結果

問題 No.1784 Not a star yet...
ユーザー PCTprobabilityPCTprobability
提出日時 2021-11-28 09:21:11
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 79 ms / 2,000 ms
コード長 9,567 bytes
コンパイル時間 6,216 ms
コンパイル使用メモリ 306,732 KB
実行使用メモリ 12,040 KB
最終ジャッジ日時 2024-07-21 12:19:00
合計ジャッジ時間 9,283 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge3
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
5,248 KB
testcase_01 AC 1 ms
5,376 KB
testcase_02 AC 2 ms
5,376 KB
testcase_03 AC 2 ms
5,376 KB
testcase_04 AC 2 ms
5,376 KB
testcase_05 AC 2 ms
5,376 KB
testcase_06 AC 2 ms
5,376 KB
testcase_07 AC 2 ms
5,376 KB
testcase_08 AC 2 ms
5,376 KB
testcase_09 AC 2 ms
5,376 KB
testcase_10 AC 2 ms
5,376 KB
testcase_11 AC 2 ms
5,376 KB
testcase_12 AC 2 ms
5,376 KB
testcase_13 AC 2 ms
5,376 KB
testcase_14 AC 3 ms
5,376 KB
testcase_15 AC 5 ms
5,376 KB
testcase_16 AC 40 ms
7,424 KB
testcase_17 AC 10 ms
5,376 KB
testcase_18 AC 66 ms
10,652 KB
testcase_19 AC 26 ms
6,136 KB
testcase_20 AC 10 ms
5,376 KB
testcase_21 AC 2 ms
5,376 KB
testcase_22 AC 4 ms
5,376 KB
testcase_23 AC 3 ms
5,376 KB
testcase_24 AC 55 ms
9,472 KB
testcase_25 AC 69 ms
11,272 KB
testcase_26 AC 16 ms
5,376 KB
testcase_27 AC 43 ms
7,808 KB
testcase_28 AC 6 ms
5,376 KB
testcase_29 AC 4 ms
5,376 KB
testcase_30 AC 60 ms
10,120 KB
testcase_31 AC 55 ms
9,180 KB
testcase_32 AC 19 ms
5,376 KB
testcase_33 AC 29 ms
5,376 KB
testcase_34 AC 32 ms
5,376 KB
testcase_35 AC 22 ms
5,376 KB
testcase_36 AC 31 ms
5,376 KB
testcase_37 AC 32 ms
5,376 KB
testcase_38 AC 30 ms
5,376 KB
testcase_39 AC 20 ms
5,376 KB
testcase_40 AC 27 ms
5,376 KB
testcase_41 AC 19 ms
5,376 KB
testcase_42 AC 22 ms
5,376 KB
testcase_43 AC 73 ms
11,912 KB
testcase_44 AC 74 ms
12,032 KB
testcase_45 AC 75 ms
11,912 KB
testcase_46 AC 75 ms
12,032 KB
testcase_47 AC 74 ms
11,908 KB
testcase_48 AC 73 ms
12,032 KB
testcase_49 AC 74 ms
12,040 KB
testcase_50 AC 72 ms
11,912 KB
testcase_51 AC 74 ms
12,032 KB
testcase_52 AC 75 ms
12,032 KB
testcase_53 AC 75 ms
11,912 KB
testcase_54 AC 74 ms
11,912 KB
testcase_55 AC 74 ms
12,032 KB
testcase_56 AC 73 ms
12,040 KB
testcase_57 AC 79 ms
11,908 KB
testcase_58 AC 73 ms
12,032 KB
testcase_59 AC 75 ms
12,036 KB
testcase_60 AC 74 ms
12,040 KB
testcase_61 AC 74 ms
12,032 KB
testcase_62 AC 76 ms
11,912 KB
testcase_63 AC 1 ms
5,376 KB
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 # 

#include <bits/stdc++.h>
using namespace std;
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#endif
using ll = long long;
using ld = long double;
using ull = unsigned long long;
#define endl "\n"
typedef pair<int, int> Pii;
#define REP(i, n) for (int i = 0; i < (n); ++i)
#define REP3(i, m, n) for (int i = (m); (i) < int(n); ++ (i))
#define FOR(i,a,b) for(ll i=a;i<=(ll)(b);i++)
#define rep(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define ALL(x) begin(x), end(x)
#define PB push_back
#define rrep(i,a,b) for(int i=a;i>=b;i--)
#define fore(i,a) for(auto &i:a)
#define all(s) (s).begin(),(s).end()
