結果

問題 No.2504 NOT Path Painting
ユーザー ForestedForested
提出日時 2023-10-13 21:30:43
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 143 ms / 2,000 ms
コード長 8,437 bytes
コンパイル時間 1,306 ms
コンパイル使用メモリ 132,292 KB
最終ジャッジ日時 2025-02-17 07:07:43
ジャッジサーバーID
(参考情報)
judge5 / judge2
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ファイルパターン 結果
other AC * 21
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ソースコード

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プレゼンテーションモードにする

#ifndef LOCAL
#define FAST_IO
#endif
// ============
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cmath>
#include <cstring>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
#define OVERRIDE(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i)
#define REP3(i, m, n) for (i32 i = (i32)(m); i < (i32)(n); ++i)
#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER(i, n) for (i32 i = (i32)(n) - 1; i >= 0; --i)
#define ALL(x) begin(x), end(x)
using namespace std;
using u32 = unsigned int;
using u64 = unsigned long long;
using i32 = signed int;
using i64 = signed long long;
using f64 = double;
using f80 = long double;
template <typename T>
using Vec = vector<T>;
template <typename T>
bool chmin(T &x, const T &y) {
if (x > y) {
x = y;
return true;
}
return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
if (x < y) {
x = y;
return true;
}
return false;
}
#ifdef INT128
using u128 = __uint128_t;
using i128 = __int128_t;
istream &operator>>(istream &is, i128 &x) {
i64 v;
is >> v;
x = v;
return is;
}
ostream &operator<<(ostream &os, i128 x) {
os << (i64)x;
return os;
}
istream &operator>>(istream &is, u128 &x) {
u64 v;
is >> v;
x = v;
return is;
}
ostream &operator<<(ostream &os, u128 x) {
os << (u64)x;
return os;
}
#endif
[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;
struct SetUpIO {
SetUpIO() {
#ifdef FAST_IO
ios::sync_with_stdio(false);
cin.tie(nullptr);
#endif
cout << fixed << setprecision(15);
}
} set_up_io;
// ============
#ifdef DEBUGF
#else
#define DBG(x) (void)0
#endif
// ============
#include <cassert>
#include <iostream>
#include <type_traits>
// ============
constexpr bool is_prime(unsigned n) {
if (n == 0 || n == 1) {
return false;
}
for (unsigned i = 2; i * i <= n; ++i) {
if (n % i == 0) {
return false;
}
}
return true;
}
constexpr unsigned mod_pow(unsigned x, unsigned y, unsigned mod) {
unsigned ret = 1, self = x;
while (y != 0) {
if (y & 1) {
ret = (unsigned) ((unsigned long long) ret * self % mod);
}
self = (unsigned) ((unsigned long long) self * self % mod);
y /= 2;
}
return ret;
}
template <unsigned mod>
constexpr unsigned primitive_root() {
static_assert(is_prime(mod), "`mod` must be a prime number.");
if (mod == 2) {
return 1;
}
unsigned primes[32] = {};
int it = 0;
{
unsigned m = mod - 1;
for (unsigned i = 2; i * i <= m; ++i) {
if (m % i == 0) {
primes[it++] = i;
while (m % i == 0) {
m /= i;
}
}
}
if (m != 1) {
primes[it++] = m;
}
}
for (unsigned i = 2; i < mod; ++i) {
bool ok = true;
for (int j = 0; j < it; ++j) {
if (mod_pow(i, (mod - 1) / primes[j], mod) == 1) {
ok = false;
break;
}
}
if (ok)
return i;
}
return 0;
}
// y >= 1
template <typename T>
constexpr T safe_mod(T x, T y) {
x %= y;
if (x < 0) {
x += y;
}
return x;
}
// y != 0
template <typename T>
constexpr T floor_div(T x, T y) {
if (y < 0) {
x *= -1;
y *= -1;
}
if (x >= 0) {
return x / y;
} else {
return -((-x + y - 1) / y);
}
}
// y != 0
template <typename T>
constexpr T ceil_div(T x, T y) {
if (y < 0) {
x *= -1;
y *= -1;
}
if (x >= 0) {
return (x + y - 1) / y;
