#742281 (C++17) No.1856 Mex Sum 2

• 問題: No.1856 Mex Sum 2
• ユーザー: kwm_t
• 提出日時: 2022-02-26 19:12:28
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 1,461 ms / 3,000 ms
• コード長: 3,392 bytes
• コンパイル時間: 4,790 ms
• コンパイル使用メモリ: 269,504 KB
• 実行使用メモリ: 36,224 KB
• 最終ジャッジ日時: 2023-09-17 21:48:42
• 合計ジャッジ時間: 44,829 ms
• ジャッジサーバーID （参考情報）: judge12 / judge13

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	5 ms; 4,412 KB
testcase_01	AC	4 ms; 4,416 KB
testcase_02	AC	8 ms; 4,644 KB
testcase_03	AC	5 ms; 4,508 KB
testcase_04	AC	5 ms; 4,528 KB
testcase_05	AC	5 ms; 4,592 KB
testcase_06	AC	5 ms; 4,476 KB
testcase_07	AC	5 ms; 4,640 KB
testcase_08	AC	5 ms; 4,472 KB
testcase_09	AC	5 ms; 4,428 KB
testcase_10	AC	5 ms; 4,580 KB
testcase_11	AC	5 ms; 4,532 KB
testcase_12	AC	5 ms; 4,500 KB
testcase_13	AC	5 ms; 4,504 KB
testcase_14	AC	4 ms; 4,588 KB
testcase_15	AC	5 ms; 4,692 KB
testcase_16	AC	5 ms; 4,648 KB
testcase_17	AC	7 ms; 4,412 KB
testcase_18	AC	5 ms; 4,428 KB
testcase_19	AC	5 ms; 4,612 KB
testcase_20	AC	5 ms; 4,416 KB
testcase_21	AC	5 ms; 4,460 KB
testcase_22	AC	7 ms; 4,416 KB
testcase_23	AC	4 ms; 4,644 KB
testcase_24	AC	7 ms; 4,640 KB
testcase_25	AC	7 ms; 4,536 KB
testcase_26	AC	5 ms; 4,412 KB
testcase_27	AC	4 ms; 4,420 KB
testcase_28	AC	4 ms; 4,428 KB
testcase_29	AC	300 ms; 10,884 KB
testcase_30	AC	156 ms; 7,936 KB
testcase_31	AC	288 ms; 10,888 KB
testcase_32	AC	439 ms; 13,320 KB
testcase_33	AC	494 ms; 15,332 KB
testcase_34	AC	287 ms; 10,612 KB
testcase_35	AC	160 ms; 7,840 KB
testcase_36	AC	72 ms; 5,956 KB
testcase_37	AC	278 ms; 10,252 KB
testcase_38	AC	54 ms; 5,696 KB
testcase_39	AC	7 ms; 4,940 KB
testcase_40	AC	10 ms; 4,868 KB
testcase_41	AC	10 ms; 4,964 KB
testcase_42	AC	1,377 ms; 34,000 KB
testcase_43	AC	1,160 ms; 28,080 KB
testcase_44	AC	1,249 ms; 30,740 KB
testcase_45	AC	1,372 ms; 33,716 KB
testcase_46	AC	1,162 ms; 28,392 KB
testcase_47	AC	1,262 ms; 30,980 KB
testcase_48	AC	1,398 ms; 34,688 KB
testcase_49	AC	1,388 ms; 34,444 KB
testcase_50	AC	999 ms; 24,112 KB
testcase_51	AC	1,450 ms; 35,996 KB
testcase_52	AC	1,448 ms; 35,724 KB
testcase_53	AC	1,458 ms; 36,080 KB
testcase_54	AC	1,450 ms; 36,064 KB
testcase_55	AC	1,457 ms; 36,032 KB
testcase_56	AC	1,451 ms; 36,080 KB
testcase_57	AC	1,461 ms; 35,996 KB
testcase_58	AC	1,455 ms; 36,000 KB
testcase_59	AC	1,449 ms; 36,224 KB
testcase_60	AC	1,445 ms; 36,056 KB
testcase_61	AC	1,453 ms; 36,136 KB
testcase_62	AC	1,452 ms; 36,012 KB
testcase_63	AC	1,460 ms; 36,116 KB
testcase_64	AC	1,452 ms; 36,040 KB
testcase_65	AC	1,454 ms; 36,116 KB
testcase_66	AC	1,455 ms; 36,112 KB

