結果
| 問題 |
No.3139 Interval MEX ?
|
| ユーザー |
 ecottea
|
| 提出日時 | 2025-05-06 03:36:38 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 102 ms / 2,000 ms |
| コード長 | 16,399 bytes |
| コンパイル時間 | 4,963 ms |
| コンパイル使用メモリ | 266,036 KB |
| 実行使用メモリ | 13,008 KB |
| 最終ジャッジ日時 | 2025-05-06 03:36:53 |
| 合計ジャッジ時間 | 15,075 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 57 |
ソースコード
#ifndef HIDDEN_IN_VS // 折りたたみ用
// 警告の抑制
#define _CRT_SECURE_NO_WARNINGS
// ライブラリの読み込み
#include <bits/stdc++.h>
using namespace std;
// 型名の短縮
using ll = long long; using ull = unsigned long long; // -2^63 ～ 2^63 = 9e18（int は -2^31 ～ 2^31 = 2e9）
using pii = pair<int, int>; using pll = pair<ll, ll>; using pil = pair<int, ll>; using pli = pair<ll, int>;
using vi = vector<int>; using vvi = vector<vi>; using vvvi = vector<vvi>; using vvvvi = vector<vvvi>;
using vl = vector<ll>; using vvl = vector<vl>; using vvvl = vector<vvl>; using vvvvl = vector<vvvl>;
using vb = vector<bool>; using vvb = vector<vb>; using vvvb = vector<vvb>;
using vc = vector<char>; using vvc = vector<vc>; using vvvc = vector<vvc>;
using vd = vector<double>; using vvd = vector<vd>; using vvvd = vector<vvd>;
template <class T> using priority_queue_rev = priority_queue<T, vector<T>, greater<T>>;
using Graph = vvi;
// 定数の定義
const double PI = acos(-1);
int DX[4] = { 1, 0, -1, 0 }; // 4 近傍（下，右，上，左）
int DY[4] = { 0, 1, 0, -1 };
int INF = 1001001001; ll INFL = 4004004003094073385LL; // (int)INFL = INF, (int)(-INFL) = -INF;
// 入出力高速化
struct fast_io { fast_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } fastIOtmp;
// 汎用マクロの定義
#define all(a) (a).begin(), (a).end()
#define sz(x) ((int)(x).size())
#define lbpos(a, x) (int)distance((a).begin(), std::lower_bound(all(a), (x)))
#define ubpos(a, x) (int)distance((a).begin(), std::upper_bound(all(a), (x)))
#define Yes(b) {cout << ((b) ? "Yes\n" : "No\n");}
#define rep(i, n) for(int i = 0, i##_len = int(n); i < i##_len; ++i) // 0 から n-1 まで昇順
#define repi(i, s, t) for(int i = int(s), i##_end = int(t); i <= i##_end; ++i) // s から t まで昇順
#define repir(i, s, t) for(int i = int(s), i##_end = int(t); i >= i##_end; --i) // s から t まで降順
#define repe(v, a) for(const auto& v : (a)) // a の全要素（変更不可能）
#define repea(v, a) for(auto& v : (a)) // a の全要素（変更可能）
#define repb(set, d) for(int set = 0, set##_ub = 1 << int(d); set < set##_ub; ++set) // d ビット全探索（昇順）
#define repis(i, set) for(int i = lsb(set), bset##i = set; i < 32; bset##i -= 1 << i, i = lsb(bset##i)) // set の全要素（昇順）
#define repp(a) sort(all(a)); for(bool a##_perm = true; a##_perm; a##_perm = next_permutation(all(a))) // a の順列全て（昇順）
#define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} // 重複除去
#define EXIT(a) {cout << (a) << endl; exit(0);} // 強制終了
#define inQ(x, y, u, l, d, r) ((u) <= (x) && (l) <= (y) && (x) < (d) && (y) < (r)) // 半開矩形内判定
// 汎用関数の定義
template <class T> inline ll powi(T n, int k) { ll v = 1; rep(i, k) v *= n; return v; }
template <class T> inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // 最大値を更新（更新されたら true を返す）
