結果

問題 No.2503 Typical Path Counting Problem on a Grid
ユーザー Алексей ДанилюкАлексей Данилюк
提出日時 2023-10-13 22:07:26
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 240 ms / 2,000 ms
コード長 6,603 bytes
コンパイル時間 1,303 ms
コンパイル使用メモリ 127,360 KB
実行使用メモリ 42,612 KB
最終ジャッジ日時 2023-10-13 22:07:34
合計ジャッジ時間 4,084 ms
ジャッジサーバーID
（参考情報） 		judge13 / judge14
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 122 ms
42,612 KB
testcase_01 AC 132 ms
42,612 KB
testcase_02 AC 131 ms
42,540 KB
testcase_03 AC 172 ms
42,572 KB
testcase_04 AC 240 ms
42,572 KB
testcase_05 AC 158 ms
42,604 KB
testcase_06 AC 223 ms
42,576 KB
testcase_07 AC 226 ms
42,552 KB
testcase_08 AC 178 ms
42,580 KB
testcase_09 AC 240 ms
42,600 KB
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ソースコード

diff # 

//#pragma GCC optimize("Ofast")
//#pragma GCC target("avx,avx2,fma")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4.1,sse4.2,sse4a,avx,avx2,popcnt,tune=native")
#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <cmath>
#include <vector>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <queue>
#include <ctime>
#include <cassert>
#include <complex>
#include <string>
#include <cstring>
#include <chrono>
#include <random>
#include <bitset>
#include <array>
#include <climits>
using namespace std;

#ifdef LOCAL
	#define eprintf(...) {fprintf(stderr, __VA_ARGS__);fflush(stderr);}
#else
	#define eprintf(...) 42
#endif

using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int, int>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
ll myRand(ll B) {
	return (ull)rng() % B;
}

#define mp make_pair
#define all(x) (x).begin(),(x).end()

clock_t startTime;
double getCurrentTime() {
	return (double)(clock() - startTime) / CLOCKS_PER_SEC;
}

ll floor_div(ll x, ll y) {
	assert(y != 0);
	if (y < 0) {
		y = -y;
		x = -x;
	}
	if (x >= 0) return x / y;
	return (x + 1) / y - 1;
}
ll ceil_div(ll x, ll y) {
	assert(y != 0);
	if (y < 0) {
		y = -y;
		x = -x;
	}
	if (x <= 0) return x / y;
	return (x - 1) / y + 1;
}


const uint MOD = 998244353;
template<uint mod = MOD> struct mint { // 1000000007  1000000009
	uint x;

	mint() : x(0) {}
	mint(ll _x) {
		_x %= mod;
		if (_x < 0) _x += mod;
		x = _x;
	}

	mint& operator += (const mint &a) {
		x += a.x;
		if (x >= mod) x -= mod;
		return *this;
	}
	mint& operator -= (const mint &a) {
		x += mod - a.x;
		if (x >= mod) x -= mod;
		return *this;
	}
	mint& operator *= (const mint &a) {
		x = (ull)x * a.x % mod;
		return *this;
	}
	mint pow(ll pw) const {
		mint res = 1;
		mint cur = *this;
		while(pw) {
			if (pw & 1) res *= cur;
			cur *= cur;
			pw >>= 1;
		}
		return res;
	}
	mint inv() const {
		assert(x != 0);
		uint t = x;
		uint res = 1;
		while(t != 1) {
			uint z = mod / t;
			res = (ull)res * (mod - z) % mod;
			t = mod - t * z;
		}
		return res;
	}
	mint& operator /= (const mint &a) {
		return *this *= a.inv();
	}
	mint operator + (const mint &a) const {
		return mint(*this) += a;
	}
	mint operator - (const mint &a) const {
		return mint(*this) -= a;
	}
	mint operator * (const mint &a) const {
		return mint(*this) *= a;
	}
	mint operator / (const mint &a) const {
		return mint(*this) /= a;
	}

	bool sqrt(mint &res) const {
		if (mod == 2 || x == 0) {
			res = *this;
			return true;
		}
		if (pow((mod - 1) / 2) != 1) return false;
		if (mod % 4 == 3) {
			res = pow((mod + 1) / 4);
			return true;
		}
		int pw = (mod - 1) / 2;
		int K = 30;
		while((1 << K) > pw) K--;
		while(true) {
			mint t = myRand(mod);
			mint a = 0, b = 0, c = 1;
			for (int k = K; k >= 0; k--) {
				a = b * b;
				b = b * c * 2;
				c = c * c + a * *this;
				if (((pw >> k) & 1) == 0) continue;
				a = b;
				b = b * t + c;
				c = c * t + a * *this;
			}
			if (b == 0) continue;
			c -= 1;
			c *= mint() - b.inv();
			if (c * c == *this) {
				res = c;
				return true;
			}
		}
		assert(false);
	}

	bool operator == (const mint &a) const {
		return x == a.x;
	}
	bool operator != (const mint &a) const {
		return x != a.x;
	}
	bool operator < (const mint &a) const {
		return x < a.x;
	}
};
template<uint mod = MOD> struct Factorials {
	using Mint = mint<mod>;
	vector<Mint> f, fi;

