QOJ.ac
QOJ
| ID | 题目 | 提交者 | 结果 | 用时 | 内存 | 语言 | 文件大小 | 提交时间 | 测评时间 |
|---|---|---|---|---|---|---|---|---|---|
| #280863 | #4811. Be Careful | zhangmj2008 | WA | 1ms | 3896kb | C++17 | 20.8kb | 2023-12-09 18:07:55 | 2023-12-09 18:07:56 |
Judging History
answer
#include <bits/stdc++.h>
using namespace std;
typedef long long ll; typedef unsigned long long ull;
const int INF = 1e9; const ll LLNF = 4e18;
template< class Tp > void chkmax( Tp &x , Tp y ) { x = max( x , y ); }
template< class Tp > void chkmin( Tp &x , Tp y ) { x = min( x , y ); }
namespace atcoder {
namespace internal {
// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n) {
int x = 0;
while ((1U << x) < (unsigned int)(n)) x++;
return x;
}
// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsf(unsigned int n) {
#ifdef _MSC_VER
unsigned long index;
_BitScanForward(&index, n);
return index;
#else
return __builtin_ctz(n);
#endif
}
} // namespace internal
} // namespace atcoder
namespace atcoder {
namespace internal {
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value,
__uint128_t,
unsigned __int128>;
template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
is_signed_int128<T>::value ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value &&
std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type>::type;
#else
template <class T> using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<is_integral<T>::value &&
std::is_unsigned<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type;
#endif
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
} // namespace atcoder
namespace atcoder {
namespace internal {
// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
unsigned int _m;
unsigned long long im;
// @param m `1 <= m < 2^31`
barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
// @return m
unsigned int umod() const { return _m; }
// @param a `0 <= a < m`
// @param b `0 <= b < m`
// @return `a * b % m`
unsigned int mul(unsigned int a, unsigned int b) const {
// [1] m = 1
// a = b = im = 0, so okay
// [2] m >= 2
// im = ceil(2^64 / m)
// -> im * m = 2^64 + r (0 <= r < m)
// let z = a*b = c*m + d (0 <= c, d < m)
// a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
// c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
// ((ab * im) >> 64) == c or c + 1
unsigned long long z = a;
z *= b;
#ifdef _MSC_VER
unsigned long long x;
_umul128(z, im, &x);
#else
unsigned long long x =
(unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned int v = (unsigned int)(z - x * _m);
if (_m <= v) v += _m;
return v;
}
};
// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
long long d = n - 1;
while (d % 2 == 0) d /= 2;
constexpr long long bases[3] = {2, 7, 61};
for (long long a : bases) {
long long t = d;
long long y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) {
return false;
}
}
return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);
// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
a = safe_mod(a, b);
if (a == 0) return {b, 0};
// Contracts:
// [1] s - m0 * a = 0 (mod b)
// [2] t - m1 * a = 0 (mod b)
// [3] s * |m1| + t * |m0| <= b
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while (t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b
// [3]:
// (s - t * u) * |m1| + t * |m0 - m1 * u|
// <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
// = s * |m1| + t * |m0| <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
// by [3]: |m0| <= b/g
// by g != b: |m0| < b/g
if (m0 < 0) m0 += b / s;
return {s, m0};
}
// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0) x /= 2;
for (int i = 3; (long long)(i)*i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) {
x /= i;
}
}
}
if (x > 1) {
divs[cnt++] = x;
}
for (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