template <class T> inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // 最小値を更新（更新されたら true を返す）
template <class T> inline T getb(T set, int i) { return (set >> i) & T(1); }
template <class T> inline T smod(T n, T m) { n %= m; if (n < 0) n += m; return n; } // 非負mod
// 演算子オーバーロード
template <class T, class U> inline istream& operator>>(istream& is, pair<T, U>& p) { is >> p.first >> p.second; return is; }
template <class T> inline istream& operator>>(istream& is, vector<T>& v) { repea(x, v) is >> x; return is; }
template <class T> inline vector<T>& operator--(vector<T>& v) { repea(x, v) --x; return v; }
template <class T> inline vector<T>& operator++(vector<T>& v) { repea(x, v) ++x; return v; }
#endif // 折りたたみ用
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#ifdef _MSC_VER
#include "localACL.hpp"
#endif
using mint = modint998244353;
//using mint = static_modint<(int)1e9 + 7>;
//using mint = modint; // mint::set_mod(m);
namespace atcoder {
inline istream& operator>>(istream& is, mint& x) { ll x_; is >> x_; x = x_; return is; }
inline ostream& operator<<(ostream& os, const mint& x) { os << x.val(); return os; }
}
using vm = vector<mint>; using vvm = vector<vm>; using vvvm = vector<vvm>; using vvvvm = vector<vvvm>; using pim = pair<int, mint>;
#endif
#ifdef _MSC_VER // 手元環境（Visual Studio）
#include "local.hpp"
#else // 提出用（gcc）
inline int popcount(int n) { return __builtin_popcount(n); }
inline int popcount(ll n) { return __builtin_popcountll(n); }
inline int lsb(int n) { return n != 0 ? __builtin_ctz(n) : 32; }
inline int lsb(ll n) { return n != 0 ? __builtin_ctzll(n) : 64; }
inline int msb(int n) { return n != 0 ? (31 - __builtin_clz(n)) : -1; }
inline int msb(ll n) { return n != 0 ? (63 - __builtin_clzll(n)) : -1; }
#define dump(...)
#define dumpel(v)
#define dump_math(v)
#define input_from_file(f)
#define output_to_file(f)
#define Assert(b) { if (!(b)) { vc MLE(1<<30); EXIT(MLE.back()); } } // RE の代わりに MLE を出す
#endif
//【階乗など（法が大きな素数）】
/*
* Factorial_mint(int N) : O(n)
* N まで計算可能として初期化する．
*
* mint fact(int n) : O(1)
* n! を返す．
*
* mint fact_inv(int n) : O(1)
* 1/n! を返す（n が負なら 0 を返す）
*
* mint inv(int n) : O(1)
* 1/n を返す．
*
* mint perm(int n, int r) : O(1)
* 順列の数 nPr を返す．
*
* mint perm_inv(int n, int r) : O(1)
* 順列の数の逆数 1/nPr を返す．
*
* mint bin(int n, int r) : O(1)
* 二項係数 nCr を返す．
*
* mint bin_inv(int n, int r) : O(1)
* 二項係数の逆数 1/nCr を返す．
*
* mint mul(vi rs) : O(|rs|)
* 多項係数 nC[rs] を返す．（n = Σrs）
*
* mint hom(int n, int r) : O(1)
* 重複組合せの数 nHr = n+r-1Cr を返す（0H0 = 1 とする）
*
* mint neg_bin(int n, int r) : O(1)
* 負の二項係数 nCr = (-1)^r -n+r-1Cr を返す（n ≦ 0, r ≧ 0）
*
* mint pochhammer(int x, int n) : O(1)
* ポッホハマー記号 x^(n) を返す（n ≧ 0）
*
* mint pochhammer_inv(int x, int n) : O(1)
* ポッホハマー記号の逆数 1/x^(n) を返す（n ≧ 0）
*/
class Factorial_mint {
int n_max;
// 階乗と階乗の逆数の値を保持するテーブル
vm fac, fac_inv;
public:
// n! までの階乗とその逆数を前計算しておく．O(n)
Factorial_mint(int n) : n_max(n), fac(n + 1), fac_inv(n + 1) {
// verify : https://atcoder.jp/contests/dwacon6th-prelims/tasks/dwacon6th_prelims_b
fac[0] = 1;
