結果
| 問題 |
No.2951 Similar to Mex
|
| コンテスト | |
| ユーザー |
 apricity
|
| 提出日時 | 2024-11-22 23:53:41 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 389 ms / 2,000 ms |
| コード長 | 9,895 bytes |
| コンパイル時間 | 1,431 ms |
| コンパイル使用メモリ | 129,672 KB |
| 最終ジャッジ日時 | 2025-02-25 05:53:11 |
|
ジャッジサーバーID （参考情報） |
judge4 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 42 |
ソースコード
#include<iostream>
#include<string>
#include<vector>
#include<algorithm>
#include<numeric>
#include<cmath>
#include<utility>
#include<tuple>
#include<cstdint>
#include<cstdio>
#include<iomanip>
#include<map>
#include<queue>
#include<set>
#include<stack>
#include<deque>
#include<unordered_map>
#include<unordered_set>
#include<bitset>
#include<cctype>
#include<chrono>
#include<random>
#include<cassert>
#include<cstddef>
#include<iterator>
#include<string_view>
#include<type_traits>
#ifdef LOCAL
# include "debug_print.hpp"
# define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)
#else
# define debug(...) (static_cast<void>(0))
#endif
using namespace std;
#define rep1(a) for(int i = 0; i < a; i++)
#define rep2(i, a) for(int i = 0; i < a; i++)
#define rep3(i, a, b) for(int i = a; i < b; i++)
#define rep4(i, a, b, c) for(int i = a; i < b; i += c)
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define rrep1(a) for(int i = (a)-1; i >= 0; i--)
#define rrep2(i, a) for(int i = (a)-1; i >= 0; i--)
#define rrep3(i, a, b) for(int i = (b)-1; i >= a; i--)
#define rrep4(i, a, b, c) for(int i = (b)-1; i >= a; i -= c)
#define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__)
#define ALL(v) v.begin(), v.end()
#define RALL(v) v.rbegin(), v.rend()
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() );
#define pb push_back
using ll = long long;
using D = double;
using LD = long double;
using P = pair<int, int>;
using vi = vector<int>;
using vl = vector<ll>;
template <class T> using vc = vector<T>;
template <class T> using vvc = vector<vc<T>>;
template <class T> using vvvc = vector<vvc<T>>;
template <class T> using vvvvc = vector<vvvc<T>>;
template <class T> using vvvvvc = vector<vvvvc<T>>;
#define vv(type, name, h, ...) \
vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...) \
vector<vector<vector<type>>> name( \
h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...) \
vector<vector<vector<vector<type>>>> name( \
a, vector<vector<vector<type>>>( \
b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))
template<typename T> using PQ = priority_queue<T,vector<T>>;
template<typename T> using minPQ = priority_queue<T, vector<T>, greater<T>>;
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }
void yesno(bool flag) {cout << (flag?"Yes":"No") << "\n";}
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>
istream &operator>>(istream &is, pair<T, U> &p) {
is >> p.first >> p.second;
return is;
}
template<typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
int s = (int)v.size();
for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
return os;
}
template<typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (auto &x : v) is >> x;
return is;
}
void in() {}
template<typename T, class... U>
void in(T &t, U &...u) {
cin >> t;
in(u...);
}
void out() { cout << "\n"; }
template<typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
cout << t;
if (sizeof...(u)) cout << sep;
out(u...);
}
void outr() {}
template<typename T, class... U, char sep = ' '>
void outr(const T &t, const U &...u) {
cout << t;
outr(u...);
}
template <uint32_t mod>
struct LazyMontgomeryModInt {
using mint = LazyMontgomeryModInt;
using i32 = int32_t;
using u32 = uint32_t;
using u64 = uint64_t;
static constexpr u32 get_r() {
u32 ret = mod;
for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
return ret;
}
static constexpr u32 r = get_r();
static constexpr u32 n2 = -u64(mod) % mod;
static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
static_assert(r * mod == 1, "this code has bugs.");
u32 a;
constexpr LazyMontgomeryModInt() : a(0) {}
constexpr LazyMontgomeryModInt(const int64_t &b)
: a(reduce(u64(b % mod + mod) * n2)){};
static constexpr u32 reduce(const u64 &b) {
return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