} // namespace internal
} // namespace atcoder
namespace atcoder {
namespace internal {
struct modint_base {};
struct static_modint_base : modint_base {};
template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;
} // namespace internal
template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
static_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
static_modint(T v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
static_modint(T v) {
_v = (unsigned int)(v % umod());
}
static_modint(bool v) { _v = ((unsigned int)(v) % umod()); }
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
mint& operator*=(const mint& rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
if (prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto eg = internal::inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = internal::is_prime<m>;
};
template <int id> struct dynamic_modint : internal::modint_base {
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m) {
assert(1 <= m);
bt = internal::barrett(m);
}
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
dynamic_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
dynamic_modint(T v) {
long long x = (long long)(v % (long long)(mod()));
if (x < 0) x += mod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
dynamic_modint(T v) {
_v = (unsigned int)(v % mod());
}
dynamic_modint(bool v) { _v = ((unsigned int)(v) % mod()); }
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v += mod() - rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator*=(const mint& rhs) {
_v = bt.mul(_v, rhs._v);
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
auto eg = internal::inv_gcd(_v, mod());
assert(eg.first == 1);
return eg.second;
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static internal::barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt = 998244353;
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
namespace internal {
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
} // namespace internal
} // namespace atcoder
using modint = atcoder::modint998244353;
void solve( ) {
constexpr int N = 1000;
vector< modint > fact( N + 1 ); fact[0] = 1; for( int i = 1; i <= N; i ++ ) fact[i] = fact[i - 1] * i;
vector< modint > ifact( N + 1 ); ifact[N] = fact[N].inv( ); for( int i = N; i >= 1; i -- ) ifact[i - 1] = ifact[i] * i;
auto binom = [&] ( int n , int m ) -> modint { return ( m < 0 || m > n ) ? ( 0 ) : ( fact[n] * ifact[m] * ifact[n - m] ); } ;
int n; cin >> n;
vector< vector< int > > S( n + 1 ); for( int i = 1; i <= n - 1; i ++ ) { int u , v; cin >> u >> v; S[u].emplace_back( v ); }
vector< int > deg( n + 1 ); for( int u = 1; u <= n; u ++ ) deg[u] = ( int ) S[u].size( );
vector< vector< modint > > f( n + 1 ); vector< int > siz( n + 1 );
auto work = [&] ( int u ) -> void {
int lim = deg[u];
int maxsizv = 0 , pleaf = 0; for( int v : S[u] ) chkmax( maxsizv , siz[v] ) , pleaf += ( deg[v] == 0 );
chkmin( lim , maxsizv + 1 + pleaf );
vector< modint > F( lim + 1 );
int C = 0; int M = INF;
for( int c = 0; c <= n; c ++ ) {
int m = c; for( int v : S[u] ) if( siz[v] >= c ) m ++;
if( M >= m ) M = m , C = c;
}
vector< vector< modint > > X , Y; int nX = 0 , nY = 0 , nZ = 0;
for( int v : S[u] ) {
if( siz[v] == -1 ) nZ ++;
else if( siz[v] <= C - 1 ) X.emplace_back( f[v] ) , nX ++;
else Y.emplace_back( f[v] ) , nY ++;
}
vector< modint > a( 1 << C );
for( int P = 0; P < ( 1 << C ); P ++ ) {
a[P] = ( __builtin_popcount( P ) & 1 ) ? ( -1 ) : ( 1 );
for( vector< modint > xi : X ) {
modint t = 0; for( int l = 0; l < ( int ) xi.size( ); l ++ ) if( ( ~P >> l ) & 1 ) t += xi[l];
a[P] *= t;
}
}
for( int p = 0; p < C; p ++ ) for( int P = 0; P < ( 1 << C ); P ++ ) if( ( P >> p ) & 1 )