repi(i, 1, n) fac[i] = fac[i - 1] * i;
fac_inv[n] = fac[n].inv();
repir(i, n - 1, 0) fac_inv[i] = fac_inv[i + 1] * (i + 1);
}
Factorial_mint() : n_max(0) {} // ダミー
// n! を返す．
mint fact(int n) const {
// verify : https://atcoder.jp/contests/dwacon6th-prelims/tasks/dwacon6th_prelims_b
Assert(0 <= n && n <= n_max);
return fac[n];
}
// 1/n! を返す（n が負なら 0 を返す）
mint fact_inv(int n) const {
// verify : https://atcoder.jp/contests/abc289/tasks/abc289_h
Assert(n <= n_max);
if (n < 0) return 0;
return fac_inv[n];
}
// 1/n を返す．
mint inv(int n) const {
// verify : https://atcoder.jp/contests/exawizards2019/tasks/exawizards2019_d
Assert(n > 0);
Assert(n <= n_max);
return fac[n - 1] * fac_inv[n];
}
// 順列の数 nPr を返す．
mint perm(int n, int r) const {
// verify : https://atcoder.jp/contests/abc172/tasks/abc172_e
Assert(n <= n_max);
if (r < 0 || n - r < 0) return 0;
return fac[n] * fac_inv[n - r];
}
// 順列の数 nPr の逆数を返す．
mint perm_inv(int n, int r) const {
Assert(n <= n_max);
Assert(0 <= r); Assert(r <= n);
return fac_inv[n] * fac[n - r];
}
// 二項係数 nCr を返す．
mint bin(int n, int r) const {
// verify : https://judge.yosupo.jp/problem/binomial_coefficient_prime_mod
Assert(n <= n_max);
if (r < 0 || n - r < 0) return 0;
return fac[n] * fac_inv[r] * fac_inv[n - r];
}
// 二項係数の逆数 1/nCr を返す．
mint bin_inv(int n, int r) const {
// verify : https://www.codechef.com/problems/RANDCOLORING
Assert(n <= n_max);
Assert(r >= 0);
Assert(n - r >= 0);
return fac_inv[n] * fac[r] * fac[n - r];
}
// 多項係数 nC[rs] を返す．
mint mul(const vi& rs) const {
// verify : https://yukicoder.me/problems/no/2141
if (*min_element(all(rs)) < 0) return 0;
int n = accumulate(all(rs), 0);
Assert(n <= n_max);
mint res = fac[n];
repe(r, rs) res *= fac_inv[r];
return res;
}
// 重複組合せの数 nHr = n+r-1Cr を返す（0H0 = 1 とする）
mint hom(int n, int r) {
// verify : https://mojacoder.app/users/riantkb/problems/toj_ex_2
if (n == 0) return (int)(r == 0);
Assert(n + r - 1 <= n_max);
if (r < 0 || n - 1 < 0) return 0;
return fac[n + r - 1] * fac_inv[r] * fac_inv[n - 1];
}
// 負の二項係数 nCr を返す（n ≦ 0, r ≧ 0）
mint neg_bin(int n, int r) {
// verify : https://atcoder.jp/contests/abc345/tasks/abc345_g
if (n == 0) return (int)(r == 0);
Assert(-n + r - 1 <= n_max);
if (r < 0 || -n - 1 < 0) return 0;
return (r & 1 ? -1 : 1) * fac[-n + r - 1] * fac_inv[r] * fac_inv[-n - 1];
}
// ポッホハマー記号 x^(n) を返す（n ≧ 0）
mint pochhammer(int x, int n) {
// verify : https://atcoder.jp/contests/agc070/tasks/agc070_c
int x2 = x + n - 1;
if (x <= 0 && 0 <= x2) return 0;
if (x > 0) {
Assert(x2 <= n_max);
return fac[x2] * fac_inv[x - 1];
}
else {
Assert(-x <= n_max);
return (n & 1 ? -1 : 1) * fac[-x] * fac_inv[-x2 - 1];
}
}
// ポッホハマー記号の逆数 1/x^(n) を返す（n ≧ 0）
mint pochhammer_inv(int x, int n) {
// verify : https://atcoder.jp/contests/agc070/tasks/agc070_c
int x2 = x + n - 1;
Assert(!(x <= 0 && 0 <= x2));
if (x > 0) {
Assert(x2 <= n_max);
return fac_inv[x2] * fac[x - 1];
}
else {
Assert(-x <= n_max);
return (n & 1 ? -1 : 1) * fac_inv[-x] * fac[-x2 - 1];
}
}
};
// O(N^3)
vm TLE(int n, int m) {
Factorial_mint fm(n + 10);
