結果

問題 No.2115 Making Forest Easy
ユーザー Sumitacchan
提出日時 2022-10-28 23:40:23
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 781 ms / 2,000 ms
コード長 7,243 bytes
コンパイル時間 2,397 ms
コンパイル使用メモリ 212,552 KB
最終ジャッジ日時 2025-02-08 15:21:37
ジャッジサーバーID
(参考情報)
judge4 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 2
other AC * 50
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;
//using namespace atcoder;
struct fast_ios { fast_ios(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
#define FOR(i, begin, end) for(int i=(begin);i<(end);i++)
#define REP(i, n) FOR(i,0,n)
#define IFOR(i, begin, end) for(int i=(end)-1;i>=(begin);i--)
#define IREP(i, n) IFOR(i,0,n)
#define Sort(v) sort(v.begin(), v.end())
#define Reverse(v) reverse(v.begin(), v.end())
#define all(v) v.begin(),v.end()
#define SZ(v) ((int)v.size())
#define Lower_bound(v, x) distance(v.begin(), lower_bound(v.begin(), v.end(), x))
#define Upper_bound(v, x) distance(v.begin(), upper_bound(v.begin(), v.end(), x))
#define chmax(a, b) a = max(a, b)
#define chmin(a, b) a = min(a, b)
#define bit(n) (1LL<<(n))
#define debug(x) cout << #x << "=" << x << endl;
#define vdebug(v) { cout << #v << "=" << endl; REP(i_debug, (int)v.size()){ cout << v[i_debug] << ","; } cout << endl; }
#define mdebug(m) { cout << #m << "=" << endl; REP(i_debug, (int)m.size()){ REP(j_debug, (int)m[i_debug].size()){ cout << m[i_debug][j_debug] << ",";
    } cout << endl;} }
#define pb push_back
#define fi first
#define se second
#define int long long
#define INF 1000000000000000000
template<typename T> istream &operator>>(istream &is, vector<T> &v){ for (auto &x : v) is >> x; return is; }
template<typename T> ostream &operator<<(ostream &os, vector<T> &v){ for(int i = 0; i < (int)v.size(); i++) { cout << v[i]; if(i != (int)v.size() - 1
    ) cout << endl; }; return os; }
template<typename T1, typename T2> ostream &operator<<(ostream &os, pair<T1, T2> p){ cout << '(' << p.first << ',' << p.second << ')'; return os; }
template<typename T> void Out(T x) { cout << x << endl; }
template<typename T1, typename T2> void chOut(bool f, T1 y, T2 n) { if(f) Out(y); else Out(n); }
using vec = vector<int>;
using mat = vector<vec>;
using Pii = pair<int, int>;
using v_bool = vector<bool>;
using v_Pii = vector<Pii>;
//int dx[4] = {1,0,-1,0};
//int dy[4] = {0,1,0,-1};
//char d[4] = {'D','R','U','L'};
//const int mod = 1000000007;
const int mod = 998244353;
template<long long MOD>
struct ModInt{
using ll = long long;
ll val;
void setval(ll v) { val = v % MOD; };
ModInt(): val(0) {}
ModInt(ll v) { setval(v); };
ModInt operator+(const ModInt &x) const { return ModInt(val + x.val); }
ModInt operator-(const ModInt &x) const { return ModInt(val - x.val + MOD); }
ModInt operator*(const ModInt &x) const { return ModInt(val * x.val); }
ModInt operator/(const ModInt &x) const { return *this * x.inv(); }
ModInt operator-() const { return ModInt(MOD - val); }
ModInt operator+=(const ModInt &x) { return *this = *this + x; }
ModInt operator-=(const ModInt &x) { return *this = *this - x; }
ModInt operator*=(const ModInt &x) { return *this = *this * x; }
ModInt operator/=(const ModInt &x) { return *this = *this / x; }
bool operator==(const ModInt &x) const { return (*this).val == x.val; }
friend ostream& operator<<(ostream &os, const ModInt &x) { os << x.val; return os; }
