結果

問題 No.1333 Squared Sum
ユーザー 👑 tute7627tute7627
提出日時 2021-01-08 22:08:53
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,289 ms / 2,000 ms
コード長 12,224 bytes
コンパイル時間 3,151 ms
コンパイル使用メモリ 223,196 KB
最終ジャッジ日時 2025-01-17 12:17:26
ジャッジサーバーID
（参考情報） 		judge3 / judge4
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ファイルパターン 結果
other AC * 44
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ソースコード

diff # 

//#define _GLIBCXX_DEBUG

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

#define endl '\n'
#define lfs cout<<fixed<<setprecision(10)
#define ALL(a)  (a).begin(),(a).end()
#define ALLR(a)  (a).rbegin(),(a).rend()
#define spa << " " <<
#define fi first
#define se second
#define MP make_pair
#define MT make_tuple
#define PB push_back
#define EB emplace_back
#define rep(i,n,m) for(ll i = (n); i < (ll)(m); i++)
#define rrep(i,n,m) for(ll i = (ll)(m) - 1; i >= (ll)(n); i--)
using ll = long long;
using ld = long double;
const ll MOD1 = 1e9+7;
const ll MOD9 = 998244353;
const ll INF = 1e18;
using P = pair<ll, ll>;
template<typename T1, typename T2>bool chmin(T1 &a,T2 b){if(a>b){a=b;return true;}else return false;}
template<typename T1, typename T2>bool chmax(T1 &a,T2 b){if(a<b){a=b;return true;}else return false;}
ll median(ll a,ll b, ll c){return a+b+c-max({a,b,c})-min({a,b,c});}
void ans1(bool x){if(x) cout<<"Yes"<<endl;else cout<<"No"<<endl;}
void ans2(bool x){if(x) cout<<"YES"<<endl;else cout<<"NO"<<endl;}
void ans3(bool x){if(x) cout<<"Yay!"<<endl;else cout<<":("<<endl;}
template<typename T1,typename T2>void ans(bool x,T1 y,T2 z){if(x)cout<<y<<endl;else cout<<z<<endl;}  
template<typename T>void debug(vector<vector<T>>&v,ll h,ll w){for(ll i=0;i<h;i++){cout<<v[i][0];for(ll j=1;j<w;j++)cout spa v[i][j];cout<<endl;}};
void debug(vector<string>&v,ll h,ll w){for(ll i=0;i<h;i++){for(ll j=0;j<w;j++)cout<<v[i][j];cout<<endl;}};
template<typename T>void debug(vector<T>&v,ll n){if(n!=0)cout<<v[0];for(ll i=1;i<n;i++)cout spa v[i];cout<<endl;};
template<typename T>vector<vector<T>>vec(ll x, ll y, T w){vector<vector<T>>v(x,vector<T>(y,w));return v;}
ll gcd(ll x,ll y){ll r;while(y!=0&&(r=x%y)!=0){x=y;y=r;}return y==0?x:y;}
vector<ll>dx={1,-1,0,0,1,1,-1,-1};vector<ll>dy={0,0,1,-1,1,-1,1,-1};
template<typename T>vector<T> make_v(size_t a,T b){return vector<T>(a,b);}
template<typename... Ts>auto make_v(size_t a,Ts... ts){return vector<decltype(make_v(ts...))>(a,make_v(ts...));}
template<typename T1, typename T2>ostream &operator<<(ostream &os, const pair<T1, T2>&p){return os << p.first << " " << p.second;}
template<typename T>ostream &operator<<(ostream &os, const vector<T> &v){for(auto &z:v)os << z << " ";cout<<"|"; return os;}
//mt19937 mt(chrono::steady_clock::now().time_since_epoch().count());
int popcount(ll x){return __builtin_popcountll(x);};
int poplow(ll x){return __builtin_ctzll(x);};
int pophigh(ll x){return 63 - __builtin_clzll(x);};
template< typename Monoid, typename OperatorMonoid,typename F, typename G, typename H>
struct LazySegmentTree {
  ll sz, height, n;
  vector< Monoid > data;
  vector< OperatorMonoid > lazy;
  const F f;
  const G g;
  const H h;
  Monoid M1;
  OperatorMonoid OM0;
  LazySegmentTree(ll n, const F &f,const G &g, const H &h, Monoid M1, OperatorMonoid OM0):n(n),f(f),g(g),h(h),M1(M1),OM0(OM0){
    sz = 1;
    height = 0;
    while(sz < n) sz <<= 1, height++;
    data.assign(2 * sz, M1);
    lazy.assign(2 * sz, OM0);
  }