vm c(n + 1);
repi(x, 0, n) {
//dump("-------------- x:", x, "-----------------");
vvm dp(n + 1, vm(x + 1));
dp[0][0] = 1;
rep(i, n) repi(j, 0, min(i, x)) {
int k = min(i + m, x) - j;
dp[i + 1][j] += dp[i][j] * (i + m - k);
if (j + 1 <= x) {
dp[i + 1][j + 1] += dp[i][j] * k;
}
}
//dumpel(dp);
c[x] = dp[n][x];
}
//dump(c);
// rep(i, n) c[i] -= c[i + 1];
return c;
}
void zikken() {
int N = 10;
vvvm tbl(N, vvm(N));
repi(n, 1, N) repi(m, 1, N) {
tbl[n - 1][m - 1] = TLE(n, m);
}
dump_math(tbl); // 3D P-recursive．
exit(0);
}
/*
{{{1,1},{2,1},{3,1},{4,1},{5,1},{6,1},{7,1},{8,1},{9,1},{10,1}},{{2,2,1},{6,4,2},{12,6,2},{20,8,2},{30,10,2},{42,12,2},{56,14,2},{72,16,2},{90,18,2},{110,20,2}},{{6,6,4,1},{24,18,12,4},{60,36,18,6},{120,60,24,6},{210,90,30,6},{336,126,36,6},{504,168,42,6},{720,216,48,6},{990,270,54,6},{1320,330,60,6}},{{24,24,18,8,1},{120,96,72,36,8},{360,240,144,72,18},{840,480,240,96,24},{1680,840,360,120,24},{3024,1344,504,144,24},{5040,2016,672,168,24},{7920,2880,864,192,24},{11880,3960,1080,216,24},{17160,5280,1320,240,24}},{{120,120,96,54,16,1},{720,600,480,288,108,16},{2520,1800,1200,720,288,54},{6720,4200,2400,1200,480,96},{15120,8400,4200,1800,600,120},{30240,15120,6720,2520,720,120},{55440,25200,10080,3360,840,120},{95040,39600,14400,4320,960,120},{154440,59400,19800,5400,1080,120},{240240,85800,26400,6600,1200,120}},{{720,720,600,384,162,32,1},{5040,4320,3600,2400,1152,324,32},{20160,15120,10800,7200,3600,1152,162},{60480,40320,25200,14400,7200,2400,384},{151200,90720,50400,25200,10800,3600,600},{332640,181440,90720,40320,15120,4320,720},{665280,332640,151200,60480,20160,5040,720},{1235520,570240,237600,86400,25920,5760,720},{2162160,926640,356400,118800,32400,6480,720},{3603600,1441440,514800,158400,39600,7200,720}},{{5040,5040,4320,3000,1536,486,64,1},{40320,35280,30240,21600,12000,4608,972,64},{181440,141120,105840,75600,43200,18000,4608,486},{604800,423360,282240,176400,100800,43200,12000,1536},{1663200,1058400,635040,352800,176400,75600,21600,3000},{3991680,2328480,1270080,635040,282240,105840,30240,4320},{8648640,4656960,2328480,1058400,423360,141120,35280,5040},{17297280,8648640,3991680,1663200,604800,181440,40320,5040},{32432400,15135120,6486480,2494800,831600,226800,45360,5040},{57657600,25225200,10090080,3603600,1108800,277200,50400,5040}},{{40320,40320,35280,25920,15000,6144,1458,128,1},{362880,322560,282240,211680,129600,60000,18432,2916,128},{1814400,1451520,1128960,846720,529200,259200,90000,18432,1458},{6652800,4838400,3386880,2257920,1411200,705600,259200,60000,6144},{19958400,13305600,8467200,5080320,2822400,1411200,529200,129600,15000},{51891840,31933440,18627840,10160640,5080320,2257920,846720,211680,25920},{121080960,69189120,37255680,18627840,8467200,3386880,1128960,282240,35280},{259459200,138378240,69189120,31933440,13305600,4838400,1451520,322560,40320},{518918400,259459200,121080960,51891840,19958400,6652800,1814400,362880,40320},{980179200,461260800,201801600,80720640,28828800,8870400,2217600,403200,40320}},{{362880,362880