.size() && count < G.n - 1 ){ auto [c, u, v] = que.top(); que.pop(); if (!uf.same(u, v)) { uf.merge(u, v); from.push_back(u); to.push_back(v); cost.push_back(c); count++; } } if (count != G.n - 1) return Graph(0); return Graph(G.n, from, to, cost, true); } #include using namespace std; template inline istream& operator>>(istream& is, pair& p); template inline istream& operator>>(istream& is, vector& v); template inline ostream& operator<<(ostream& os, const pair& p); template inline ostream& operator<<(ostream& os, const vector& v); template ostream &operator<<(ostream &os, const map &mp); template ostream &operator<<(ostream &os, const set &st); template ostream &operator<<(ostream &os, const multiset &st); template ostream &operator<<(ostream &os, queue q); template ostream &operator<<(ostream &os, deque q); template ostream &operator<<(ostream &os, stack st); template ostream &operator<<(ostream &os, priority_queue pq); template inline istream& operator>>(istream& is, pair& p) { is >> p.first >> p.second; return is; } template inline istream& operator>>(istream& is, vector& v) { repe(x, v) is >> x; return is; } template inline ostream& operator<<(ostream& os, const pair& p) { os << p.first << " " << p.second; return os; } template inline ostream& operator<<(ostream& os, const vector& v) { rep(i, sz(v)) { os << v.at(i); if (i != sz(v) - 1) os << " "; } return os; } template ostream &operator<<(ostream &os, const map &mp) { for (auto &[key, val] : mp) { os << key << ":" << val << " "; } return os; } template ostream &operator<<(ostream &os, const set &st) { auto itr = st.begin(); for (int i = 0; i < (int)st.size(); i++) { os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; } template ostream &operator<<(ostream &os, const multiset &st) { auto itr = st.begin(); for (int i = 0; i < (int)st.size(); i++) { os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; } template ostream &operator<<(ostream &os, queue q) { while (q.size()) { os << q.front() << " "; q.pop(); } return os; } template ostream &operator<<(ostream &os, deque q) { while (q.size()) { os << q.front() << " "; q.pop_front(); } return os; } template ostream &operator<<(ostream &os, stack st) { while (st.size()) { os << st.top() << " "; st.pop(); } return os; } template ostream &operator<<(ostream &os, priority_queue pq) { while (pq.size()) { os << pq.top() << " "; pq.pop(); } return os; } template inline vector& operator--(vector& v) { repe(x, v) --x; return v; } template inline vector& operator++(vector& v) { repe(x, v) ++x; return v; } #define debug(...) debug_func(0, #__VA_ARGS__, __VA_ARGS__) // debug print #ifdef LOCAL_TEST template void debug_func(int i, T name) { (void)i; (void)name; cerr << endl; } template void debug_func(int i, const T1 &name, const T2 &a, const T3 &...b) { for ( ; name[i] != ',' && name[i] != '\0'; i++ ) cerr << name[i]; cerr << ":" << a << " "; debug_func(i + 1, name, b...); } #endif #ifndef LOCAL_TEST template void debug_func(const T &...) {} #endif ll ans(0); template Graph kruskal2(const Graph& G){ atcoder::dsu uf(G.n); priority_queue, vector>, greater>> que; rep(i, G.n) repe(e, G[i]) { que.emplace(e.cost, i, e.to); } int count = 0; vi from,to; vector cost; while(que.size() && count < G.n - 1 ){ auto [c, u, v] = que.top(); que.pop(); if (!uf.same(u, v)) { ans += c * uf.size(u) * uf.size(v); uf.merge(u, v); from.push_back(u); to.push_back(v); cost.push_back(c); count++; } } if (count != G.n - 1) return Graph(0); return Graph(G.n, from, to, cost, true); } int main() { int n,m; cin >> n >> m; vi from(m), to(m); vl cost(m); rep(i, m) cin >> from[i] >> to[i] >> cost[i]; --from; --to; Graph g(n, from, to, cost, true); Graph g2 = kruskal2(g); debug(g2); cout << ans << endl; }