  void set(ll k, const Monoid &x) {
    data[k + sz] = x;
  }

  void build() {
    for(ll k = sz - 1; k > 0; k--) {
      data[k] = f(data[2 * k + 0], data[2 * k + 1]);
    }
  }

  inline void propagate(ll k) {
    if(lazy[k] != OM0) {
      lazy[2 * k + 0] = h(lazy[2 * k + 0], lazy[k]);
      lazy[2 * k + 1] = h(lazy[2 * k + 1], lazy[k]);
      data[k] = reflect(k);
      lazy[k] = OM0;
    }
  }

  inline Monoid reflect(ll k) {
    return lazy[k] == OM0 ? data[k] : g(data[k], lazy[k]);
  }

  inline void recalc(ll k) {
    while(k >>= 1) data[k] = f(reflect(2 * k + 0), reflect(2 * k + 1));
  }

  inline void thrust(ll k) {
    for(ll i = height; i > 0; i--) propagate(k >> i);
  }

  void update(ll a, ll b, const OperatorMonoid &x) {
	if(a>=b)return;
    thrust(a += sz);
    thrust(b += sz - 1);
    for(ll l = a, r = b + 1; l < r; l >>= 1, r >>= 1) {
      if(l & 1) lazy[l] = h(lazy[l], x), ++l;
      if(r & 1) --r, lazy[r] = h(lazy[r], x);
    }
    recalc(a);
    recalc(b);
  }

  Monoid query(ll a, ll b) {
    thrust(a += sz);
    thrust(b += sz - 1);
    Monoid L = M1, R = M1;
    for(ll l = a, r = b + 1; l < r; l >>= 1, r >>= 1) {
      if(l & 1) L = f(L, reflect(l++));
      if(r & 1) R = f(reflect(--r), R);
    }
    return f(L, R);
  }

  Monoid operator[](const ll &k) {
    return query(k, k + 1);
  }

  template< typename C >
  ll find_subtree(ll a, const C &check, Monoid &M, bool type) {
    while(a < sz) {
      propagate(a);
      Monoid nxt = type ? f(reflect(2 * a + type), M) : f(M, reflect(2 * a + type));
      if(check(nxt)) a = 2 * a + type;
      else M = nxt, a = 2 * a + 1 - type;
    }
    return a - sz;
  }

  template< typename C >
  ll find_first(ll a, const C &check) {
    Monoid L = M1;
    if(a <= 0) {
      if(check(f(L, reflect(1)))) return find_subtree(1, check, L, false);
      return -1;
    }
    thrust(a + sz);
    ll b = sz;
    for(a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
      if(a & 1) {
        Monoid nxt = f(L, reflect(a));
        if(check(nxt)) return find_subtree(a, check, L, false);
        L = nxt;
        ++a;
      }
    }
    return -1;
  }


