#840311 (C++17(gcc12)) No.1761 Sequence Distance

• 問題: No.1761 Sequence Distance
• ユーザー: ecottea
• 提出日時: 2023-02-16 02:30:30
• 言語: C++17(gcc12) (gcc 12.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 1,316 ms / 8,000 ms
• コード長: 8,191 bytes
• コンパイル時間: 3,983 ms
• コンパイル使用メモリ: 274,640 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-07-18 07:42:56
• 合計ジャッジ時間: 16,582 ms
• ジャッジサーバーID （参考情報）: judge3 / judge2

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	1 ms; 5,248 KB
testcase_01	AC	2 ms; 5,376 KB
testcase_02	AC	329 ms; 5,376 KB
testcase_03	AC	2 ms; 5,376 KB
testcase_04	AC	1 ms; 5,376 KB
testcase_05	AC	2 ms; 5,376 KB
testcase_06	AC	5 ms; 5,376 KB
testcase_07	AC	2 ms; 5,376 KB
testcase_08	AC	4 ms; 5,376 KB
testcase_09	AC	2 ms; 5,248 KB
testcase_10	AC	3 ms; 5,376 KB
testcase_11	AC	5 ms; 5,376 KB
testcase_12	AC	2 ms; 5,376 KB
testcase_13	AC	3 ms; 5,376 KB
testcase_14	AC	2 ms; 5,376 KB
testcase_15	AC	3 ms; 5,376 KB
testcase_16	AC	3 ms; 5,376 KB
testcase_17	AC	2 ms; 5,376 KB
testcase_18	AC	5 ms; 5,376 KB
testcase_19	AC	2 ms; 5,376 KB
testcase_20	AC	3 ms; 5,376 KB
testcase_21	AC	230 ms; 5,376 KB
testcase_22	AC	17 ms; 5,376 KB
testcase_23	AC	1,018 ms; 5,376 KB
testcase_24	AC	305 ms; 5,376 KB
testcase_25	AC	854 ms; 5,376 KB
testcase_26	AC	975 ms; 5,376 KB
testcase_27	AC	306 ms; 5,376 KB
testcase_28	AC	252 ms; 5,376 KB
testcase_29	AC	729 ms; 5,376 KB
testcase_30	AC	134 ms; 5,376 KB
testcase_31	AC	387 ms; 5,376 KB
testcase_32	AC	24 ms; 5,376 KB
testcase_33	AC	508 ms; 5,376 KB
testcase_34	AC	5 ms; 5,376 KB
testcase_35	AC	45 ms; 5,376 KB
testcase_36	AC	662 ms; 5,376 KB
testcase_37	AC	75 ms; 5,376 KB
testcase_38	AC	142 ms; 5,376 KB
testcase_39	AC	365 ms; 5,376 KB
testcase_40	AC	127 ms; 5,376 KB
testcase_41	AC	1,139 ms; 5,376 KB
testcase_42	AC	1,316 ms; 5,376 KB
testcase_43	AC	1,315 ms; 5,376 KB
testcase_44	AC	2 ms; 5,376 KB

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; // -2^63 ～ 2^63 = 9 * 10^18（int は -2^31 ～ 2^31 = 2 * 10^9）
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 vl = vector<ll>;		using vvl = vector<vl>;		using vvvl = vector<vvl>;
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);
const vi DX = { 1, 0, -1, 0 }; // 4 近傍（下，右，上，左）
const vi DY = { 0, 1, 0, -1 };
int INF = 1001001001; ll INFL = 4004004004004004004LL;
double EPS = 1e-12;

// 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 < (1 << int(d)); ++set) // d ビット全探索（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 smod(n, m) ((((n) % (m)) + (m)) % (m)) // 非負mod
#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

// 汎用関数の定義
template <class T> inline ll pow(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）

// 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; }

// 手元環境（Visual Studio）
#ifdef _MSC_VER
#include "local.hpp"
// 提出用（gcc）
#else
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) : -1; }
inline int lsb(ll n) { return n != 0 ? __builtin_ctzll(n) : -1; }
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 gcd __gcd
#define dump(...)
#define dumpel(v)
#define dump_list(v)
#define dump_list2D(v)
#define input_from_file(f)
#define output_to_file(f)
#define Assert(b) { if (!(b)) while (1) cout << "OLE"; }
#endif

#endif // 折りたたみ用


#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;

