結果
問題 | No.1207 グラフX |
ユーザー |
![]() |
提出日時 | 2020-08-30 14:48:39 |
言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 273 ms / 2,000 ms |
コード長 | 20,251 bytes |
コンパイル時間 | 2,201 ms |
コンパイル使用メモリ | 186,420 KB |
実行使用メモリ | 45,312 KB |
最終ジャッジ日時 | 2024-11-15 07:55:35 |
合計ジャッジ時間 | 11,761 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge3 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 46 |
ソースコード
#include <bits/stdc++.h>using namespace std;#pragma region macros_and_aliases#define rep(i, n) for(long long i = 0; i < (n); i++)#define rrep(i, n) for(long long i = (n)-1; i > -1; i--)#define Rep(i, m, n) for(long long i = (m); i < (n); i++)#define rRep(i, m, n) for(long long i = (n)-1; i >= (m); i--)#define REP(i, m, n, p) for(long long i = m; i < n; i += p)#define foa(s, v) for(auto &s : v)#define all(v) (v).begin(), (v).end()#define rall(v) (v).rbegin(), (v).rend()#define bcnt(n) __builtin_popcountll(n)#define endk endl#define ednl endl#define enld endlusing ll = long long;using ld = long double;using vb = vector<bool>;using vi = vector<int>;using vvi = vector<vector<int>>;using vvvi = vector<vector<vector<int>>>;using vll = vector<ll>;using vvll = vector<vll>;using vvvll = vector<vvll>;using mll = map<long long, long long>;using pll = pair<long long, long long>;using qll = queue<long long>;using sll = set<long long>;using vpll = vector<pair<long long, long long>>;template <class T = ll>using V = vector<T>;template <class T = ll>using VV = V<V<T>>;template <class T = ll>using VVV = V<V<V<T>>>;//昇順pq(小さい方から取り出す)template <class T = ll>using pqup = priority_queue<T, vector<T>, greater<T>>;//降順pq(大きい方から取り出す)template <class T = ll>using pqdn = priority_queue<T>;#pragma region debug#define debug(var) \do { \std::cout << #var << " : "; \view(var); \} while(0)template <typename T>void view(T e) {std::cout << e << "\n";}template <typename T>void view(const std::vector<T> &v) {for(const auto &e : v) {std::cout << e << " ";}std::cout << "\n";}template <typename T>void view(const std::set<T> &s) {for(auto &t : s) {std::cout << t << " ";}std::cout << "\n";}template <typename T>void view(const std::vector<std::vector<T>> &vv) {std::cout << "\n";for(const auto &v : vv) {view(v);}}template <typename T, typename U>void view(const std::vector<std::pair<T, U>> &v) {std::cout << "\n";for(const auto &c : v) {std::cout << c.first << " " << c.second << "\n";}}template <typename T, typename U>void view(const std::map<T, U> &m) {std::cout << "\n";for(auto &t : m) {std::cout << t.first << " " << t.second << "\n";}}#pragma endregion#pragma region input#define VEC(type, name, size) \vector<type> name(size); \IN(name)#define VVEC(type, name, h, w) \vector<vector<type>> name(h, vector<type>(w)); \IN(name)#define INT(...) \int __VA_ARGS__; \IN(__VA_ARGS__)#define LL(...) \long long __VA_ARGS__; \IN(__VA_ARGS__)#define STR(...) \string __VA_ARGS__; \IN(__VA_ARGS__)#define CHAR(...) \char __VA_ARGS__; \IN(__VA_ARGS__)#define DOUBLE(...) \double __VA_ARGS__; \IN(__VA_ARGS__)#define LD(...) \long double __VA_ARGS__; \IN(__VA_ARGS__)template <class T>void scan(T &a) {cin >> a;}template <class T>void scan(vector<T> &a) {for(auto &i : a) scan(i);}template <class T, class L>void scan(pair<T, L> &p) {scan(p.first);scan(p.second);}void IN() {}template <class Head, class... Tail>void IN(Head &head, Tail &... tail) {scan(head);IN(tail...);}template <class T>inline void print(T x) {cout << x << '\n';}template <typename T1, typename T2>ostream &operator<<(ostream &os, const pair<T1, T2> &p) {os << p.first << " " << p.second;return os;}template <typename T1, typename T2>istream &operator>>(istream &is, pair<T1, T2> &p) {is >> p.first >> p.second;return is;}#pragma endregion#pragma endregion#pragma region constantslong long const limLL = 9223372036854775807; // POW(2,63)-1 ~ 9.22e18long long const dekai = 3e16;const long double pi = acos(-1);int dx[4] = {1, 0, -1, 0};int dy[4] = {0, 1, 0, -1};int ddx[8] = {-1, -1, -1, 0, 0, 1, 1, 1};int ddy[8] = {-1, 0, 1, -1, 1, -1, 0, 1};const int mod = 1000000007;// const int mod = 998244353;#pragma endregion#pragma region basic_proceduretemplate <class T>inline bool isin(T x, T lef, T rig) {return ((lef <= x) && (x < rig));}template <class T>inline bool chmin(T &a, T b) {if(a > b) {a = b;return true;}return false;}template <class T>inline bool chmax(T &a, T b) {if(a < b) {a = b;return true;}return false;}void Yes(bool f = 1) { cout << (f ? "Yes" : "No") << "\n"; }void No() { cout << "No\n"; }void YES(bool f = 1) { cout << (f ? "YES" : "NO") << "\n"; }void NO() { cout << "NO\n"; }void err() {cout << -1 << "\n";exit(0);}vector<long long> vin(long long n) { //整数n個の入力を受け取ってベクトルに突っ込んで返すvector<long long> v(n);for(long long i = 0; i < n; i++) {cin >> v[i];}return v;}//ベクトルの出力(検証済)// vectorの中身を出力する 答えの出力に利用可能template <class T>void vout(vector<T> &v, bool tate = 0) {if(v.size() > 0) {for(auto it = v.begin(); it < v.end(); it++) {cout << *it;if(it != v.end() - 1) {if(tate)cout << endl;elsecout << " ";}}}cout << endl;}template <class T>void add(vector<T> &v, T val) { //ベクトルの各要素に加算for(auto &a : v) a += val;return;}// vectorの中身を数える map<要素,個数>を返すtemplate <class T>map<T, long long> cntv(vector<T> v) {map<T, long long> m;for(auto &g : v) {if(m.count(g))m[g]++;elsem[g] = 1;}return m;}//配列圧縮(検証済)//{1,36,1,3,8,-2,-92}を//{2, 5,2,3,4, 1, 0}にするtemplate <class T>vector<long long> press(vector<T> &v) {long long n = v.size();vector<long long> w(n);map<T, long long> m;for(T &p : v) m[p] = 0;long long i = 0;for(auto &p : m) {p.second = i;i++;}for(long long i = 0; i < n; i++) w.at(i) = m[v.at(i)];return w;}template <class T>T divup(T a, T b) {//端数繰りあがり割り算assert(b != 0);T x = abs(a);T y = abs(b);T z = (x + y - 1) / y;if((a < 0 && b > 0) || (a > 0 && b < 0))return -z;else if(a == 0)return 0;elsereturn z;}long long POW(long long a, long long n) {long long res = 1;while(n > 0) {if(n & 1) res = res * a;a = a * a;n >>= 1;}return res;}template <class T>int sgn(T x) { //符号関数if(x < 0) return -1;if(x == 0) return 0;return 1;}long long modpow(long long a, long long n, long long mod) { // a^n modif(mod == 1) return 0LL;long long res = 1;while(n > 0) {if(n & 1) res = res * a % mod;a = a * a % mod;n >>= 1;}return res;}// a * x % mod == __gcd(a,mod)なるxを返す// a が modの倍数でないことが条件long long modinv(long long a, long long mod) {long long b = mod, u = 1, v = 0;while(b) {long long t = a / b;a -= t * b;swap(a, b);u -= t * v;swap(u, v);}u %= mod;if(u < 0) u += mod;return u;}vvll comb(100, vll(100, -1));long long com(long long n, long long k) { //普通の二項計数(overflowに注意)assert(n < 100 && k < 100);if(n < k || k < 0 || n < 0) return 0;if(comb[n][k] != -1) return comb[n][k];ll res;if(n - k < k)res = com(n, n - k);else if(k == 0)res = 1;elseres = com(n - 1, k - 1) + com(n - 1, k);comb[n][k] = res;return res;}// nCk modを求めるconst ll MAX = 