結果

問題 No.2116 Making Forest Hard
ユーザー 👑 hos.lyric
提出日時 2022-10-28 23:04:18
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,557 ms / 8,000 ms
コード長 9,617 bytes
コンパイル時間 2,347 ms
コンパイル使用メモリ 142,932 KB
実行使用メモリ 492,100 KB
最終ジャッジ日時 2024-07-06 02:18:49
合計ジャッジ時間 36,600 ms
ジャッジサーバーID
(参考情報)
judge1 / judge3
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 * 53
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

#pragma GCC optimize ("Ofast")
#pragma GCC optimize ("unroll-loops")
#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using Int = long long;
template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i
    >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
static constexpr unsigned M = M_;
unsigned x;
constexpr ModInt() : x(0U) {}
constexpr ModInt(unsigned x_) : x(x_ % M) {}
constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }
ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
ModInt pow(long long e) const {
if (e < 0) return inv().pow(-e);
ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
}
ModInt inv() const {
unsigned a = M, b = x; int y = 0, z = 1;
for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
assert(a == 1U); return ModInt(y);
}
ModInt operator+() const { return *this; }
ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
explicit operator bool() const { return x; }
bool operator==(const ModInt &a) const { return (x == a.x); }
bool operator!=(const ModInt &a) const { return (x != a.x); }
friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
////////////////////////////////////////////////////////////////////////////////
constexpr unsigned MO = 998244353;
using Mint = ModInt<MO>;
using Pair = pair<Mint, Mint>;
Pair operator+(const Pair &a, const Pair &b) { return make_pair(a.first + b.first, a.second + b.second); }
Pair operator-(const Pair &a, const Pair &b) { return make_pair(a.first - b.first, a.second - b.second); }
Pair operator*(const Pair &a, const Pair &b) { return make_pair(a.first * b.first, a.first * b.second + a.second * b.first); }
Pair &operator+=(Pair &a, const Pair &b) { return a = a + b; }
Pair &operator-=(Pair &a, const Pair &b) { return a = a - b; }
Pair &operator*=(Pair &a, const Pair &b) { return a = a * b; }
constexpr Pair ZERO(0, 0);
Pair operator*(const Mint &k, const Pair &a) { return make_pair(k * a.first, k * a.second); }
struct Node {
int l, r;
Pair f, g;
Pair lz;
Node() {}
void push(Node &l_, Node &r_) {
if (!(lz.first == 1 && lz.second == 0)) {
l_.mul(lz);
r_.mul(lz);
lz.first = 1;
lz.second = 0;
}
}
void pull(const Node &l_, const Node &r_) {
f = l_.f + r_.f;
g = l_.g + r_.g;
}
void mul(const Pair &val) {
f *= val;
g *= val;
lz *= val;
}
};
int nodesLen = 1;
Node nodes[14'000'010];
int newNode() {
const int u = nodesLen++;
nodes[u].lz.first = 1;
return u;
}
void rangeMul(int a, int l, int r, int ql, int qr, const Pair &val) {
#ifdef LOCAL
assert(a);
#endif
if (qr <= l || r <= ql) {
//
} else if (ql <= l && r <= qr) {
nodes[a].mul(val);
} else {
const int mid = (l + r) / 2;
int &al = nodes[a].l;
int &ar = nodes[a].r;
if (!al) {
al = newNode();
ar = newNode();
}
nodes[a].push(nodes[al], nodes[ar]);
rangeMul(al, l, mid, ql, qr, val);
rangeMul(ar, mid, r, ql, qr, val);
nodes[a].pull(nodes[al], nodes[ar]);
}
}
void pointAdd(int a, int l, int r, int q, const Pair &f, const Pair &g) {
#ifdef LOCAL
assert(a);
#endif
if (q + 1 <= l || r <= q) {
//
} else if (q <= l && r <= q + 1) {
nodes[a].f += f;