//using mint = modint1000000007;
using mint = modint998244353;
//using mint = modint; // mint::set_mod(m);

istream& operator>>(istream& is, mint& x) { ll x_; is >> x_; x = x_; return is; }
ostream& operator<<(ostream& os, const mint& x) { os << x.val(); return os; }
using vm = vector<mint>; using vvm = vector<vm>; using vvvm = vector<vvm>;
#endif


template <class T>
T naive(int n, int m) {
	vector<vector<vector<T>>> dp(n + 1, vector<vector<T>>(n + 1, vector<T>(m + 1)));
	vector<vector<vector<T>>> acc(n + 1, vector<vector<T>>(n + 1, vector<T>(m + 1)));
	dp[0][0][0] = 1;
	
	repi(i1, 1, n) repi(i2, 1, n) repi(j, 0, m) {
		acc[i1][i2][j] = acc[i1 - 1][i2][j] + acc[i1][i2 - 1][j]
			- acc[i1 - 1][i2 - 1][j] + dp[i1 - 1][i2 - 1][j];
		
		int nj = j - abs(i1 - i2);
		if (nj >= 0) dp[i1][i2][j] += acc[i1][i2][nj];
	}

	T res = 0;
	repi(i1, 0, n) repi(i2, 0, n) res += dp[i1][i2][m];

	return res;
}


void zikken() {
	int N = 20;
	vvl a(N, vl(N));

	rep(n, N) rep(m, N) a[m][n] = naive<ll>(n, m);
	dump_list2D(a);

	exit(0);
}
/*
{{1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768,65536,131072,262144,524288},
{0,0,2,8,24,64,160,384,896,2048,4608,10240,22528,49152,106496,229376,491520,1048576,2228224,4718592},
{0,0,0,4,20,72,224,640,1728,4480,11264,27648,66560,157696,368640,851968,1949696,4423680,9961472,22282240},
{0,0,0,0,8,48,200,704,2240,6656,18816,51200,135168,348160,878592,2179072,5324800,12845056,30638080,72351744},
{0,0,0,0,2,24,136,592,2224,7584,24128,72832,210944,590848,1609728,4284416,11177984,28663808,72400896,180453376},
{0,0,0,0,0,8,72,400,1792,7040,25248,84608,268928,819200,2409472,6881280,19165184,52232192,139681792,367362048},
{0,0,0,0,0,4,40,256,1304,5760,22976,84800,294336,971904,3079168,9420800,27975680,80957440,229048320,635256832},
{0,0,0,0,0,0,18,152,888,4352,19040,76544,287744,1023744,3478144,11362304,35885056,110051328,328904704,960790528},
{0,0,0,0,0,0,8,92,604,3208,15072,64896,260832,990208,3581312,12422400,41548032,134584832,423781376,1301170176},
{0,0,0,0,0,0,2,48,392,2304,11600,52992,225280,903552,3449472,12616448,44435456,151343104,500244992,1609582592},
{0,0,0,0,0,0,0,24,250,1640,8824,42464,189248,794624,3175040,12153088,44784000,159506432,550928384,1850614784},
{0,0,0,0,0,0,0,8,144,1120,6568,33440,155904,681856,2833760,11278720,43219840,160083968,574948352,2007638016},
{0,0,0,0,0,0,0,4,84,764,4864,26128,126992,576064,2477952,10201408,40435008,154953088,575923200,2081435648},
{0,0,0,0,0,0,0,0,40,488,3514,20152,102360,481024,2135552,9060352,36993280,146042880,559348736,2083796992},
{0,0,0,0,0,0,0,0,18,304,2504,15428,81988,398664,1822496,7945088,33306016,134978560,530804608,2031044608},
{0,0,0,0,0,0,0,0,8,176,1726,11624,65088,328080,1543512,6902080,29635776,122956544,495003648,1939467264},
{0,0,0,0,0,0,0,0,2,100,1168,8672,51370,268728,1300456,5956656,26147344,110813472,455597760,1823197312},
{0,0,0,0,0,0,0,0,0,48,750,6312,40072,218680,1090184,5113712,22922304,99071360,415180480,1693380864},
{0,0,0,0,0,0,0,0,0,24,472,4528,30980,177020,910360,4372896,20000520,88046464,375518528,1558339968},
{0,0,0,0,0,0,0,0,0,8,278,3144,23560,142064,756370,3725016,17383032,77885888,337691584,1423864064}}
*/


mint solve(int n, int m) {
	int K = (int)(sqrt(m) + 1);

	// dp_i[j][k] : 長さ i，総和 j, 高さ k のパスのスコア和
	vvm dp(m + 1, vm(K + 1));
	dp[0][0] = 1;

	rep(i, n) {
		vvm ndp(m + 1, vm(K + 1));

		repi(j, 0, m) repi(k, 0, K) {
			// 上がる
			if (j + k + 1 <= m && k + 1 <= K) {
				ndp[j + k + 1][k + 1] += dp[j][k] * (k == 0 ? 2 : 1);
			}

			// 水平
			if (j + k <= m) ndp[j + k][k] += dp[j][k] * 2;

			// 下がる
			if (j + k - 1 <= m && k - 1 >= 0) {
				ndp[j + k - 1][k - 1] += dp[j][k];
			}
		}

		dp = move(ndp);
		dump("------", i, "------"); dumpel(dp);
	}

	return dp[m][0];
}


int main() {
//	input_from_file("input.txt");
//	output_to_file("output.txt");
	
//	zikken();

	int n, m;
	cin >> n >> m;

	dump(naive<mint>(n, m));

	cout << solve(n, m) << endl;
}