Competitive-Coding/min_edge_weight.cpp at main · S-Rohan-1904/Competitive-Coding · GitHub

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#include <bits/stdc++.h>
using namespace std;

#define rep(i, l, r) for (int i = l; i < r; i++)
#define rrep(i, r, l) for (int i = r-1; i >=0; i--)
#define ll long long
#define nline '\n'
#define prn cout << "NO" << nline
#define pry cout << "YES" << nline
#define vi vector<int>
#define vvi vector<vi>
#define eb emplace_back
#define all(a) (a).begin(), (a).end()
#define rall(a) (a).rbegin(), (a).rend()
#define inparr(v)   \
  for (auto &x : v) \
    cin >> x;
#define pii pair<int, int>
#define pll pair<ll, ll>
#define vpii vector<pii>
#define vvpii vector<vector<pii>>
#define mp make_pair
#define ff first
#define ss second
#define float long double

#define int long long

//---- Debugger ---- //
#ifdef LOCAL
#define debarr(a,n) cout<<#a<<" : ";for(int i=0;i<n;i++) cerr<<a[i]<<" "; cerr<<nline;
#define debmat(mat,row,col) cout<<#mat<<" :\n";for(int i=0;i<row;i++) {for(int j=0;j<col;j++) cerr<<mat[i][j]<<" ";cerr<<nline;}
#define pr(...) dbs(#__VA_ARGS__, __VA_ARGS__)
template <class S, class T>ostream& operator <<(ostream& os, const pair<S, T>& p) {return os << "(" << p.first << ", " << p.second << ")";}
template <class T>ostream& operator <<(ostream& os, const vector<T>& p) {os << "[ "; for (auto& it : p) os << it << " "; return os << "]";}
template <class T>ostream& operator <<(ostream& os, const unordered_set<T>& p) {os << "[ "; for (auto& it : p) os << it << " "; return os << "]";}
template <class S, class T>ostream& operator <<(ostream& os, const unordered_map<S, T>& p) {os << "[ "; for (auto& it : p) os << it << " "; return os << "]";}
template <class T>ostream& operator <<(ostream& os, const set<T>& p) {os << "[ "; for (auto& it : p) os << it << " "; return os << "]";}
template <class T>ostream& operator <<(ostream& os, const multiset<T>& p) {os << "[ "; for (auto& it : p) os << it << " "; return os << "]";}
template <class S, class T>ostream& operator <<(ostream& os, const map<S, T>& p) {os << "[ "; for (auto& it : p) os << it << " "; return os << "]";}
template <class T> void dbs(string str, T t) {cerr << str << " : " << t << "\n";}
template <class T, class... S> void dbs(string str, T t, S... s) {int idx = str.find(','); cerr << str.substr(0, idx) << " : " << t << ","; dbs(str.substr(idx + 1), s...);}
template <class T> void prc(T a, T b) {cerr << "["; for (T i = a; i != b; ++i) {if (i != a) cerr << ", "; cerr << *i;} cerr << "]\n";}
#else
#define pr(...)
#endif
//----------------- //

const int MOD = 1e9 + 7;
const int INF = 1e9 + 1;

vi rnk;
vi par;
vector<pair<int,pair<int,int>>> edges;

int find(int x) {
    if(par[x] == x) return x;
    return par[x] = find(par[x]);
}

void merge(int x, int y) {
    int xroot = find(x);
    int yroot = find(y);
    if(xroot != yroot) {
        if(rnk[xroot] >= rnk[yroot]) swap(xroot, yroot);

        rnk[yroot] += rnk[xroot];
        par[xroot] = yroot;
    }
}

void solve() {
  int n;
  cin>>n;
  int m = n-1;
  par.resize(n+1);
  rnk.resize(n+1);
  rep(i,1,n+1) {
    par[i] = i;
    rnk[i] = 1;
  }
  rep(i,0,m) {
    int u,v,w;
    cin>>u>>v>>w;
    edges.push_back({w, {u,v}});
  }

  sort(rall(edges));
  int ans = 0;

  for(auto edge : edges) {
    int w = edge.ff;
    int u = edge.ss.ff;
    int v = edge.ss.ss;
    pr(u,v,w);
    int x = find(u);
    int y = find(v);
    pr(rnk[x], rnk[x]);
    ans += w * rnk[x] * rnk[y];
    merge(u,v);
  }

  cout<<ans<<nline;
  edges.clear();
  pr(nline);
}

signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int t = 1;
  cin >> t;
  while (t--)
    solve();
}