nodes[a].g += g;
} else {
const int mid = (l + r) / 2;
int &al = nodes[a].l;
int &ar = nodes[a].r;
if (!al) {
al = newNode();
ar = newNode();
}
nodes[a].push(nodes[al], nodes[ar]);
pointAdd(al, l, mid, q, f, g);
pointAdd(ar, mid, r, q, f, g);
nodes[a].pull(nodes[al], nodes[ar]);
}
}
Pair rangeSum(int a, int l, int r, int ql, int qr) {
#ifdef LOCAL
assert(a);
#endif
if (qr <= l || r <= ql) {
return ZERO;
} else if (ql <= l && r <= qr) {
return nodes[a].f;
} else {
const int mid = (l + r) / 2;
int &al = nodes[a].l;
int &ar = nodes[a].r;
if (!al) {
al = newNode();
ar = newNode();
}
nodes[a].push(nodes[al], nodes[ar]);
Pair ret = ZERO;
ret += rangeSum(al, l, mid, ql, qr);
ret += rangeSum(ar, mid, r, ql, qr);
nodes[a].pull(nodes[al], nodes[ar]);
return ret;
}
}
int create(int l, int r, int q, const Pair &f, const Pair &g) {
if (q + 1 <= l || r <= q) {
const int a = newNode();
return a;
} else if (q <= l && r <= q + 1) {
const int a = newNode();
nodes[a].f = f;
nodes[a].g = g;
return a;
} else {
const int mid = (l + r) / 2;
const int al = create(l, mid, q, f, g);
const int ar = create(mid, r, q, f, g);
const int a = newNode();
nodes[a].l = al;
nodes[a].r = ar;
nodes[a].pull(nodes[al], nodes[ar]);
return a;
}
}
constexpr Mint INV2 = (1 + MO) / 2;
int N;
vector<int> C;
vector<int> A, B;
vector<vector<int>> graph;
int csLen;
vector<int> cs;
Mint ans;
vector<set<int>> ss;
vector<int> rs;
void dfs(int u, int p) {
for (const int v : graph[u]) if (p != v) {
dfs(v, u);
}
const int pos = lower_bound(cs.begin(), cs.end(), C[u]) - cs.begin();
ss[u].insert(pos);
rs[u] = create(0, csLen, pos, Pair(1, 1), Pair(cs[pos], cs[pos]));
for (const int v : graph[u]) if (p != v) {
ans += INV2 * nodes[rs[v]].g.second;
bool sw = false;
if (ss[u].size() < ss[v].size()) {
sw = true;
swap(ss[u], ss[v]);
swap(rs[u], rs[v]);
}
vector<int> xs(ss[v].begin(), ss[v].end());
const int len = xs.size();
xs.push_back(csLen);
vector<Pair> gs(len);
// xu < xv
vector<Pair> hs(len);
for (int j = 0; j < len; ++j) {
gs[j] = INV2 * rangeSum(rs[v], 0, csLen, xs[j], xs[j] + 1);
hs[j] = gs[j] * rangeSum(rs[u], 0, csLen, 0, xs[j]);
}
// cerr<<u<<" "<<v<<" "<<xs<<": "<<gs<<" "<<hs<<endl;
// xu >= xv
{
Pair sum = sw ? ZERO : Pair(INV2, 0);
rangeMul(rs[u], 0, csLen, 0, xs[0], sum);
for (int j = 0; j < len; ++j) {
sum += gs[j];
rangeMul(rs[u], 0, csLen, xs[j], xs[j + 1], sum);
}
}
for (int j = 0; j < len; ++j) {
const Pair h = sw ? (gs[j] + hs[j]) : hs[j];
pointAdd(rs[u], 0, csLen, xs[j], h, cs[xs[j]] * h);
}
for (int j = 0; j < len; ++j) {
ss[u].insert(xs[j]);
}
}
// cerr<<"DONE u = "<<u<<endl;
// cerr<<" ss[u] = ";pv(ss[u].begin(),ss[u].end());
// cerr<<" ";for(const int x:ss[u])cerr<<Mint(2).pow(N-1)*rangeSum(rs[u],0,csLen,x,x+1)<<"/"<<Mint(2).pow(N-1)<<" ";cerr<<endl;
}
int main() {
for (; ~scanf("%d", &N); ) {
C.resize(N);
for (int u = 0; u < N; ++u) {
scanf("%d", &C[u]);
}
A.resize(N - 1);
B.resize(N - 1);
for (int i = 0; i < N - 1; ++i) {
scanf("%d%d", &A[i], &B[i]);
--A[i];
--B[i];
}
cs = C;
sort(cs.begin(), cs.end());
cs.erase(unique(cs.begin(), cs.end()), cs.end());
csLen = cs.size();
graph.assign(N, {});
for (int i = 0; i < N - 1; ++i) {
graph[A[i]].push_back(B[i]);
graph[B[i]].push_back(A[i]);
}
ans = 0;
ss.assign(N, {});
rs.assign(N, 0);
const int rt = 998244353 % N;
dfs(rt, -1);
ans += nodes[rs[rt]].g.second;
ans *= Mint(2).pow(N - 1);
printf("%u\n", ans.x);
}
return 0;
}
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