Submission #7487474

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Source Code Expand

#include <bits/stdc++.h>
using namespace std;
using lint = long long;
template<class T = int> using V = vector<T>;
template<class T = int> using VV = V< V<T> >;

struct UnionFind {
  const int n;
  V<> t; // root ? -sz : par
  UnionFind(int n) : n(n), t(n, -1) {}
  int find(int v) { return t[v] < 0 ? v : t[v] = find(t[v]); }
  void unite(int u, int v) {
    if ((u = find(u)) == (v = find(v))) return;
    if (-t[u] < -t[v]) swap(u, v);
    t[u] += t[v];
    t[v] = u;
  }
  bool same(int u, int v) { return find(u) == find(v); }
  int size(int v) { return -t[find(v)]; }
};

int main() {
  cin.tie(nullptr); ios::sync_with_stdio(false);
  int n, q; cin >> n >> q;
  struct Edge {
    int u, v, w;
    bool operator<(const Edge& r) const { return w > r.w; }
  };
  priority_queue<Edge> pq;
  while (q--) {
    int a, b, c; cin >> a >> b >> c;
    pq.emplace(Edge{a, b, c});
    pq.emplace(Edge{(a + 1) % n, b, c + 1});
  }

  UnionFind uf(n);
  lint res = 0;
  while (uf.size(0) < n) {
    auto e = pq.top(); pq.pop();
    if (uf.same(e.u, e.v)) continue;
    uf.unite(e.u, e.v);
    res += e.w;
    pq.emplace(Edge{(e.u + 1) % n, (e.v + 1) % n, e.w + 2});
  }
  cout << res << '\n';
}

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