結果
問題 | No.1967 Sugoroku Optimization |
ユーザー |
|
提出日時 | 2022-06-03 22:59:02 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 29 ms / 2,000 ms |
コード長 | 7,257 bytes |
コンパイル時間 | 2,064 ms |
コンパイル使用メモリ | 198,556 KB |
最終ジャッジ日時 | 2025-01-29 17:56:27 |
ジャッジサーバーID (参考情報) |
judge4 / judge3 |
(要ログイン)
ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 21 |
ソースコード
#include <bits/stdc++.h>using namespace std;#define rep(i, n) for (int i = 0; i < n; i++)#define rep2(i, x, n) for (int i = x; i <= n; i++)#define rep3(i, x, n) for (int i = x; i >= n; i--)#define each(e, v) for (auto &e : v)#define pb push_back#define eb emplace_back#define all(x) x.begin(), x.end()#define rall(x) x.rbegin(), x.rend()#define sz(x) (int)x.size()using ll = long long;using pii = pair<int, int>;using pil = pair<int, ll>;using pli = pair<ll, int>;using pll = pair<ll, ll>;template <typename T>bool chmax(T &x, const T &y) {return (x < y) ? (x = y, true) : false;}template <typename T>bool chmin(T &x, const T &y) {return (x > y) ? (x = y, true) : false;}template <typename T>int flg(T x, int i) {return (x >> i) & 1;}template <typename T>void print(const vector<T> &v, T x = 0) {int n = v.size();for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' ');if (v.empty()) cout << '\n';}template <typename T>void printn(const vector<T> &v, T x = 0) {int n = v.size();for (int i = 0; i < n; i++) cout << v[i] + x << '\n';}template <typename T>int lb(const vector<T> &v, T x) {return lower_bound(begin(v), end(v), x) - begin(v);}template <typename T>int ub(const vector<T> &v, T x) {return upper_bound(begin(v), end(v), x) - begin(v);}template <typename T>void rearrange(vector<T> &v) {sort(begin(v), end(v));v.erase(unique(begin(v), end(v)), end(v));}template <typename T>vector<int> id_sort(const vector<T> &v, bool greater = false) {int n = v.size();vector<int> ret(n);iota(begin(ret), end(ret), 0);sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; });return ret;}template <typename S, typename T>pair<S, T> operator+(const pair<S, T> &p, const pair<S, T> &q) {return make_pair(p.first + q.first, p.second + q.second);}template <typename S, typename T>pair<S, T> operator-(const pair<S, T> &p, const pair<S, T> &q) {return make_pair(p.first - q.first, p.second - q.second);}template <typename S, typename T>istream &operator>>(istream &is, pair<S, T> &p) {S a;T b;is >> a >> b;p = make_pair(a, b);return is;}template <typename S, typename T>ostream &operator<<(ostream &os, const pair<S, T> &p) {return os << p.first << ' ' << p.second;}struct io_setup {io_setup() {ios_base::sync_with_stdio(false);cin.tie(NULL);cout << fixed << setprecision(15);}} io_setup;const int inf = (1 << 30) - 1;const ll INF = (1LL << 60) - 1;// const int MOD = 1000000007;const int MOD = 998244353;template <int mod>struct Mod_Int {int x;Mod_Int() : x(0) {}Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}static int get_mod() { return mod; }Mod_Int &operator+=(const Mod_Int &p) {if ((x += p.x) >= mod) x -= mod;return *this;}Mod_Int &operator-=(const Mod_Int &p) {if ((x += mod - p.x) >= mod) x -= mod;return *this;}Mod_Int &operator*=(const Mod_Int &p) {x = (int)(1LL * x * p.x % mod);return *this;}Mod_Int &operator/=(const Mod_Int &p) {*this *= p.inverse();return *this;}Mod_Int &operator++() { return *this += Mod_Int(1); }Mod_Int operator++(int) {Mod_Int tmp = *this;++*this;return tmp;}Mod_Int &operator--() { return *this -= Mod_Int(1); }Mod_Int operator--(int) {Mod_Int tmp = *this;--*this;return tmp;}Mod_Int operator-() const { return Mod_Int(-x); }Mod_Int operator+(const Mod_Int &p) const { return Mod_Int(*this) += p; }Mod_Int operator-(const Mod_Int &p) const { return Mod_Int(*this) -= p; }Mod_Int operator*(const Mod_Int &p) const { return Mod_Int(*this) *= p; }Mod_Int operator/(const Mod_Int &p) const { return Mod_Int(*this) /= p; }bool operator==(const Mod_Int &p) const { return x == p.x; }bool operator!=(const Mod_Int &p) const { return x != p.x; }Mod_Int inverse() const {assert(*this != Mod_Int(0));return pow(mod - 2);}Mod_Int pow(long long k) const {Mod_Int now = *this, ret = 1;for (; k > 0; k >>= 1, now *= now) {if (k & 1) ret *= now;}return ret;}friend ostream &operator<<(ostream &os, const Mod_Int &p) { return os << p.x; }friend istream &operator>>(istream &is, Mod_Int &p) {long long a;is >> a;p = Mod_Int<mod>(a);return is;}};using mint = Mod_Int<MOD>;template <typename T>struct Combination {static vector<T> _fac, _ifac;Combination() {}static void init(int n) {_fac.resize(n + 1), _ifac.resize(n + 1);_fac[0] = 1;for (int i = 1; i <= n; i++) _fac[i] = _fac[i - 1] * i;_ifac[n] = _fac[n].inverse();for (int i = n; i >= 1; i--) _ifac[i - 1] = _ifac[i] * i;}static T fac(int k) { return _fac[k]; }static T ifac(int k) { return _ifac[k]; }static T inv(int k) { return fac(k - 1) * ifac(k); }static T P(int n, int k) {if (k < 0 || n < k) return 0;return fac(n) * ifac(n - k);}static T C(int n, int k) {if (k < 0 || n < k) return 0;return fac(n) * ifac(n - k) * ifac(k);}static T H(int n, int k) { // k 個の区別できない玉を n 個の区別できる箱に入れる場合の数if (n < 0 || k < 0) return 0;return k == 0 ? 1 : C(n + k - 1, k);}static T second_stirling_number(int n, int k) { // n 個の区別できる玉を、k 個の区別しない箱に、各箱に 1 個以上玉が入るように入れる場合の数T ret = 0;for (int i = 0; i <= k; i++) {T tmp = C(k, i) * T(i).pow(n);ret += ((k - i) & 1) ? -tmp : tmp;}return ret * ifac(k);}static T bell_number(int n, int k) { // n 個の区別できる玉を、k 個の区別しない箱に入れる場合の数if (n == 0) return 1;k = min(k, n);vector<T> pref(k + 1);pref[0] = 1;for (int i = 1; i <= k; i++) {if (i & 1) {pref[i] = pref[i - 1] - ifac(i);} else {pref[i] = pref[i - 1] + ifac(i);}}T ret = 0;for (int i = 1; i <= k; i++) ret += T(i).pow(n) * ifac(i) * pref[k - i];return ret;}};template <typename T>vector<T> Combination<T>::_fac = vector<T>();template <typename T>vector<T> Combination<T>::_ifac = vector<T>();using comb = Combination<mint>;int main() {int N, K;cin >> N >> K;vector<mint> dp(N + 1, 0), ndp(N + 1, 0);dp[N] = 1;comb::init(N);rep(i, K) {fill(all(ndp), 0);vector<mint> s(N + 2, 0);rep(j, N + 1) s[j + 1] = s[j] + dp[j];ndp[N] = 1;rep3(j, N - 1, 0) {ndp[j] = s[N + 1] - s[j + 1];ndp[j] *= comb::inv(N - j);}swap(dp, ndp);}cout << dp[0] << '\n';}