	Factorials() : f(), fi() {}
	Factorials(int n) {
		n += 10;
		f = vector<Mint>(n);
		fi = vector<Mint>(n);
		f[0] = 1;
		for (int i = 1; i < n; i++)
			f[i] = f[i - 1] * i;
		fi[n - 1] = f[n - 1].inv();
		for (int i = n - 1; i > 0; i--)
			fi[i - 1] = fi[i] * i;
	}

	Mint C(int n, int k) {
		if (k < 0 || k > n) return 0;
		return f[n] * fi[k] * fi[n - k];
	}
};
template<uint mod = MOD> struct Powers {
	using Mint = mint<mod>;
	vector<Mint> p, pi;

	Powers() : p(), pi() {}
	Powers(int n, Mint x) {
		n += 10;
		if (x == 0) {
			p = vector<Mint>(n);
			p[0] = 1;
		} else {
			p = vector<Mint>(n);
			pi = vector<Mint>(n);
			p[0] = pi[0] = 1;
			Mint xi = x.inv();
			for (int i = 1; i < n; i++) {
				p[i] = p[i - 1] * x;
				pi[i] = pi[i - 1] * xi;
			}
		}
	}

	Mint pow(int n) {
		if (n >= 0)
			return p[n];
		else
			return pi[-n];
	}
};
template<uint mod = MOD> struct Inverses {
	using Mint = mint<mod>;
	vector<Mint> ii;

	Inverses() : ii() {}
	Inverses(int n) {
		n += 10;
		ii = vector<Mint>(n);
		ii[1] = 1;
		for (int x = 2; x < n; x++)
			ii[x] = Mint() - ii[mod % x] * (mod / x);
	}

	Mint inv(Mint x) {
		assert(x != 0);
		uint t = x.x;
		uint res = 1;
		while(t >= (int)ii.size()) {
			uint z = mod / t;
			res = (ull)res * (mod - z) % mod;
			t = mod - t * z;
		}
		return ii[t] * res;
	}
};
using Mint = mint<>;

struct Matrix {
	Mint a[2][2];

	Matrix() {
		a[0][0] = a[1][1] = 1;
		a[0][1] = a[1][0] = 0;
	}

	Matrix operator * (const Matrix &A) const {
		Matrix R = Matrix();
		for (int i = 0; i < 2; i++)
			for (int j = 0; j < 2; j++) {
				R.a[i][j] = 0;
				for (int h = 0; h < 2; h++)
					R.a[i][j] += a[i][h] * A.a[h][j];
			}
		return R;
	}
};

Matrix bin_pow(Matrix A, ll p) {
	if (p == 0) return Matrix();
	if (p & 1) return A * bin_pow(A, p - 1);
	return bin_pow(A * A, p / 2);
}

const int N = (int)1e7 + 77;
Mint dp[N];

void solve() {
	ll n, m;
	scanf("%lld%lld", &n, &m);
	if (n > m) swap(n, m);
	m -= n;
	n++;
	/*
	if (m == 0) {
		Mint ans = dp[n] * dp[n] + dp[n - 1] * dp[n - 1] * (n - 1);
		printf("%u\n", ans.x);
		return;
	}
	*/
	Matrix A = Matrix();
	A.a[0][0] = A.a[1][1] = 0;
	A.a[0][0] = 2 * n - 1;
	A.a[0][1] = 1;
	A.a[1][0] = n - 1;
	A.a[1][1] = 0;
	A = bin_pow(A, m);
	Mint ans = 0;
	ans += dp[n] * (A.a[0][0] * dp[n] + A.a[0][1] * dp[n - 1] * (n - 1));
	ans += dp[n - 1] * (A.a[1][0] * dp[n] + A.a[1][1] * dp[n - 1] * (n - 1));
	printf("%u\n", ans.x);
	return;
}

int main() {
	startTime = clock();
//	freopen("input.txt", "r", stdin);
//	freopen("output.txt", "w", stdout);

	dp[1] = 1;
	for (int i = 1; i + 3 < N; i++) {
		dp[i + 1] += dp[i] * 2 * i;
		dp[i + 2] += dp[i] * i;
	}


	int t;
	scanf("%d", &t);
	for (int i = 1; i <= t; i++) {
		eprintf("--- Case #%d start ---\n", i);
		//printf("Case #%d: ", i);

		solve();

		//printf("%lld\n", (ll)solve());

		/*
		if (solve()) {
			printf("Yes\n");
		} else {
			printf("No\n");
		}
		*/

		eprintf("--- Case #%d end ---\n", i);
		eprintf("time = %.5lf\n", getCurrentTime());
		eprintf("++++++++++++++++++++\n");
	}


	return 0;
}
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