}
constexpr mint &operator+=(const mint &b) {
if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
return *this;
}
constexpr mint &operator-=(const mint &b) {
if (i32(a -= b.a) < 0) a += 2 * mod;
return *this;
}
constexpr mint &operator*=(const mint &b) {
a = reduce(u64(a) * b.a);
return *this;
}
constexpr mint &operator/=(const mint &b) {
*this *= b.inverse();
return *this;
}
constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
constexpr bool operator==(const mint &b) const {
return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
}
constexpr bool operator!=(const mint &b) const {
return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
}
constexpr mint operator-() const { return mint() - mint(*this); }
constexpr mint operator+() const { return mint(*this); }
constexpr mint pow(u64 n) const {
mint ret(1), mul(*this);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
constexpr mint inverse() const {
int x = get(), y = mod, u = 1, v = 0, t = 0, tmp = 0;
while (y > 0) {
t = x / y;
x -= t * y, u -= t * v;
tmp = x, x = y, y = tmp;
tmp = u, u = v, v = tmp;
}
return mint{u};
}
friend ostream &operator<<(ostream &os, const mint &b) {
return os << b.get();
}
friend istream &operator>>(istream &is, mint &b) {
int64_t t;
is >> t;
b = LazyMontgomeryModInt<mod>(t);
return (is);
}
constexpr u32 get() const {
u32 ret = reduce(a);
return ret >= mod ? ret - mod : ret;
}
static constexpr u32 get_mod() { return mod; }
};
template<typename T> struct Binomial {
vector<T> fact_, inv_, finv_;
constexpr Binomial() {}
constexpr Binomial(int n) noexcept : fact_(n, 1), inv_(n, 1), finv_(n, 1) {
init(n);
}
constexpr void init(int n) noexcept {
constexpr int mod = T::get_mod();
fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1);
for(int i = 2; i < n; i++){
fact_[i] = fact_[i-1] * i;
inv_[i] = -inv_[mod%i] * (mod/i);
finv_[i] = finv_[i-1] * inv_[i];
}
}
constexpr T com(int n, int k) const noexcept {
if (n < k || n < 0 || k < 0) return 0;
return fact_[n] * finv_[k] * finv_[n-k];
}
constexpr T perm(int n, int k) const noexcept {
if (n < k || n < 0 || k < 0) return 0;
return fact_[n] * finv_[n-k];
}
constexpr T fact(int n) const noexcept {
if (n < 0) return 0;
return fact_[n];
}
constexpr T inv(int n) const noexcept {
if (n < 0) return 0;
return inv_[n];
}
constexpr T finv(int n) const noexcept {
if (n < 0) return 0;
return finv_[n];
}
constexpr T com_naive(int n, int k) const noexcept {
if (n < 0 || k < 0 || n < k) return 0;
T res = T(1);
k = min(k, n-k);
for (int i = 1; i <= k; i++)res *= (n--) * inv(i);
return res;
}
template <typename I>
constexpr T multi(const vector<I> &v) const noexcept {
static_assert(is_integral<I>::value);
I n = 0;
for (auto& x : v) {
if (x < 0) return 0;
n += x;
}
T res = fact(n);
for (auto &x : v) res *= finv(x);
return res;
}
// [x^k] (1-x)^{-n} = com(n+k-1, k)
constexpr T neg(int n, int k) const noexcept {
if (n < 0 || k < 0) return 0;
return k == 0 ? 1 : com(n+k-1, k);
}
};
const int mod = 998244353;
//const int mod = 1000000007;
using mint = LazyMontgomeryModInt<mod>;
Binomial<mint> bc(303);
// mint dp[303][303][303];
//
// int main(){
// ios_base::sync_with_stdio(false);
// cin.tie(nullptr);
// int n,m,k; in(n,m,k);
// dp[m+1][m+1][0] = 1;
// rrep(p,1,m+1)rep(i,p+1,m+2)rep(s,n+1){
// rep(t,1,n-s+1) dp[p][i][s+t] += dp[p+1][i][s] * (k >= p ? i : 1) * bc.finv(t);
// dp[p][p][s] += dp[p+1][i][s] * (k >= p ? p : 1);
// }
// mint ans = 0;
// rep(i,1,m+2){
// mint r = 1;
// rep(j,m+1,k+1) r *= j;
// ans += dp[1][i][n] * r;
// }
// ans *= bc.fact(n);
// out(ans);
// }
mint dp[303][303];
mint f[303][303];
int main(){
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
int n,m,k; in(n,m,k);
dp[m+1][0] = 1;
rrep(i,1,m+1)rep(s,1,m+1){
rep(j,i+1,m+2) {
mint r = 1;
if(i <= k) r *= i;
if(i+1 <= k) r *= mint(j).pow(min(k,j-1)-i);
dp[i][s] += dp[j][s-1] * r;
}
}
f[0][0] = 1;
rep(i,1,m+1)rep(j,n+1) rep(k,1,j+1) f[i][j] += f[i-1][j-k] * bc.finv(k);
mint ans = 0;
mint r = 1;
rep(i,m+1,k+1) r *= i;
rep(i,1,m+2)rep(s,m+1){
ans += dp[i][s] * mint(i).pow(min(i-1,k)) * f[m-s][n] * bc.fact(n);
}
ans *= r;
out(ans);
}