feat(cf): 891 g

codeforces/891/g.cc

@@ -0,0 +1,175 @@
+#include <bits/stdc++.h>  // {{{
+
+// https://codeforces.com/blog/entry/96344
+
+#pragma GCC optimize("O2,unroll-loops")
+#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
+
+using namespace std;
+
+template <typename T>
+[[nodiscard]] static T MIN() {
+  return std::numeric_limits<T>::min();
+}
+
+template <typename T>
+[[nodiscard]] static T MAX() {
+  return std::numeric_limits<T>::max();
+}
+
+template <typename T>
+[[nodiscard]] static T sc(auto&& x) {
+  return static_cast<T>(x);
+}
+
+template <typename T>
+[[nodiscard]] static T sz(auto&& x) {
+  return static_cast<T>(x.size());
+}
+
+#define prln(...) std::println(__VA_ARGS__)
+#define pr(...) std::print(__VA_ARGS__)
+
+#ifdef LOCAL
+#define dbgln(...) std::println(__VA_ARGS__)
+#define dbg(...) std::print(__VA_ARGS__)
+#endif
+
+inline static void NO() {
+  prln("NO");
+}
+
+inline static void YES() {
+  prln("YES");
+}
+
+using ll = long long;
+using ld = long double;
+template <typename T>
+using ve = std::vector<T>;
+template <typename T, size_t N>
+using ar = std::array<T, N>;
+template <typename T1, typename T2>
+using pa = std::pair<T1, T2>;
+template <typename... Ts>
+using tu = std::tuple<Ts...>;
+template <typename... Ts>
+using dq = std::deque<Ts...>;
+template <typename... Ts>
+using qu = std::queue<Ts...>;
+template <typename... Ts>
+using pq = std::priority_queue<Ts...>;
+template <typename... Ts>
+using st = std::stack<Ts...>;
+auto lb = [](auto... args) {
+  return std::lower_bound(args...);
+};
+auto ub = [](auto... args) {
+  return std::upper_bound(args...);
+};
+
+#define ff first
+#define ss second
+#define eb emplace_back
+#define pb push_back
+#define all(x) (x).begin(), (x).end()
+#define rall(x) (x).rbegin(), (x).rend()
+//  }}}
+
+template <typename T>
+struct union_find {
+ public:
+  explicit union_find(size_t capacity)
+      : par(capacity), rank(capacity, 0), size(capacity, 1) {
+    iota(all(par), 0);
+  };
+
+  void join(T u, T v) noexcept {
+    u = find(u), v = find(v);
+
+    if (u == v)
+      return;
+
+    if (rank[u] < rank[v])
+      std::swap(u, v);
+
+    if (rank[u] == rank[v])
+      ++rank[u];
+
+    par[v] = u;
+    size[u] += size[v];
+    size[v] = size[u];
+  }
+
+  [[nodiscard]] T find(T const& u) noexcept {
+    if (u != par[u])
+      par[u] = find(par[u]);
+    return par[u];
+  }
+
+  std::vector<int> par;
+  std::vector<int> rank;
+  std::vector<int> size;
+};
+
+constexpr static int MOD = 998244353;
+
+long long modpow(long long a, long long b,
+                 long long mod = std::numeric_limits<long long>::max()) {
+  long long ans = 1;
+  a %= mod;
+  while (b > 0) {
+    if (b & 1) {
+      ans *= a;
+      ans %= MOD;
+    }
+    a *= a;
+    a %= MOD;
+    b >>= 1;
+  }
+  return ans;
+}
+
+void solve() {
+  int n;
+  ll S;
+  cin >> n >> S;
+  ve<tu<ll, int, int>> e;
+
+  for (int i = 0; i < n - 1; ++i) {
+    int u, v;
+    ll w;
+    cin >> u >> v >> w;
+    e.eb(w, u, v);
+  }
+
+  sort(all(e));
+
+  union_find<int> uf(n + 1);
+  ll ans = 1;
+
+  for (auto& [w, u, v] : e) {
+    ans = (ans * modpow(S - w + 1,
+                        (1LL * uf.size[uf.find(u)] * uf.size[uf.find(v)] - 1),
+                        MOD)) %
+          MOD;
+    uf.join(u, v);
+  }
+
+  prln("{}", ans);
+}
+
+int main() {  // {{{
+  cin.tie(nullptr)->sync_with_stdio(false);
+  cin.exceptions(cin.failbit);
+
+  int t = 1;
+  cin >> t;
+
+  while (t--) {
+    solve();
+  }
+
+  return 0;
+}
+// }}}