  template< typename C >
  ll find_last(ll b, const C &check) {
    Monoid R = M1;
    if(b >= sz) {
      if(check(f(reflect(1), R))) return find_subtree(1, check, R, true);
      return -1;
    }
    thrust(b + sz - 1);
    ll a = sz;
    for(b += sz; a < b; a >>= 1, b >>= 1) {
      if(b & 1) {
        Monoid nxt = f(reflect(--b), R);
        if(check(nxt)) return find_subtree(b, check, R, true);
        R = nxt;
      }
    }
    return -1;
  }
  void print(){
    for(ll i=0;i<n;i++)if((*this)[i]==M1)cout<<"x|";else cout<<(*this)[i]<<"|";
    cout<<endl;
  }
};
struct edge{
  ll to=-1,cost=0;
  edge(){};
  edge(ll t,ll c):to(t),cost(c){};
};
struct HLD{
  ll n, root;
  ll cnt = 0;
  vector<ll>sz;//部分木サイズ
  vector<ll>par,head;
  vector<vector<struct edge>>g;//隣接リスト
  vector<struct edge>edges;//データ構造に乗せるedge列
  vector<ll>in,out;//[in,out)で部分木、[ina,inb]でa~bのパス(aが上)
  //inは頂点のindexを表す。また、edge列の下側の頂点である
  HLD(vector<vector<struct edge>>&G,ll r = -1)
      :g(G),n(G.size()),root(r){
    par.assign(n,-1),in.assign(n,-1);
    out.assign(n,-1),head.assign(n,-1),sz.assign(n,-1);
    edges.assign(n,edge());
    dfs_build();
  }
  void dfs_build(){
    if(root == -1){//根がどこでも良い場合(森でも可)
      for(ll i=0;i<n;i++){
        if(sz[i] == -1){
          head[i] = i;
          dfs_sz(i);
          dfs_hld(i);
        }
      }
    }
    else{
      head[root] = root;
      dfs_sz(root);
      dfs_hld(root);
    }
  }
  void dfs_sz(ll k){
    sz[k] = 1;
    for(auto &e: g[k]){
      if(e.to == par[k])continue;
      par[e.to] = k;
      dfs_sz(e.to);
      sz[k] += sz[e.to];
      if(sz[e.to] > sz[g[k][0].to])swap(e, g[k][0]);
    }
  }
  void dfs_hld(ll k){
    in[k] = cnt++;
    for(auto e:g[k]){
      if(e.to == par[k])continue;
      head[e.to] = (e.to == g[k][0].to ? head[k]: e.to);
      edges[cnt] = e;
      dfs_hld(e.to);
    }
    out[k] = cnt;
  }
  ll lca(ll p,ll q){
    while(1){
      if(in[p] < in[q])swap(p,q);
      if(head[p] == head[q])return q;
      p = par[head[p]];
    }
  }
  vector<pair<ll,ll>>query_path(ll p,ll q,bool isEdge){
    ll r=lca(p,q);
    vector<pair<ll,ll>>ret;
    for(ll i=0;i<2;i++){
      if(i == 1)swap(p,q);
      while(1){
        if(isEdge&&p==r)break;
        if(head[p]==head[r]){
          ret.emplace_back(in[r]+(isEdge?1:i),in[p]+1);
          break;
        }
        ret.emplace_back(in[head[p]],in[p]+1);
        p = par[head[p]];
      }
    }
    return ret;
  }
  vector<vector<pair<ll,ll>>>query_order_path(ll p,ll q,bool isEdge){
	//非可換クエリ用、配列0を順番を反転したデータ構造に、配列1を通常のデータ構造に
    vector<vector<pair<ll,ll>>>ret(2);
    ll r=lca(p,q);
    for(ll i=0;i<2;i++){
      if(i == 1)swap(p,q);
      while(1){
        if(isEdge&&p==r)break;
        if(head[p]==head[r]){
          if(i==0) ret[i].emplace_back(n-(in[p]+1),n-(in[r]+(isEdge?1:i)));
          else ret[i].emplace_back(in[r]+(isEdge?1:i),in[p]+1);
          break;
        }
        if(i==0) ret[i].emplace_back(n-(in[p]+1),n-(in[head[p]]));
        else ret[i].emplace_back(in[head[p]],in[p]+1);
        p = par[head[p]];
      }
    }
    reverse(ret[1].begin(), ret[1].end());
    return ret;
  }
  pair<ll,ll>query_subtree(ll p,bool isEdge){
    return make_pair(in[p]+isEdge,out[p]);
  }
  //uのv方向の子 子孫関係は前もって確認すること
  ll child(ll u,ll v){
    while(1){
      if(head[u]==head[v]){
        v=g[u][0].to;
        break;
      }
      v=head[v];
      if(par[v]==u)break;
      v=par[v];
    }
    return v;
  }
};
template< int mod >
struct ModInt {
  int x;

