結果
| 問題 |
No.1614 Majority Painting on Tree
|
| コンテスト | |
| ユーザー |
 rniya
|
| 提出日時 | 2022-10-17 20:19:22 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 1,838 ms / 5,000 ms |
| コード長 | 9,305 bytes |
| コンパイル時間 | 2,250 ms |
| コンパイル使用メモリ | 207,744 KB |
| 最終ジャッジ日時 | 2025-02-08 07:43:04 |
|
ジャッジサーバーID （参考情報） |
judge3 / judge1 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 45 |
ソースコード
#define LOCAL
#include <bits/stdc++.h>
using namespace std;
#pragma region Macros
typedef long long ll;
typedef __int128_t i128;
typedef unsigned int uint;
typedef unsigned long long ull;
#define ALL(x) (x).begin(), (x).end()
template <typename T> istream& operator>>(istream& is, vector<T>& v) {
for (T& x : v) is >> x;
return is;
}
template <typename T> ostream& operator<<(ostream& os, const vector<T>& v) {
for (size_t i = 0; i < v.size(); i++) {
os << v[i] << (i + 1 == v.size() ? "" : " ");
}
return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const pair<T, U>& p) {
os << '(' << p.first << ',' << p.second << ')';
return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const map<T, U>& m) {
os << '{';
for (auto itr = m.begin(); itr != m.end();) {
os << '(' << itr->first << ',' << itr->second << ')';
if (++itr != m.end()) os << ',';
}
os << '}';
return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const unordered_map<T, U>& m) {
os << '{';
for (auto itr = m.begin(); itr != m.end();) {
os << '(' << itr->first << ',' << itr->second << ')';
if (++itr != m.end()) os << ',';
}
os << '}';
return os;
}
template <typename T> ostream& operator<<(ostream& os, const set<T>& s) {
os << '{';
for (auto itr = s.begin(); itr != s.end();) {
os << *itr;
if (++itr != s.end()) os << ',';
}
os << '}';
return os;
}
template <typename T> ostream& operator<<(ostream& os, const multiset<T>& s) {
os << '{';
for (auto itr = s.begin(); itr != s.end();) {
os << *itr;
if (++itr != s.end()) os << ',';
}
os << '}';
return os;
}
template <typename T> ostream& operator<<(ostream& os, const unordered_set<T>& s) {
os << '{';
for (auto itr = s.begin(); itr != s.end();) {
os << *itr;
if (++itr != s.end()) os << ',';
}
os << '}';
return os;
}
template <typename T> ostream& operator<<(ostream& os, const deque<T>& v) {
for (size_t i = 0; i < v.size(); i++) {
os << v[i] << (i + 1 == v.size() ? "" : " ");
}
return os;
}
template <typename T, size_t N> ostream& operator<<(ostream& os, const array<T, N>& v) {
for (size_t i = 0; i < N; i++) {
os << v[i] << (i + 1 == N ? "" : " ");
}
return os;
}
template <int i, typename T> void print_tuple(ostream&, const T&) {}
template <int i, typename T, typename H, class... Args> void print_tuple(ostream& os, const T& t) {
if (i) os << ',';
os << get<i>(t);
print_tuple<i + 1, T, Args...>(os, t);
}
template <typename... Args> ostream& operator<<(ostream& os, const tuple<Args...>& t) {
os << '{';
print_tuple<0, tuple<Args...>, Args...>(os, t);
return os << '}';
}
void debug_out() { cerr << '\n'; }
template <class Head, class... Tail> void debug_out(Head&& head, Tail&&... tail) {
cerr << head;
if (sizeof...(Tail) > 0) cerr << ", ";
debug_out(move(tail)...);
}
#ifdef LOCAL
#define debug(...) \
cerr << " "; \
cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n'; \
cerr << " "; \
debug_out(__VA_ARGS__)
#else
#define debug(...) void(0)
#endif
template <typename T> T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; }
template <typename T> T lcm(T x, T y) { return x / gcd(x, y) * y; }
int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
int topbit(long long t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
int botbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); }
int botbit(long long a) { return a == 0 ? 64 : __builtin_ctzll(a); }
int popcount(signed t) { return __builtin_popcount(t); }
int popcount(long long t) { return __builtin_popcountll(t); }
bool ispow2(int i) { return i && (i & -i) == i; }
long long MSK(int n) { return (1LL << n) - 1; }
template <class T> T ceil(T x, T y) {
assert(y >= 1);
return (x > 0 ? (x + y - 1) / y : x / y);
