結果
問題 | No.2116 Making Forest Hard |
ユーザー |
👑 |
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 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 53 |
ソースコード
#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 LOCALassert(a);#endifif (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 LOCALassert(a);#endifif (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 LOCALassert(a);#endifif (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 < xvvector<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;}