結果

問題 No.1207 グラフX
ユーザー theory_and_me
提出日時 2020-08-30 15:08:36
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 295 ms / 2,000 ms
コード長 5,849 bytes
コンパイル時間 3,264 ms
コンパイル使用メモリ 212,256 KB
最終ジャッジ日時 2025-01-13 22:30:26
ジャッジサーバーID
(参考情報)
judge4 / judge5
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 3
other AC * 46
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#include <bits/stdc++.h>
using namespace std;
#define REP(i,n) for(ll i=0;i<(ll)n;i++)
#define dump(x) cerr << #x << " = " << (x) << endl;
#define spa << " " <<
#define fi first
#define se second
#define ALL(a) (a).begin(),(a).end()
#define ALLR(a) (a).rbegin(),(a).rend()
using ld = long double;
using ll = long long;
using ull = unsigned long long;
using pii = pair<int, int>;
using pll = pair<long, long>;
using pdd = pair<ld, ld>;
template<typename T> struct V : vector<T> { using vector<T>::vector; };
V() -> V<ll>;
V(size_t) -> V<ll>;
template<typename T> V(size_t, T) -> V<T>;
template<typename T> vector<T> make_vec(size_t n, T a) { return vector<T>(n, a); }
template<typename... Ts> auto make_vec(size_t n, Ts... ts) { return vector<decltype(make_vec(ts...))>(n, make_vec(ts...)); }
template<class S, class T> ostream& operator << (ostream& os, const pair<S, T> v){os << "(" << v.first << ", " << v.second << ")"; return os;}
template<typename T> ostream& operator<<(ostream &os, const vector<T> &v) { for (auto &e : v) os << e << ' '; return os; }
template<class T> ostream& operator<<(ostream& os, const vector<vector<T>> &v){ for(auto &e : v){os << e << "\n";} return os;}
struct fast_ios { fast_ios(){ cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
template<class T> bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T> bool chmin(T &a, const T &b) { if (a>b) { a=b; return 1; } return 0; }
void fail() { cout << -1 << '\n'; exit(0); }
inline int popcount(const int x) { return __builtin_popcount(x); }
inline int popcount(const ll x) { return __builtin_popcountll(x); }
template<typename T> void debug(vector<vector<T>>&v,ll h,ll w){for(ll i=0;i<h;i++)
{cerr<<v[i][0];for(ll j=1;j<w;j++)cerr spa v[i][j];cerr<<endl;}};
template<typename T> void debug(vector<T>&v,ll n){if(n!=0)cerr<<v[0];
for(ll i=1;i<n;i++)cerr spa v[i];
cerr<<endl;};
const ll INF = (1ll<<62);
// const ld EPS = 1e-10;
// const ld PI = acos(-1.0);
const ll mod = (int)1e9 + 7;
//const ll mod = 998244353;
template <std::uint_fast64_t Modulus> class modint {
// long long modint
//
using u64 = std::uint_fast64_t;
public:
u64 a;
constexpr modint(const u64 x = 0) noexcept : a(x % Modulus) {}
constexpr u64 &value() noexcept { return a; }
constexpr const u64 &value() const noexcept { return a; }
constexpr modint operator+(const modint rhs) const noexcept {
return modint(*this) += rhs;
}
constexpr modint operator-(const modint rhs) const noexcept {
return modint(*this) -= rhs;
}
constexpr modint operator*(const modint rhs) const noexcept {
return modint(*this) *= rhs;
}
constexpr modint operator/(const modint rhs) const noexcept {
return modint(*this) /= rhs;
}
constexpr modint &operator+=(const modint rhs) noexcept {
a += rhs.a;
if (a >= Modulus) {
a -= Modulus;
}
return *this;
}
constexpr modint &operator-=(const modint rhs) noexcept {
if (a < rhs.a) {
a += Modulus;
}
a -= rhs.a;
return *this;
}
constexpr modint &operator*=(const modint rhs) noexcept {
a = a * rhs.a % Modulus;
return *this;
}
constexpr modint &operator/=(modint rhs) noexcept {
u64 exp = Modulus - 2;
while (exp) {
if (exp % 2) {
*this *= rhs;
}
rhs *= rhs;
exp /= 2;
}
return *this;
}
};
using mint = modint<mod>;
using vm = vector<mint>;
using vvm = vector<vm>;
ostream& operator << (ostream& os, const mint v){
os << v.value(); return os;
}
template <class T, class U> constexpr T power(T x, U exp) {
T ret = static_cast<T>(1);
while (exp) {
if (exp % static_cast<U>(2) == static_cast<U>(1))
ret *= x;
exp /= static_cast<U>(2);
x *= x;
}
return ::std::move(ret);
}
// par[i] ·iroot-()irootroot
// root(x) root
struct UnionFindSize {
vector<int> par;
UnionFindSize(int n) : par(n, -1) { }
void init(int n) { par.assign(n, -1); }
int root(int x) {
if (par[x] < 0) return x;
else return par[x] = root(par[x]);
}
bool issame(int x, int y) {
return root(x) == root(y);
}
bool merge(int x, int y) {
x = root(x); y = root(y);
if (x == y) return false;
if (par[x] > par[y]) swap(x, y); // merge technique
par[x] += par[y];
par[y] = x;
return true;
}
int size(int x) {
return -par[root(x)];
}
void print(){
cout << "uf: ";
for(int i=0;i<(int)par.size();i++) cout << root(i) << " ";
cout << endl;
}
};
using Graph = V<V<pll>>;
int main(){
ll N, M, X;
cin >> N >> M >> X;
V<ll> x(M), y(M), z(M);
REP(i, M) cin >> x[i] >> y[i] >> z[i];
REP(i, M) x[i]--, y[i]--;
V<ll> ids(M);
iota(ALL(ids), 0);
sort(ALL(ids), [&](ll x, ll y){
return z[x] < z[y];
});
UnionFindSize uf(N);
Graph G(N);
mint res = 0;
for(auto idx: ids){
if(uf.merge(x[idx], y[idx])){
G[x[idx]].emplace_back(y[idx], z[idx]);
G[y[idx]].emplace_back(x[idx], z[idx]);
}
}
auto dfs = [&](auto self, ll now, ll par)->ll{
ll sz = 1;
for(auto tup: G[now]){
ll next = tup.first;
ll zz = tup.second;
if(next == par) continue;
ll tmp_sz = self(self, next, now);
res += mint(tmp_sz) * (N-tmp_sz) * power(mint(X), zz);
sz += tmp_sz;
}
return sz;
};
dfs(dfs, 0, -1);
cout << res << endl;
return 0;
}
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