#define drep2(i, m, n) for (int i = (m)-1; i >= (n); --i)
#define drep(i, n) drep2(i, n, 0)
#define rever(vec) reverse(vec.begin(), vec.end())
#define sor(vec) sort(vec.begin(), vec.end())
#define fi first
#define se second
#define pb push_back
#define P pair<ll,ll>
#define PQminll priority_queue<ll, vector<ll>, greater<ll>>
#define PQmaxll priority_queue<ll,vector<ll>,less<ll>>
#define PQminP priority_queue<P, vector<P>, greater<P>>
#define PQmaxP priority_queue<P,vector<P>,less<P>>
#define NP next_permutation
typedef string::const_iterator State;
class ParseError {};
//const ll mod = 1000000009;
const ll mod = 998244353;
//const ll mod = 1000000007;
const ll inf = 4100000000000000000ll;
const ld eps = ld(0.00000000000001);
//static const long double pi = 3.141592653589793;
template<class T>void vcin(vector<T> &n){for(int i=0;i<int(n.size());i++) cin>>n[i];}
template<class T,class K>void vcin(vector<T> &n,vector<K> &m){for(int i=0;i<int(n.size());i++) cin>>n[i]>>m[i];}
template<class T>void vcout(vector<T> &n){for(int i=0;i<int(n.size());i++){cout<<n[i]<<" ";}cout<<endl;}
template<class T>void vcin(vector<vector<T>> &n){for(int i=0;i<int(n.size());i++){for(int j=0;j<int(n[i].size());j++){cin>>n[i][j];}}}
template<class T>void vcout(vector<vector<T>> &n){for(int i=0;i<int(n.size());i++){for(int j=0;j<int(n[i].size());j++){cout<<n[i][j]<<" ";}cout<<endl;}cout<<endl;}
void yes(bool a){cout<<(a?"yes":"no")<<endl;}
void YES(bool a){cout<<(a?"YES":"NO")<<endl;}
void Yes(bool a){cout<<(a?"Yes":"No")<<endl;}
void possible(bool a){ cout<<(a?"possible":"impossible")<<endl; }
void Possible(bool a){ cout<<(a?"Possible":"Impossible")<<endl; }
void POSSIBLE(bool a){ cout<<(a?"POSSIBLE":"IMPOSSIBLE")<<endl; }
template<class T>void print(T a){cout<<a<<endl;}
template<class T>auto min(const T& a){ return *min_element(all(a)); }
template<class T>auto max(const T& a){ return *max_element(all(a)); }
template<class T,class F>void print(pair<T,F> a){cout<<a.fi<<" "<<a.se<<endl;}
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 (b<a) { a=b; return 1; } return 0;}
template<class T> void ifmin(T t,T u){if(t>u){cout<<-1<<endl;}else{cout<<t<<endl;}}
template<class T> void ifmax(T t,T u){if(t>u){cout<<-1<<endl;}else{cout<<t<<endl;}}
ll fastgcd(ll u,ll v){ll shl=0;while(u&&v&&u!=v){bool eu=!(u&1);bool ev=!(v&1);if(eu&&ev){++shl;u>>=1;v>>=1;}else if(eu&&!ev){u>>=1;}else if(!eu&&ev){v>>=1;}else if(u>=v){u=(u-v)>>1;}else{ll tmp=u;u=(v-u)>>1;v=tmp;}}return !u?v<<shl:u<<shl;}
ll modPow(ll a, ll n, ll mod) { if(mod==1) return 0;ll ret = 1; ll p = a % mod; while (n) { if (n & 1) ret = ret * p % mod; p = p * p % mod; n >>= 1; } return ret; }
vector<ll> divisor(ll x){ vector<ll> ans; for(ll i = 1; i * i <= x; i++){ if(x % i == 0) {ans.push_back(i); if(i*i!=x){ ans.push_back(x / ans[i]);}}}sor(ans); return ans; }
ll pop(ll x){return __builtin_popcountll(x);}
ll poplong(ll x){ll y=-1;while(x){x/=2;y++;}return y;}