,322560,246960,155520,75000,24576,4374,256,1},{3628800,3265920,2903040,2257920,1481760,777600,300000,73728,8748,256},{19958400,16329600,13063680,10160640,6773760,3704400,1555200,450000,73728,4374},{79833600,59875200,43545600,30481920,20321280,11289600,4939200,1555200,300000,24576},{259459200,179625600,119750400,76204800,45722880,25401600,11289600,3704400,777600,75000},{726485760,467026560,287400960,167650560,91445760,45722880,20321280,6773760,1481760,155520},{817970047,91484287,622702080,335301120,167650560,76204800,30481920,10160640,2257920,246960},{158369788,338644094,247159807,622702080,287400960,119750400,43545600,13063680,2903040,322560},{835657976,677288188,338644094,91484287,467026560,179625600,59875200,16329600,3265920,362880},{673071599,835657976,158369788,817970047,726485760,259459200,79833600,19958400,3628800,362880}},{{3628800,3628800,3265920,2580480,1728720,933120,375000,98304,13122,512,1},{39916800,36288000,32659200,26127360,18063360,10372320,4665600,1500000,294912,26244,512},{239500800,199584000,163296000,130636800,91445760,54190080,25930800,9331200,2250000,294912,13122},{39592447,798336000,598752000,435456000,304819200,182891520,90316800,34574400,9331200,1500000,98304},{637695741,598103294,798011647,199259647,762048000,457228800,228614400,90316800,25930800,4665600,375000},{914842870,277147129,677288188,877520894,678261247,914457600,457228800,182891520,54190080,10372320,933120},{110344163,193745646,914842870,237554682,358278141,678261247,762048000,304819200,91445760,18063360,1728720},{695797690,585453527,391707881,475109364,237554682,877520894,199259647,435456000,130636800,26127360,2580480},{68178273,370624936,783415762,391707881,914842870,677288188,798011647,598752000,163296000,32659200,3265920},{809428145,741249872,370624936,585453527,193745646,277147129,598103294,798336000,199584000,36288000,3628800}}};
*/
// O(N M)
vm TLE2(int n, int m) {
Factorial_mint fm(n + m + 10);
vvm dp(n + 2, vm(m + 1));
repi(j, 1, m) dp[1][j] = fm.fact(n + j - 1) * fm.fact_inv(j - 1);
repi(i, 1, n + 1) dp[i][1] = mint(2 + n - i).pow(i - 1) * fm.fact(n - i + 1);
repi(i, 2, n + 1) repi(j, 2, m) {
// よく見ると斜め方向なら 1D P-recursive．
dp[i][j] = (2 + n - i) * dp[i - 1][j - 1] * fm.inv(j - 1);
}
dumpel(dp);
vm c(n + 1);
repi(i, 0, n) c[i] = dp[i + 1][m];
rep(i, n) c[i] -= c[i + 1];
return c;
}
// O(N + M) くらい
vm solve(int n, int m) {
Factorial_mint fm(n + m + 10);
vm c(n + 1);
repi(I, 1, n + 1) {
int L = min(I - 1, m - 1);
if (L == I - 1) {
int j = m - L;
c[I - 1] = fm.fact(n + j - 1) * fm.fact_inv(j - 1);
}
else {
int i = I - L;
c[I - 1] = mint(2 + n - i).pow(i - 1) * fm.fact(n - i + 1);
}
dump(c[I - 1]);
// これでいい．
int J = m;
c[I - 1] *= fm.pochhammer(2 + n - I, L) * fm.perm_inv(J - 1, L);
}
dump(c);
rep(i, n) c[i] -= c[i + 1];
return c;
}
int main() {
// input_from_file("input.txt");
// output_to_file("output.txt");
// zikken();
int n, m;
cin >> n >> m;
dump(TLE(n, m)); dump("======");
dump(TLE2(n, m)); dump("======");
auto res = solve(n, m);
repi(i, 0, n) cout << res[i] << "\n";
}