friend istream& operator>>(istream &is, ModInt &x) { is >> x.val; x.val = (x.val % MOD + MOD) % MOD; return is; }
ModInt pow(ll n) const {
ModInt a = 1;
if(n == 0) return a;
int i0 = 64 - __builtin_clzll(n);
for(int i = i0 - 1; i >= 0; i--){
a = a * a;
if((n >> i) & 1) a *= (*this);
}
return a;
}
ModInt inv() const { return this->pow(MOD - 2); }
void add_product(ModInt a, ModInt b){
(val += a.val * b.val) %= MOD;
}
void sbt_product(ModInt a, ModInt b){
(val -= a.val * b.val) %= MOD;
if(val < 0) val += MOD;
}
};
using mint = ModInt<mod>; mint pow(mint x, long long n) { return x.pow(n); }
//using mint = double; //for debug
using mvec = vector<mint>;
using mmat = vector<mvec>;
struct Combination{
vector<mint> fact, invfact;
Combination(int N){
fact = vector<mint>({mint(1)});
invfact = vector<mint>({mint(1)});
fact_initialize(N);
}
void fact_initialize(int N){
int i0 = fact.size();
if(i0 >= N + 1) return;
fact.resize(N + 1);
invfact.resize(N + 1);
for(int i = i0; i <= N; i++) fact[i] = fact[i - 1] * i;
invfact[N] = (mint)1 / fact[N];
for(int i = N - 1; i >= i0; i--) invfact[i] = invfact[i + 1] * (i + 1);
}
mint nCr(int n, int r){
if(n < 0 || r < 0 || r > n) return mint(0);
if((int)fact.size() < n + 1) fact_initialize(n);
return fact[n] * invfact[r] * invfact[n - r];
}
mint nPr(int n, int r){
if(n < 0 || r < 0 || r > n) return mint(0);
if((int)fact.size() < n + 1) fact_initialize(n);
return fact[n] * invfact[n - r];
}
mint Catalan(int n){
if(n < 0) return 0;
else if(n == 0) return 1;
if((int)fact.size() < 2 * n + 1) fact_initialize(2 * n);
return fact[2 * n] * invfact[n + 1] * invfact[n];
}
};
template<typename T>
struct edge{ int to; T cost; int id; };
template<typename T = long long>
struct Graph
{
int N;
vector<vector<edge<T>>> E;
vec A;
mvec dp, dq;
const mint inv2 = 499122177;
Graph(int N): N(N){
E = vector<vector<edge<T>>>(N, vector<edge<T>>(0));
dp.resize(N);
dq.resize(N);
}
void add_Directed_edge(int from, int to, T cost = 1, int id = 0){
E[from].push_back(edge<T>({ to, cost, id }));
}
void add_Undirected_edge(int v1, int v2, T cost = 1, int id = 0){
add_Directed_edge(v1, v2, cost, id);
add_Directed_edge(v2, v1, cost, id);
}
void dfs1(int v, int x, int p = -1){
if(A[v] < x) dp[v] = 1;
else dp[v] = 0;
for(auto e: E[v]) if(e.to != p){
dfs1(e.to, x, v);
dp[v] *= (mint)1 - ((mint)1 - dp[e.to]) * inv2;
}
}
void dfs2(int v, int x, mint &ans, int p = -1){
if(p == -1) dq[v] = 1;
vec ch;
for(auto e: E[v]) if(e.to != p){
ch.pb(e.to);
}
int n = SZ(ch);
mint q0 = (mint)1 - ((mint)1 - dq[v]) * inv2;
if(A[v] < x){
mvec dl(n + 1, 0), dr(n + 1, 0);
dl[0] = dr[0] = 1;
REP(i, n){
mint q = (mint)1 - ((mint)1 - dp[ch[i]]) * inv2;
dl[i + 1] = dl[i] * q;
}
REP(i, n){
mint q = (mint)1 - ((mint)1 - dp[ch[n - 1 - i]]) * inv2;
dr[i + 1] = dr[i] * q;
}
REP(i, n){
dq[ch[i]] = dl[i] * dr[n - 1 - i] * q0;
}
}else{
REP(i, n){
dq[ch[i]] = 0;
}
}
REP(i, n) dfs2(ch[i], x, ans, v);
ans += (mint)1 - dp[v] * q0;
}
};
signed main(){
int N; cin >> N;
vec A(N); cin >> A;
Graph G(N);
REP(i, N - 1){
int u, v; cin >> u >> v;
u--; v--;
G.add_Undirected_edge(u, v);
}
G.A = A;
mint ans = 0;
FOR(x, 1, 1001){
G.dfs1(0, x);
G.dfs2(0, x, ans);
}
ans *= pow((mint)2, N - 1);
Out(ans);
return 0;
}
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