P hyou(P a){ll x=fastgcd(abs(a.fi),abs(a.se));a.fi/=x;a.se/=x;if(a.se<0){a.fi*=-1;a.se*=-1;}return a;}
P Pplus(P a,P b){ return hyou({a.fi*b.se+b.fi*a.se,a.se*b.se});}
P Ptimes(P a,ll b){ return hyou({a.fi*b,a.se});}
P Ptimes(P a,P b){ return hyou({a.fi*b.fi,a.se*b.se});}
P Pminus(P a,P b){ return hyou({a.fi*b.se-b.fi*a.se,a.se*b.se});}
P Pgyaku(P a){ return hyou({a.se,a.fi});}

void cincout(){
  ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
  cout<< fixed << setprecision(10);
}
using mint = modint998244353;
ll U,V;
void Set(ll u,ll v){
  U=u;
  V=v;
}
ll ind(ll i,ll j){
  return i*(V+1)+j;
}
template<class T>
int solve_linear_equations(vector<vector<T>> a,vector<T> b,vector<T> &res){
  ll n=a.size(),m=a[0].size();
  ll x=0;
  for(int i=0;i<min(n,m);i++){
    ll ind=-1;
    for(int j=x;j<n;j++){
      if(a[j][i].val()) ind=j;
    }
    if(ind==-1) continue;
    swap(a[x],a[ind]);
    swap(b[x],b[ind]);
    for(int j=0;j<n;j++){
      if(x==j) continue;
      if(a[j][i].val()){
        mint y=a[j][i]/a[x][i];
        for(int k=0;k<m;k++) a[j][k]-=a[x][k]*y;
        b[j]-=b[x]*y;
      }
    }
    mint z=a[x][i];
    for(int j=0;j<m;j++) a[x][j]/=z;
    b[x]/=z;
    x++;
  }
  for(int i=x;i<n;i++) if(b[i].val()) return -1;
  vector<ll> r;
  for(int i=0;i<n;i++){
    ll ind=-1;
    for(int j=0;j<m;j++){
      if(a[i][j].val()){
        ind=j;
        break;
      }
    }
    if(ind!=-1) r.pb(ind);
  }
  res.resize(m);
  for(int i=m-1;i>=0;i--){
    ll ind=-1;
    for(int j=0;j<r.size();j++){
      if(r[j]==i){
        ind=j;
        break;
      }
    }
    if(ind==-1) continue;
    mint now=b[ind];
    for(int j=i+1;j<m;j++) now-=a[ind][j]*res[j];
    res[i]=now;
  }
  return x;
}
vector<mint> vplus(vector<mint> a,vector<mint> b,mint x){
  for(int i=0;i<a.size();i++) a[i]+=b[i]*x;
  return a;
}
int main() {
  cincout();
  ll n;
  cin>>n;
  assert(2<=n&&n<=250);
  vector<ll> a(n-1),b(n-1),l(n-1);
  map<ll,ll> m;
  ll Sum=0;
  map<P,bool> seen;
  for(int i=0;i<n-1;i++){
    cin>>a[i]>>b[i]>>l[i];
    a[i]--;
    b[i]--;
    assert(a[i]!=b[i]);
    if(seen[{a[i],b[i]}]) assert(false);
    seen[{a[i],b[i]}]=true;
    seen[{b[i],a[i]}]=true;
    assert(0<=min(a[i],b[i])&&max(a[i],b[i])<=n-1);
    assert(1<=l[i]&&l[i]<=2);
    m[l[i]]++;
    Sum+=l[i];
  }
  assert(Sum%mod!=0);
  ll x=-1,y=-1;
  for(auto e:m){
    if(x==-1) x=e.fi;
    else y=e.fi;
  }
  if(y==-1){
    vector<ll> s(n),t(n);
    ll u=0,v=0;
    for(int i=0;i<n-1;i++){
      if(l[i]==x){
        u++;
        s[a[i]]++;
        s[b[i]]++;
      }
      else{
        v++;
        t[a[i]]++;
        t[b[i]]++;
      }
    }
    if(u>v){
      swap(u,v);
      swap(s,t);
      swap(x,y);
    }
    Set(u,v);
    mint k=u*x+v*y;
    mint p=n*(n-1)/2-(n-2);
    vector<vector<mint>> g((u+1)*(v+1)-1,vector<mint>((u+1)*(v+1)));
    vector<mint> f((u+1)*(v+1)-1);
    for(int i=0;i<=u;i++){
      for(int j=0;j<=v;j++){
        if(i==u&&j==v) continue;
