Submission #3194517

---

Source Code Expand

#define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
#define ll long long
#define REP(i, n) for (ll (i) = 0; (i) < (n); (i)++)
#define REPI(i, a, b) for (ll (i) = (a); (i) < (b); (i)++)
#define int long long
#define MOD 1000000007
using namespace std;
using P = pair<int, int>;
using VI = vector<int>;
using VVI = vector<VI>;
using VVVI = vector<VVI>;
class UnionFind {
public:
  VI par, rank;
  UnionFind(int n) {
    par = VI(n); iota(par.begin(), par.end(), 0);
    rank = VI(n, 0);
  }
  int root(int x) {
    if (par[x] == x) {
      return x;
    } else {
      return par[x] = root(par[x]);
    }
  }
  void unite(int x, int y) {
    x = root(x);
    y = root(y);
    if (x == y) { return; }
    if (rank[x] < rank[y]) {
      par[x] = y;
    } else {
      par[y] = x;
      if (rank[x] == rank[y]) { rank[x]++; }
    }
  }
  bool same(int x, int y) {
    return root(x) == root(y);
  }
};

struct edge { int u, v, cost; };
bool comp(const edge& e1, const edge& e2) { return e1.cost < e2.cost; }
struct neigh { int to, cost; };
vector<vector<neigh>> g;
vector<edge> es2;
int kruskal(int V, vector<edge>& es) {
  sort(es.begin(), es.end(), comp);
  UnionFind uf(V);
  int ans = 0;
  for (edge e: es) {
    if (uf.same(e.u, e.v)) { es2.push_back(e); continue; }
    uf.unite(e.u, e.v);
    ans += e.cost;
    g[e.u].push_back({e.v, e.cost});
    g[e.v].push_back({e.u, e.cost});
  }
  return ans;
}
vector<bool> visited;
int dfs(int v1, int v2, int acc) {
  if (v1 == v2) { return acc; }
  visited[v1] = true;
  int ans = -1;
  for (neigh nei: g[v1]) {
    if (visited[nei.to]) { continue; }
    ans = max(ans, dfs(nei.to, v2, max(acc, nei.cost)));
  }
  return ans;
}
int pow_mod(int x) {
  if (x == 0) { return 1; }
  int tmp = pow_mod(x / 2);
  return tmp * tmp % MOD * (x % 2 ? 2 : 1) % MOD;
}
signed main() {
  int N, M, X;
  cin >> N >> M >> X;
  vector<edge> es(M);
  g = vector<vector<neigh>>(N);
  REP (i, M) {
    cin >> es[i].u >> es[i].v >> es[i].cost;
    es[i].u--; es[i].v--;
  }
  int S = kruskal(N, es);
  int D = X - S;
  if (D < 0) {
    cout << 0 << endl; return 0;
  }
  int eqs = 0;
  int ups = 0;
  int lws = 0;
  for (edge e: es2) {
    visited = vector<bool>(N, false);
    int path = dfs(e.u, e.v, 0);
    assert(path <= e.cost);
    if (e.cost == path + D) { eqs++; }
    else if (e.cost > path + D) { ups++; }
    else { lws++; }
  }
  assert(eqs + ups + lws == es2.size());
  int tmp = 2 * (pow_mod(eqs) - 1) % MOD * pow_mod(ups) % MOD;
  if (D == 0) {
    cout << ((pow_mod(N-1) - 2) % MOD * pow_mod(M-N+1) % MOD + tmp) % MOD << endl;
  } else {
    cout << tmp << endl;
  }
}

Submission Info

Judge Result