  ModInt() : x(0) {}

  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

  ModInt &operator+=(const ModInt &p) {
    if((x += p.x) >= mod) x -= mod;
    return *this;
  }

  ModInt &operator-=(const ModInt &p) {
    if((x += mod - p.x) >= mod) x -= mod;
    return *this;
  }

  ModInt &operator*=(const ModInt &p) {
    x = (int) (1LL * x * p.x % mod);
    return *this;
  }

  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }

  ModInt operator-() const { return ModInt(-x); }

  friend ModInt operator+(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) += rhs;
  }
  friend ModInt operator-(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) -= rhs;
  }
  friend ModInt operator*(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) *= rhs;
  }
  friend ModInt operator/(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) /= rhs;
  }

  bool operator==(const ModInt &p) const { return x == p.x; }

  bool operator!=(const ModInt &p) const { return x != p.x; }

  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while(b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }

  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while(n > 0) {
      if(n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  friend ostream &operator<<(ostream &os, const ModInt &p) {
    return os << p.x;
  }

  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt< mod >(t);
    return (is);
  }

  static int get_mod() { return mod; }
};
using modint = ModInt< MOD1 >;modint pow(ll n, ll x){return modint(n).pow(x);}modint pow(modint n, ll x){return n.pow(x);}
//using modint=ld;
int main(){
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  ll res=0,buf=0;
  bool judge = true;
  using A=array<modint,3>;
  auto f=[&](A x,A y){
    return A({x[0]+y[0],x[1]+y[1],x[2]+y[2]});
  };
  auto gg=[&](A x,modint y){
    return A({x[0]+2*x[1]*y+y*y*x[2],x[1]+x[2]*y,x[2]});
  };
  auto h=[&](modint x,modint y){
    return x+y;
  };
  ll n;cin>>n;
  LazySegmentTree seg(n,f,gg,h,A({0,0,0}),modint(0));
  vector<vector<edge>>g(n);
  rep(i,0,n-1){
    ll a,b,c;cin>>a>>b>>c;a--;b--;
    g[a].EB(b,c);
    g[b].EB(a,c);
  }
  HLD hld(g,0);
  modint ret=0;
  {
    auto dfs=[&](auto &&f,ll k,ll par,ll d)->void{
      seg.set(hld.in[k],A({modint(d)*d,d,1}));
      for(auto e:g[k]){
        if(par==e.to)continue;
        f(f,e.to,k,d+e.cost);
      }
    };
    dfs(dfs,0,0,0);
  }
  seg.build();
  //rep(i,0,n)cout<<seg[i][0] spa seg[i][1] spa seg[i][2]<<endl;
  {
    auto sub=[&](ll k){
      auto tmp=hld.query_subtree(k,false);
      return seg.query(tmp.fi,tmp.se)[0];
    };
    auto subadd=[&](ll k,modint x){
      auto tmp=hld.query_subtree(k,false);
      seg.update(tmp.fi,tmp.se,x);
    };
    auto dfs=[&](auto &&f,ll k,ll par)->void{
      ret+=sub(0);
      for(auto e:g[k]){
        if(e.to==par)continue;
        subadd(0,e.cost);
        subadd(e.to,-2*e.cost);
        f(f,e.to,k);
        subadd(0,-e.cost);
        subadd(e.to,2*e.cost);
      }
    };
    dfs(dfs,0,-1);
  }
  //rep(i,0,n)cout<<seg[i][0] spa seg[i][1] spa seg[i][2]<<endl;
  cout<<ret/2<<endl;
  return 0;
}
0