        f[ind(i,j)]=mint(-1)/mint(n);
        f[ind(i,j)]*=k*p;
        mint q=n-i-j;
        g[ind(i,j)][ind(i,j)]-=1;
        g[ind(i,j)][ind(i,j)]*=k*p;
        g[ind(i,j)][ind(i,j)]+=q*x*i;
        if(i) g[ind(i,j)][ind(i-1,j)]+=(p-q)*x*i;
        g[ind(i,j)][ind(i,j)]+=q*y*j;
        if(j) g[ind(i,j)][ind(i,j-1)]+=(p-q)*y*j;
        if(i!=u) g[ind(i,j)][ind(i+1,j)]+=(q-1)*x*(u-i);
        g[ind(i,j)][ind(i,j)]+=(p-q+1)*x*(u-i);
        if(j!=v) g[ind(i,j)][ind(i,j+1)]+=(q-1)*y*(v-j);
        g[ind(i,j)][ind(i,j)]+=(p-q+1)*y*(v-j);
      }
    }
    vector<mint> res;
    int check=solve_linear_equations(g,f,res);
    assert(check!=-1);
    mint ans=0;
    for(int i=0;i<n;i++){
      ans+=res[ind(s[i],t[i])];
    }
    ans-=res[ind(u,v)];
    ans-=res[ind(0,1)]*v;
    ans-=res[ind(1,0)]*u;
    cout<<ans.val()<<endl;
    return 0;
  }
  vector<ll> s(n),t(n);
  ll u=0,v=0;
  for(int i=0;i<n-1;i++){
    if(l[i]==x){
      u++;
      s[a[i]]++;
      s[b[i]]++;
    }
    else{
      v++;
      t[a[i]]++;
      t[b[i]]++;
    }
  }
  if(u>v){
    swap(u,v);
    swap(s,t);
    swap(x,y);
  }
  Set(u,v);
  mint k=u*x+v*y;
  mint p=n*(n-1)/2-(n-2);
  vector<vector<mint>> g((u+1)*(v+1),vector<mint>(v+2));
  for(int j=0;j<=v;j++){
    g[ind(0,j)][j]=1;
  }
  for(int i=0;i<=u-1;i++){
    for(int j=0;j<=v;j++){
      mint q=n-i-j;
      mint R=-(q-1)*x*(u-i);
      g[ind(i+1,j)]=vplus(g[ind(i+1,j)],g[ind(i,j)],((p-q+1)*x*(u-i)+(p-q+1)*y*(v-j)+q*y*j+q*x*i-k*p)/R);
      if(i) g[ind(i+1,j)]=vplus(g[ind(i+1,j)],g[ind(i-1,j)],(p-q)*x*i/R);
      if(j) g[ind(i+1,j)]=vplus(g[ind(i+1,j)],g[ind(i,j-1)],(p-q)*y*j/R);
      if(j!=v) g[ind(i+1,j)]=vplus(g[ind(i+1,j)],g[ind(i,j+1)],(q-1)*y*(v-j)/R);
      g[ind(i+1,j)][v+1]+=mint(k*p)/mint(n*R);
    }
  }
  vector<vector<mint>> equ(v);
  vector<mint> f(v);
  for(int j=0;j<=v-1;j++){
    vector<mint> z(v+2);
    mint q=n-u-j;
    int i=u;
    z=vplus(z,g[ind(u,j)],((p-q+1)*x*(u-i)+(p-q+1)*y*(v-j)+q*y*j+q*x*i-k*p));
    z=vplus(z,g[ind(u-1,j)],(p-q)*x*i);
    if(j) z=vplus(z,g[ind(u,j-1)],(p-q)*y*j);
    z=vplus(z,g[ind(u,j+1)],(q-1)*y*(v-j));
    f[j]=-z[v+1];
    f[j]-=k*p/n;
    equ[j].resize(v+1);
    for(int k=0;k<=v;k++) equ[j][k]=z[k];
  }
  vector<mint> res(v+1);
  int check=solve_linear_equations(equ,f,res);
  assert(check!=-1);
  vector<mint> d((u+1)*(v+1));
  for(int i=0;i<=v;i++) d[ind(0,i)]=res[i];
  for(int i=0;i<=u-1;i++){
    for(int j=0;j<=v;j++){
      mint q=n-i-j;
      mint R=-(q-1)*x*(u-i);
      d[ind(i+1,j)]+=d[ind(i,j)]*((p-q+1)*x*(u-i)+(p-q+1)*y*(v-j)+q*y*j+q*x*i-k*p)/R;
      if(i) d[ind(i+1,j)]+=d[ind(i-1,j)]*((p-q)*x*i/R);
      if(j) d[ind(i+1,j)]+=d[ind(i,j-1)]*((p-q)*y*j/R);
      if(j!=v) d[ind(i+1,j)]+=d[ind(i,j+1)]*((q-1)*y*(v-j)/R);
      d[ind(i+1,j)]+=mint(k*p)/mint(n*R);
    }
  }
  mint ans=0;
  for(int i=0;i<n;i++){
    ans+=d[ind(s[i],t[i])];
  }
  ans-=d[ind(u,v)];
  ans-=d[ind(0,1)]*v;
  ans-=d[ind(1,0)]*u;
  cout<<ans.val()<<endl;
}
0