ソースコード

#include <bits/stdc++.h>
#include <atcoder/all>
using namespace std;
using namespace atcoder;
//using mint = modint1000000007;
//const int mod = 1000000007;
using mint = modint998244353;
const int mod = 998244353;
//const int INF = 1e9;
//const long long LINF = 1e18;
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define rep2(i,l,r)for(int i=(l);i<(r);++i)
#define rrep(i, n) for (int i = (n-1); i >= 0; --i)
#define rrep2(i,l,r)for(int i=(r-1);i>=(l);--i)
#define all(x) (x).begin(),(x).end()
#define allR(x) (x).rbegin(),(x).rend()
#define endl "\n"
#define P pair<int,int>
template<typename A, typename B> inline bool chmax(A & a, const B & b) { if (a < b) { a = b; return true; } return false; }
template<typename A, typename B> inline bool chmin(A & a, const B & b) { if (a > b) { a = b; return true; } return false; }
// combination mod prime
// https://www.youtube.com/watch?v=8uowVvQ_-Mo&feature=youtu.be&t=1619
struct combination {
	vector<mint> fact, ifact;
	combination(int n) :fact(n + 1), ifact(n + 1) {
		assert(n < mod);
		fact[0] = 1;
		for (int i = 1; i <= n; ++i) fact[i] = fact[i - 1] * i;
		ifact[n] = fact[n].inv();
		for (int i = n; i >= 1; --i) ifact[i - 1] = ifact[i] * i;
	}
	mint operator()(int n, int k) { return com(n, k); }
	mint com(int n, int k) {
		//負の二項係数を考慮する場合にコメントアウトを外す
		//if (n < 0) return com(-n, k) * (k % 2 ? -1 : 1);
		if (k < 0 || k > n) return 0;
		return fact[n] * ifact[k] * ifact[n - k];
	}
	mint inv(int n, int k) {
		//if (n < 0) return inv(-n, k) * (k % 2 ? -1 : 1);
		if (k < 0 || k > n) return 0;
		return ifact[n] * fact[k] * fact[n - k];
	}
	mint p(int n, int k) { return fact[n] * ifact[n - k]; }
}c(200005);
int main() {
	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	int n, m; cin >> n >> m;
	int maxmex = min(n, m + 1);
	//dp[i][j]:=長さがjで[0,i)で構成されたmexがiの数列の数
	vector<vector<mint>> dp(maxmex + 1, vector<mint>(n + 1));
	dp[0][0] = 1;
	rep(i, maxmex) {
		vector<mint>x = dp[i];
		rep(j, x.size())x[j] *= c.ifact[j];
		vector<mint>y(n + 1);
		rep2(j, 1, y.size())y[j] = c.ifact[j];
		auto z = convolution(x, y);
		rep(j, n + 1)dp[i + 1][j] = z[j] * c.fact[j];
	}
	/*rep(i, maxmex + 1) {
		rep(j, n + 1) cout << dp[i][j].val() << " ";
		cout << endl;
	}*/

	//dp2[i][j]:=長さがjでmexがiの数列の数
	vector<vector<mint>> dp2(maxmex + 1, vector<mint>(n + 1));
	rep(i, maxmex + 1) {
		vector<mint>x(n + 1);
		rep(j, n + 1)x[j] = c.ifact[j] * pow_mod(max(0, m - i), j, mod);
		vector<mint>y = dp[i];
		rep(j, y.size())y[j] *= c.ifact[j];
		auto z = convolution(x, y);
		rep(j, n + 1)dp2[i][j] = z[j] * c.fact[j];
		/*cout << endl;
		rep(j, x.size()) cout << x[j].val() << " ";
		cout << endl;
		rep(j, y.size()) cout << y[j].val() << " ";
		cout << endl;
		rep(j, z.size()) cout << z[j].val() << " ";
		cout << endl;*/
	}
	/*rep(i, maxmex + 1) {
		rep(j, n + 1) cout << dp2[i][j].val() << " ";
		cout << endl;
	}*/







	mint ans = 0;
	/*rep2(i, 1, n + 1) {//数列の長さ
		rep(j, maxmex + 1) {//mex
			rep(k, i + 1) {//以下の数。
				if ((m - j < 0) && (i - k > 0))continue;
				ans += c(n, i) * pow_mod(m + 1, n - i, mod)*j * dp[j][k] * c(i, k)*pow_mod(m - j, i - k, mod);
			}
		}
	}*/
	rep2(i, 1, n + 1) {
		rep(j, maxmex + 1)ans += c(n, i) * pow_mod(m + 1, n - i, mod) * dp2[j][i] * j;
	}
	cout << ans.val() << endl;
	return 0;
}