5100000;// この値は求める二項計数の値に応じて変える// MAX=3*10^7のとき1900msほど、ほぼ比例// MAX=5*10^6程度ならそれほど気にしなくてよい(300ms程)long long fac[MAX], finv[MAX], inv[MAX];void cominit() {// テーブルを作る前処理fac[0] = fac[1] = 1;finv[0] = finv[1] = 1;inv[1] = 1;for(ll i = 2; i < MAX; i++) {fac[i] = fac[i - 1] * i % mod;inv[i] = mod - inv[mod % i] * (mod / i) % mod;finv[i] = finv[i - 1] * inv[i] % mod;}}long long commod(ll n, ll k) { // 二項係数計算if(n < k) return 0;if(n < 0 || k < 0) return 0;return fac[n] * (finv[k] * finv[n - k] % mod) % mod;}long long pmod(ll n, ll k) { //順列計算if(n < k) return 0;if(n < 0 || k < 0) return 0;return fac[n] * finv[n - k] % mod;}long long hmod(ll n, ll k) { // nHk計算// n個の区別しないoを区別するk個の箱に入れる方法の総数//(n+k-1)C(k-1)と等しいreturn commod(n + k - 1, n);}#pragma endregionstruct mint {long long x;mint(long long x = 0) : x((x % mod + mod) % mod) {}mint operator-() const { return mint(-x); }mint &operator+=(const mint a) {if((x += a.x) >= mod) x -= mod;return *this;}mint &operator-=(const mint a) {if((x += mod - a.x) >= mod) x -= mod;return *this;}mint &operator*=(const mint a) {(x *= a.x) %= mod;return *this;}mint operator+(const mint a) const { return mint(*this) += a; }mint operator-(const mint a) const { return mint(*this) -= a; }mint operator*(const mint a) const { return mint(*this) *= a; }mint pow(long long t) const {if(!t) return 1;mint a = pow(t >> 1);a *= a;if(t & 1) a *= *this;return a;}// for prime modmint inv() const { return pow(mod - 2); }mint &operator/=(const mint a) { return *this *= a.inv(); }mint operator/(const mint a) const { return mint(*this) /= a; }};ostream &operator<<(ostream &os, const mint &a) { return os << a.x; }template <class T = long long>struct edge {T len;int from;int to;bool operator<(const edge a) const {if(len != a.len) return len < a.len;if(from != a.from) return from < a.from;return to < a.to;}bool operator>(const edge a) const {if(len != a.len) return len > a.len;if(from != a.from) return from > a.from;return to > a.to;}};template <class T = long long>struct graph { // 0-indexedT const INF = numeric_limits<T>::max() / 3;vector<vector<edge<T>>> edges;bool directed, weight;int ver;// constructorgraph() = default;graph(int vertex, bool direction = 0, bool weigh = 0) : edges(vertex) {ver = vertex;directed = direction;weight = weigh;edges.resize(vertex);}//辺の追加 (0-indexed)void update(int from, int to, T len = 1, bool direction = 1) {edge<T> e;e.len = len;e.from = from;e.to = to;edges[from].push_back(e);if(!direction) {swap(e.to, e.from);edges[to].push_back(e);}}//入力受取 (1-indexed)void input(int edge_num, int index = 1) {for(int i = 0; i < edge_num; i++) {int a;int b;cin >> a >> b;a -= index;b -= index;T c;if(weight)cin >> c;elsec = 1;update(a, b, c, directed);}}// 辺の長さを全て1とみたときの単一始点最短経路 (無理なときはINF)vector<T> bfs(int start) {// https://atcoder.jp/contests/abc007/submissions/mevector<T> ret(ver, INF);queue<int> q;q.push(start);ret[start] = 0;while(!q.empty()) {int now = q.front();q.pop();for(auto &e : edges[now]) {if(ret[e.to] != INF) continue;q.push(e.to);ret[e.to] = ret[now] + 1;}}return ret;}//長さが負のpathがないときの単一始点最短経路<vll> O((ver)log(ver)+(edge))vector<T> dijkstra(int start) {vector<T> ret(ver, (T)INF);// pqup<pair<T, int>> p; //{dist,place}priority_queue<pair<T, int>, vector<pair<T, int>>, greater<pair<T, int>>> p; //{dist,place}p.push({0, start});ret[start] = 0;while(!p.empty()) {T dist = p.top().first;int place = p.top().second;p.pop();if(ret[place] < dist) continue;for(auto &next : edges[place]) {int nextplace = next.to;T dis = next.len;if(ret[nextplace] > dist + dis) {ret[nextplace] = dist + dis;p.push({ret[nextplace], nextplace});}}}return ret;}//単一始点最短経路 O((ver)*(edge))//辿り着けないとき ret[i] = INF;//ある頂点までのコストが無限に小さくなり得るとき→ ret[i] = -INF;vector<T> BellmanFord(int start) {// https://onlinejudge.u-aizu.ac.jp/problems/GRL_1_Bvector<T> ret(ver, INF);ret[start] = 0;for(int loop = 0; loop < ver - 1; loop++) {for(int v = 0; v < ver; v++) {if(ret[v] == INF) continue;for(auto &e : edges[v]) {ret[e.to] = min(ret[e.to], ret[v] + e.len);}}}//無限降下点の検索queue<int> q;vector<bool> chk(ver, 0);for(int v = 0; v < ver; v++) {if(ret[v] == INF) continue;for(auto &e : edges[v]) {if(ret[e.to] > ret[v] + e.len) {ret[e.to] = ret[v] + e.len;if(!chk[e.to]) {q.push(e.to);chk[e.to] = 1;}}}}while(!q.empty()) {int now = q.front();q.pop();for(auto &e : edges[now]) {if(!chk[e.to]) {chk[e.to] = 1;q.push(e.to);}}}for(int i = 0; i < ver; i++)if(chk[i]) ret[i] = -INF;return ret;}//閉路に含まれない頂点列挙//要素数がver未満なら閉路が存在、そうでなければ閉路は存在しないvector<int> topo_sort() {// https://onlinejudge.u-aizu.ac.jp/courses/library/5/GRL/all/GRL_4_A// https://onlinejudge.u-aizu.ac.jp/courses/library/5/GRL/all/GRL_4_Bassert(directed);vector<int> num_input(ver);// 入次数for(int i = 0; i < ver; i++) {for(auto e : edges[i]) {num_input[e.to]++;}}// 入次数が0のノードをqueueで管理するqueue<int> que;for(int i = 0; i < ver; i++) {if(num_input[i] == 0) {que.push(i);}}vector<int> ans;while(!que.empty()) {auto node = que.front();que.pop();ans.push_back(node);// 頂点の削除for(auto e : edges[node]) {num_input[e.to]--;// 行き先の入次数が0になったらqueueに追加if(num_input[e.to] == 0) {que.push(e.to);}}}return ans;}//{{端点、端点},直径の大きさ}pair<pair<int, int>, T> DiameterOfTree(bool weigh = true) {// https://onlinejudge.u-aizu.ac.jp/courses/library/5/GRL/all/GRL_5_Avector<T> vec;vec = weigh ? dijkstra(0) : bfs(0);int v1 = -1;T dia = -1;for(int i = 0; i < ver; i++)if((dia < vec[i])) {dia = vec[i];v1 = i;}vec = weigh ? dijkstra(v1) : bfs(v1);dia = -1;int v2 = -1;for(int i = 0; i < ver; i++)if((dia < vec[i])) {v2 = i;dia = vec[i];}pair<pair<int, int>, T> ans = {{v1, v2}, dia};return ans;}//無向木構造を根から葉に伸びる有向木構造に書き換えるgraph<T> RootToLeaf(int root) { // 0-indexedgraph<T> ret(ver, 1, weight);vector<bool> chk(ver, 0);chk[root] = 1;function<void(int)> dfs = [&](int now) {for(auto &e : edges[now]) {if(chk[e.to] == 1) continue;chk[e.to] = 1;ret.update(now, e.to, e.len, 1);dfs(e.to);}};dfs(root);return ret;}//無向木構造を葉から根に伸びる有向木構造に書き換えるgraph<T> LeafToRoot(int root) { // 0-indexedgraph<T> ret(ver, 1, weight);vector<bool> chk(ver, 0);chk[root] = 1;function<void(int)> dfs = [&](int now) {for(auto &e : edges[now]) {if(chk[e.to] == 1) continue;chk[e.to] = 1;ret.update(e.to, now, e.len, 1);dfs(e.to);}};dfs(root);ret.update(root, root, 0);return ret;}// LeafToRootのvector版.par[i]=iの親の頂点vector<int> par(int root) { // 0-indexedvector<int> ret(ver, -1);ret[root] = root; // rootの親はrootfunction<void(int)> dfs = [&](int now) {for(auto &e : edges[now]) {if(ret[e.to] != -1) continue;ret[e.to] = now;dfs(e.to);}};dfs(root);return ret;}vector<edge<T>> ParentAndDistance(int root) { // 0-indexedvector<edge<T>> ret(ver);for(int i = 0; i < ver; i++) ret[i].to = -1;ret[root].to = root; // rootの親はrootret[root].len = 0; // rootの親との距離は0function<void(int)> dfs = [&](int now) {for(auto &e : edges[now]) {if(ret[e.to].to != -1) continue;ret[e.to].to = now;ret[e.to].len = e.len;dfs(e.to);}};dfs(root);return ret;}//隣接sheet.