}
template <class T> T floor(T x, T y) {
assert(y >= 1);
return (x > 0 ? x / y : (x - y + 1) / y);
}
template <class T1, class T2> inline bool chmin(T1& a, T2 b) {
if (a > b) {
a = b;
return true;
}
return false;
}
template <class T1, class T2> inline bool chmax(T1& a, T2 b) {
if (a < b) {
a = b;
return true;
}
return false;
}
template <typename T> void mkuni(vector<T>& v) {
sort(v.begin(), v.end());
v.erase(unique(v.begin(), v.end()), v.end());
}
template <typename T> int lwb(const vector<T>& v, const T& x) { return lower_bound(v.begin(), v.end(), x) - v.begin(); }
#pragma endregion
#include <iostream>
#include "atcoder/modint"
namespace atcoder {
template <int MOD> std::istream& operator>>(std::istream& is, static_modint<MOD>& x) {
int64_t v;
x = static_modint<MOD>{(is >> v, v)};
return is;
}
template <int MOD> std::ostream& operator<<(std::ostream& os, const static_modint<MOD>& x) { return os << x.val(); }
template <int ID> std::ostream& operator<<(std::ostream& os, const dynamic_modint<ID>& x) { return os << x.val(); }
} // namespace atcoder
#include <cassert>
#include <vector>
template <typename T> struct Binomial {
Binomial(int MAX = 0) : n(1), facs(1, T(1)), finvs(1, T(1)), invs(1, T(1)) {
while (n <= MAX) extend();
}
T fac(int i) {
assert(i >= 0);
while (n <= i) extend();
return facs[i];
}
T finv(int i) {
assert(i >= 0);
while (n <= i) extend();
return finvs[i];
}
T inv(int i) {
assert(i >= 0);
while (n <= i) extend();
return invs[i];
}
T P(int n, int r) {
if (n < 0 || n < r || r < 0) return T(0);
return fac(n) * finv(n - r);
}
T C(int n, int r) {
if (n < 0 || n < r || r < 0) return T(0);
return fac(n) * finv(n - r) * finv(r);
}
T H(int n, int r) {
if (n < 0 || r < 0) return T(0);
return r == 0 ? 1 : C(n + r - 1, r);
}
T C_naive(int n, int r) {
if (n < 0 || n < r || r < 0) return T(0);
T res = 1;
r = std::min(r, n - r);
for (int i = 1; i <= r; i++) res *= inv(i) * (n--);
return res;
}
private:
int n;
std::vector<T> facs, finvs, invs;
inline void extend() {
int m = n << 1;
facs.resize(m);
finvs.resize(m);
invs.resize(m);
for (int i = n; i < m; i++) facs[i] = facs[i - 1] * i;
finvs[m - 1] = T(1) / facs[m - 1];
invs[m - 1] = finvs[m - 1] * facs[m - 2];
for (int i = m - 2; i >= n; i--) {
finvs[i] = finvs[i + 1] * (i + 1);
invs[i] = finvs[i] * facs[i - 1];
}
n = m;
}
};
const int INF = 1e9;
const long long IINF = 1e18;
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const char dir[4] = {'D', 'R', 'U', 'L'};
const long long MOD = 1000000007;
// const long long MOD = 998244353;
using mint = atcoder::modint998244353;
// dp[v] = v と親との辺を色 1 で塗るような部分木の塗り方
// 対称性より色 1 とせずともどれも等しい
// dp[v] は (dp[u] * (C - 1) + dp[u] * x) の総積の valid な係数の和
// dp[u] ((C - 1) + x) だから簡単に計算できる
// 根とそれ以外の場合分けに注意
int main() {
cin.tie(0);
ios::sync_with_stdio(false);
Binomial<mint> BINOM;
int N, C;
cin >> N >> C;
vector<vector<int>> G(N);
for (int i = 0; i < N - 1; i++) {
int A, B;
cin >> A >> B;
A--, B--;
G[A].emplace_back(B);
G[B].emplace_back(A);
}
vector<vector<mint>> power(C + 1, vector<mint>(N + 1));
for (int i = 0; i <= C; i++) {
power[i][0] = 1;
for (int j = 0; j < N; j++) power[i][j + 1] = power[i][j] * i;
}
auto dfs = [&](auto self, int v, int p, int c) -> mint {
mint prod = 1;
int deg = G[v].size();
for (int& u : G[v]) {
if (u == p) continue;
prod *= self(self, u, v, c);
}
if (p == -1) {
mint tot = power[c][deg], ng = 0;
for (int i = 0; i < deg; i++) {
if (2 * i > deg) {
ng += BINOM.C(deg, i) * power[c - 1][deg - i];
}
}
return prod * (tot - ng * c);
} else {
if (deg == 1) return 1;
mint tot = power[c][deg - 1], ng1 = 0, ng2 = 0;
for (int i = 0; i < deg; i++) {
if (2 * (i + 1) > deg and i < deg - 1) ng1 += BINOM.C(deg - 1, i) * power[c - 1][deg - 1 - i];
if (2 * i > deg) ng2 += BINOM.C(deg - 1, i) * power[c - 1][deg - 1 - i];
}
return prod * (tot - ng1 - ng2 * (c - 1));
}
};
mint ans = 0;
for (int c = C; c > 0; c--) {
mint add = dfs(dfs, 0, -1, c) * BINOM.C(C, c);
if ((C - c) & 1)
ans -= add;
else
ans += add;
}
cout << ans << '\n';
return 0;
}