a[P] += a[P & ~( 1 << p )];
for( int P = 0; P < ( 1 << C ); P ++ )
a[P] *= ( __builtin_popcount( P ) & 1 ) ? ( -1 ) : ( 1 );
for( int P = 0; P < ( 1 << C ); P ++ ) {
vector< vector< modint > > b( 1 << nY , vector< modint >( nZ + 1 ) ); b[0][0] = a[P];
for( int val = 0; val <= lim; val ++ ) {
for( int Y0 = 0; Y0 < ( 1 << nY ); Y0 ++ ) for( int Z0 = 0; Z0 <= nZ; Z0 ++ ) {
modint s = binom( nZ , Z0 ) * modint( n + 1 - val ).pow( nZ - Z0 );
for( int y = 0; y < nY; y ++ ) if( ( ~Y0 >> y ) & 1 ) {
modint t = 0; for( int l = val; l < ( int ) Y[y].size( ); l ++ ) t += Y[y][l];
s *= t;
}
F[val] += b[Y0][Z0] * s;
}
vector< vector< vector< modint > > > d( nZ + 1 , vector< vector< modint > >( nY + 1 , vector< modint >( 1 << nY ) ) );
for( int Z0 = 0; Z0 <= nZ; Z0 ++ ) for( int pY0 = 0; pY0 <= nY; pY0 ++ ) for( int Y0 = 0; Y0 < ( 1 << nY ); Y0 ++ ) {
if( __builtin_popcount( Y0 ) == pY0 ) d[Z0][pY0][Y0] = b[Y0][Z0];
if( Y0 ) { int y = __builtin_ctz( Y0 ); d[Z0][pY0][Y0] += d[Z0][pY0][Y0 & ~( 1 << y )]; }
}
vector< vector< vector< modint > > > e( nZ + 1 , vector< vector< modint > >( nY + 1 , vector< modint >( 1 << nY ) ) );
for( int Zi = 0; Zi <= nZ; Zi ++ ) for( int pYi = 0; pYi <= nY; pYi ++ ) for( int Yi = 0; Yi < ( 1 << nY ); Yi ++ ) {
if( __builtin_popcount( Yi ) == pYi ) { e[Zi][pYi][Yi] = 1; for( int y = 0; y < nY; y ++ ) if( ( Yi >> y ) & 1 ) e[Zi][pYi][Yi] *= ( val < ( int ) Y[y].size( ) ? Y[y][val] : 0 ); }
if( Yi ) { int y = __builtin_ctz( Yi ); e[Zi][pYi][Yi] += e[Zi][pYi][Yi & ~( 1 << y )]; }
}
vector< vector< vector< modint > > > de( nZ + 1 , vector< vector< modint > >( nY + 1 , vector< modint >( 1 << nY ) ) );
for( int Z0 = 0; Z0 <= nZ; Z0 ++ ) for( int Zi = 0; Zi <= nZ; Zi ++ ) if( Z0 + Zi <= nZ )
for( int pY0 = 0; pY0 <= nY; pY0 ++ ) for( int pYi = 0; pYi <= nY; pYi ++ ) if( pY0 + pYi <= nY )
for( int Y = 0; Y < ( 1 << nY ); Y ++ )
de[Z0 + Zi][pY0 + pYi][Y] += binom( Z0 + Zi , Z0 ) * d[Z0][pY0][Y] * e[Zi][pYi][Y];
for( int Z = 0; Z <= nZ; Z ++ ) for( int pY = 0; pY <= nY; pY ++ ) for( int Y = 0; Y < ( 1 << nY ); Y ++ ) {
if( Y ) { int y = __builtin_ctz( Y ); de[Z][pY][Y] -= de[Z][pY][Y & ~( 1 << y )]; }
}
vector< vector< modint > > nb( 1 << nY , vector< modint >( nZ + 1 ) );
for( int Y = 0; Y < ( 1 << nY ); Y ++ ) for( int Z = 0; Z <= nZ; Z ++ ) {
nb[Y][Z] = de[Z][__builtin_popcount( Y )][Y];
if( ( ~P >> val ) & 1 ) nb[Y][Z] -= b[Y][Z];
}
b = nb;
}
}
f[u] = vector< modint >( lim + 1 );
for( int k = 0; k <= lim; k ++ ) f[u][k] = F[k] - ( k + 1 <= lim ? F[k + 1] : 0 );
while( !f[u].empty( ) && f[u].back( ) == 0 ) f[u].pop_back( );
siz[u] = ( int ) f[u].size( ) - 1;
} ;
auto dfs = [&] ( auto dfs , int u ) -> void {
for( int v : S[u] ) dfs( dfs , v );
if( deg[u] >= 1 ) work( u ); else siz[u] = -1;
} ;
dfs( dfs , 1 );
for( int k = 0; k <= n; k ++ ) cout << ( k <= siz[1] ? f[1][k].val( ) : 0 ) << "\n";
}
int main( ) {
ios::sync_with_stdio( 0 ), cin.tie( 0 ), cout.tie( 0 );
int T = 1; while( T -- ) solve( ); return 0;
}
詳細信息
Test #1:
score: 100
Accepted
time: 1ms
memory: 3596kb
input:
5 1 2 1 3 2 4 2 5
output:
55 127 34 0 0 0
result:
ok 6 numbers
Test #2:
score: 0
Accepted
time: 0ms
memory: 3896kb
input:
8 1 2 1 3 1 4 1 5 1 6 6 7 6 8
output:
69632 265534 133905 47790 12636 1944 0 0 0
result:
ok 9 numbers
Test #3:
score: 0
Accepted
time: 0ms
memory: 3548kb
input:
3 1 2 2 3
output:
1 3 0 0
result:
ok 4 number(s): "1 3 0 0"
Test #4:
score: 0
Accepted
time: 0ms
memory: 3700kb
input:
2 1 2
output:
2 1 0
result:
ok 3 number(s): "2 1 0"
Test #5:
score: -100
Wrong Answer
time: 1ms
memory: 3668kb
input:
10 1 8 1 9 6 1 2 1 1 4 1 10 1 5 7 1 3 1
output:
100000 40951 14670 4350 960 120 0 0 0 0 0
result:
wrong answer 1st numbers differ - expected: '1755647', found: '100000'