} else {
return -(-x / y);
}
}
// ============
template <unsigned mod>
class ModInt {
static_assert(mod != 0, "`mod` must not be equal to 0.");
static_assert(
mod < (1u << 31),
"`mod` must be less than (1u << 31) = 2147483648.");
unsigned val;
public:
static constexpr unsigned get_mod() {
return mod;
}
constexpr ModInt() : val(0) {}
template <typename T, std::enable_if_t<std::is_signed_v<T>> * = nullptr>
constexpr ModInt(T x) : val((unsigned) ((long long) x % (long long) mod + (x < 0 ? mod : 0))) {}
template <typename T, std::enable_if_t<std::is_unsigned_v<T>> * = nullptr>
constexpr ModInt(T x) : val((unsigned) (x % mod)) {}
static constexpr ModInt raw(unsigned x) {
ModInt<mod> ret;
ret.val = x;
return ret;
}
constexpr unsigned get_val() const {
return val;
}
constexpr ModInt operator+() const {
return *this;
}
constexpr ModInt operator-() const {
return ModInt<mod>(0u) - *this;
}
constexpr ModInt &operator+=(const ModInt &rhs) {
val += rhs.val;
if (val >= mod)
val -= mod;
return *this;
}
constexpr ModInt &operator-=(const ModInt &rhs) {
val -= rhs.val;
if (val >= mod)
val += mod;
return *this;
}
constexpr ModInt &operator*=(const ModInt &rhs) {
val = (unsigned long long)val * rhs.val % mod;
return *this;
}
constexpr ModInt &operator/=(const ModInt &rhs) {
val = (unsigned long long)val * rhs.inv().val % mod;
return *this;
}
friend constexpr ModInt operator+(const ModInt &lhs, const ModInt &rhs) {
return ModInt<mod>(lhs) += rhs;
}
friend constexpr ModInt operator-(const ModInt &lhs, const ModInt &rhs) {
return ModInt<mod>(lhs) -= rhs;
}
friend constexpr ModInt operator*(const ModInt &lhs, const ModInt &rhs) {
return ModInt<mod>(lhs) *= rhs;
}
friend constexpr ModInt operator/(const ModInt &lhs, const ModInt &rhs) {
return ModInt<mod>(lhs) /= rhs;
}
constexpr ModInt pow(unsigned long long x) const {
ModInt<mod> ret = ModInt<mod>::raw(1);
ModInt<mod> self = *this;
while (x != 0) {
if (x & 1)
ret *= self;
self *= self;
x >>= 1;
}
return ret;
}
constexpr ModInt inv() const {
static_assert(is_prime(mod), "`mod` must be a prime number.");
assert(val != 0);
return this->pow(mod - 2);
}
friend std::istream &operator>>(std::istream &is, ModInt<mod> &x) {
long long val;
is >> val;
x.val = val % mod + (val < 0 ? mod : 0);
return is;
}
friend std::ostream &operator<<(std::ostream &os, const ModInt<mod> &x) {
os << x.val;
return os;
}
friend bool operator==(const ModInt &lhs, const ModInt &rhs) {
return lhs.val == rhs.val;
}
friend bool operator!=(const ModInt &lhs, const ModInt &rhs) {
return lhs.val != rhs.val;
}
};
[[maybe_unused]] constexpr unsigned mod998244353 = 998244353;
[[maybe_unused]] constexpr unsigned mod1000000007 = 1000000007;
// ============
using M = ModInt<mod998244353>;
void solve() {
i32 n;
cin >> n;
Vec<Vec<i32>> g(n);
REP(i, n - 1) {
i32 u, v;
cin >> u >> v;
--u;
--v;
g[u].push_back(v);
g[v].push_back(u);
}
Vec<i32> par(n, -1), sz(n, 1);
const auto dfs = [&](const auto &dfs, i32 v) -> void {
for (i32 u : g[v]) {
if (u != par[v]) {
par[u] = v;
dfs(dfs, u);
sz[v] += sz[u];
}
}
};
dfs(dfs, 0);
M ans;
constexpr M INV = M(2).inv();
M tot = M(n) * M(n + 1) * INV;
M toti = tot.inv();
REP(v, n) {
M w;
for (i32 u : g[v]) {
i32 s = sz[u];
if (u == par[v]) {
s = n - sz[v];
}
w += M(s) * M(s + 1) * INV;
}
ans += tot / w;
}
REP(v, 1, n) {
M w = tot - M(sz[v]) * M(n - sz[v]);
ans -= tot / w;
}
cout << ans << '\n';
}
int main() {
i32 t;
cin >> t;
while (t--) {
solve();
}
}
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