主にwarshall用vector<vector<T>> GraphArray(void) {vector<vector<T>> ret(ver, vector<T>(ver, INF));for(int from = 0; from < ver; from++) {for(auto &e : edges[from]) {ret[from][e.to] = e.len;}ret[from][from] = 0;}return ret;}graph<T> Prim(int start = 0) {// https://onlinejudge.u-aizu.ac.jp/courses/library/5/GRL/all/GRL_2_Agraph<T> ret(ver, 0, 1);priority_queue<edge<T>, vector<edge<T>>, greater<edge<T>>> p;for(auto &e : edges[start]) {p.push(e);}vector<bool> chk(ver, 0);chk[start] = 1;while(!p.empty()) {auto ed = p.top();p.pop();if(chk[ed.to]) continue;chk[ed.to] = 1;ret.update(ed.from, ed.to, ed.len);for(auto &e : edges[ed.to]) {p.push(e);}}return ret;}//各頂点を根としたときの木の高さvector<T> height(int start = 0) {// https://onlinejudge.u-aizu.ac.jp/courses/library/5/GRL/all/GRL_5_Bvector<T> fir(ver, -1), sec(ver, -1);function<T(int, int)> dfs = [&](int now, int par) {T f = 0, s = 0; // startを根としたときのnowからの深さ1番目、2番目for(auto &e : edges[now]) {if(e.to == par) continue;s = max(s, dfs(e.to, now) + e.len);if(f < s) swap(f, s);}sec[now] = s;return fir[now] = f;};dfs(start, -1);function<void(int, int, T, T, T)> sol = [&](int now, int par, T parf, T pars, T parlen) {if(fir[now] + parlen == parf) parf = pars;sec[now] = max(sec[now], parf + parlen);if(fir[now] < sec[now]) swap(fir[now], sec[now]);for(auto &e : edges[now]) {if(e.to == par) continue;sol(e.to, now, fir[now], sec[now], e.len);}return;};sol(start, -1, -1, -1, -1);return fir;}//全方位木DP//マージ関数、上に送るための関数、単位元、はじめの根// 関数はstd::functionで渡すtemplate <class U>vector<U> zenhoui(function<U(U, U)> f, function<U(U)> g, U unit, int root = 0) {auto tr = RootToLeaf(root);vector<vector<U>> v(ver);vector<U> ret(ver); //求める答function<U(int)> dfs = [&](int now) {U res = unit;vector<U> vec;for(auto &e : tr.edges[now]) {U k = dfs(e.to);vec.push_back(k);res = f(res, k);}v[now] = vec;return g(res);};dfs(root);function<void(int, U)> dfs2 = [&](int now, U ans_par) {int sz = v[now].size();vector<U> mae(sz + 1), rev(sz + 1);mae[0] = rev[sz] = unit;for(int i = 0; i < sz; i++) mae[i + 1] = f(mae[i], v[now][i]);for(int i = sz - 1; i >= 0; i--) rev[i] = f(rev[i + 1], v[now][i]);for(int i = 0; i < sz; i++) {auto nxtans = f(ans_par, f(mae[i], rev[i + 1]));dfs2(tr.edges[now][i].to, g(nxtans));}ret[now] = f(ans_par, mae[sz]);return;};dfs2(root, unit);return ret;}// HL分解};struct UF { // Union_Find木 (平衡操作あり)vector<int> data; // data[root] = -size, data[not_root] = parentUF(int N) : data(N) {for(int i = 0; i < N; i++) {data[i] = -1;}}int root(int x) {if(data[x] < 0) return x;return data[x] = root(data[x]);}// 2つのデータx, yが属する木が同じならtrueを返すbool same(int x, int y) { return root(x) == root(y); }bool unite(int x, int y) { // xとyの木を併合x = root(x);y = root(y);if(x == y) return false;if(data[x] > data[y]) swap(x, y); // 平衡操作 sizeは-1倍なのでこれで正しいdata[x] += data[y];data[y] = x;return true;}int size(int x) { return -data[root(x)]; }};int main() {ios::sync_with_stdio(false);cin.tie(nullptr);// cout << fixed << setprecision(15);INT(n, m);ll base;cin >> base;graph<ll> gra(n);// mint ans = 0;// rep(i,m){// }UF uf(n);mint ans = 0;rep(i, m) {INT(x, y, z);x--, y--;if(!uf.same(x, y)) {gra.update(x, y, z, 0);uf.unite(x, y);}}auto tr = gra.RootToLeaf(0);function<int(int)> dfs = [&](int now) {int sum = 1;foa(e, tr.edges[now]) {int k = dfs(e.to);// mint res = k * (n - k);mint res = modpow(base, e.len, mod);res *= k;res *= n - k;ans += res;sum += k;}return sum;};dfs(0);cout << ans << endl;}