Submission #956055

#	Time	Username	Problem	Language	Result	Execution time	Memory
956055		frodakcin	Festivals in JOI Kingdom 2 (JOI23_festival2)	C++17	100 / 100	3945 ms	1996 KiB

festival2

#include <iostream>
#include <vector>
#include <cassert>
using ll = long long;

int MOD = 998244353;

#ifdef LOCAL
template<typename T>
struct vector: std::vector<T> {
	template<typename... V> vector(V&&... args): std::vector<T>(std::forward<V>(args)...) {}
	T& operator [](size_t idx) {return vector::at(idx);}
	T const& operator[](size_t idx) const {return vector::at(idx);}
};
#else
using std::vector;
#endif
using std::pair, std::cin, std::cout;

#define rep(i, a, b) for(int i = a; i < (b); ++i)
#define all(x) std::begin(x), std::end(x)
#define sz(x) (int)(x).size()
typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;

ll euclid(ll a, ll b, ll &x, ll &y) {
	if (!b) return x = 1, y = 0, a;
	ll d = euclid(b, a % b, y, x);
	return y -= a/b * x, d;
}

struct mint {
	int v;
	explicit operator int() {return v;}
	mint(): v(0) {}
	mint(int z) {
		if(z < -MOD || MOD <= z) z %= MOD;
		if (z < 0) z += MOD;
		v = z;
	}
	mint(ll z) {
		z %= MOD;
		if (z < 0) z += MOD;
		v = z;
	}
	friend mint invert(mint a) {
		ll x, y, g = euclid(a.v, MOD, x, y);
		assert(g == 1); return mint(x);
	}
	mint& operator+= (mint const& o) {if((v+=o.v)>=MOD) v-=MOD; return *this;}
	mint& operator-= (mint const& o) {if((v-=o.v)<0) v+=MOD; return *this;}
	mint& operator*= (mint const& o) {v=(ll)v*o.v%MOD; return *this;}
	mint& operator/= (mint const& o) {return *this *= invert(o);}

	friend mint operator+ (mint a, mint const& b) {return a+=b;}
	friend mint operator- (mint a, mint const& b) {return a-=b;}
	friend mint operator* (mint a, mint const& b) {return a*=b;}
	friend mint operator/ (mint const& a, mint const& b) {return a*invert(b);}
};

vector<mint> multiply(vector<mint> &&a, vector<mint> &&b) {
	assert(a.size() >= 1);
	assert(b.size() >= 1);

	if(std::min(a.size(), b.size()) <= 16) {
		vector<mint> ans(a.size() + b.size() - 1);
		for(int i = 0;i < a.size(); ++i)
			for(int j = 0;j < b.size(); ++j)
				ans[i + j] += a[i] * b[j];
		return ans;
	}
	else {
		size_t fin_sz = a.size() + b.size() - 1;
		if(a.size() < b.size()) a.resize(b.size());
		if(b.size() < a.size()) b.resize(a.size());

		// ((aH << m) + aL) * ((bH << m) + bL)
		// = (aH * bH << m + m) + (aL * bL) + ((aH * bL << m) + (aL * bH << m))

		// (aH * bL + aL * bH) = (aH + aL) * (bH + bL) - aH * bH - aL * bL;

		int m = (a.size() + 1) / 2; // LOW size >= HI size

		vector<mint> H = multiply({m+all(a)}, {m+all(b)});
		vector<mint> L = multiply({a.begin(), a.begin() + m}, {b.begin(), b.begin() + m});

		for(int i = 0;i + m < a.size(); ++i) a[i] += a[i+m], b[i] += b[i+m];
		a.resize(m);
		b.resize(m);

		vector<mint> M = multiply(std::move(a), std::move(b));
		assert(M.size() == L.size());
		for(int i = 0;i < M.size(); ++i)
		{
			M[i] -= L[i];
			if(i < H.size()) M[i] -= H[i];
		}

		vector<mint> ans = std::move(L);
		ans.resize(fin_sz);
		for(int i = 0;i < M.size() && i + m < fin_sz; ++i) ans[i+m] += M[i];
		for(int i = 0;i < H.size() && i + 2*m < fin_sz; ++i) ans[i+2*m] += H[i];
		return ans;
	}
}

int const maxn = 2e4 + 10;
mint fac[2*maxn],invfac[2*maxn];

int main(){
	int N;
	cin.tie(0);cin.sync_with_stdio(0);
	cin >> N >> MOD;
	fac[0] = mint(1);invfac[0] = mint(1);
	for(int i=1; i<2*maxn; i++){
		fac[i] = (fac[i-1] * mint(i));
		invfac[i] = mint(1) / fac[i];
	}

	vector<mint> dp(N + 1);
	vector<mint> sum_dp(N + 1);

	dp[0] = mint(1);
	sum_dp[0] = mint(1);

	auto induce = [&](int l, int m, int r) {
		auto apply = [&](vector<mint>& ans, auto &&dep_i, auto &&dep_j, auto &&dep_i_j) {
			// ans[i] += fj(j) * fij(i+j)
			// => ans[K+i-1] += fj(K-j-1) * fij(i+j)
			// => ans[K+i-1 - (off)] += fj(K-j-1) * fij(i+j - off)

			int K = m;
			int off = l + m;

			vector<mint> f1(K - l);
			for(int j = l;j < m; ++j) f1[K - j - 1] = dep_j(j);
			vector<mint> f2;
			for(int ij = l + m;ij <= r + m - 2; ++ij) f2.push_back(dep_i_j(ij));

			vector<mint> res = multiply(std::move(f1), std::move(f2));

			for(int i = m;i < r; ++i)
				ans[i] += res[i + K - 1 - (off)] * dep_i(i);
		};

		apply(dp,
				[&](int i){return mint(1);},
				[&](int j){return dp[j]*invfac[2*j];},
				[&](int ij){return fac[ij-1];});

		apply(sum_dp,
				[&](int i){return mint(i);},
				[&](int j){return dp[j]*invfac[2*j];},
				[&](int ij){return fac[ij-1];});
		apply(sum_dp,
				[&](int i){return mint(1);},
				[&](int j){return dp[j]*invfac[2*j]*mint(-j);},
				[&](int ij){return fac[ij-1];});

		apply(dp,
				[&](int i){return mint(i);},
				[&](int j){return sum_dp[j]*invfac[2*j+1];},
				[&](int ij){return fac[ij-1];});
		apply(dp,
				[&](int i){return mint(1);},
				[&](int j){return sum_dp[j]*invfac[2*j+1]*mint(-j-1);},
				[&](int ij){return fac[ij-1];});

		apply(sum_dp,
				[&](int i){return mint(i) * mint(i) - mint(i);},
				[&](int j){return sum_dp[j]*invfac[2*j+1];},
				[&](int ij){return fac[ij-1];});
		apply(sum_dp,
				[&](int i){return mint(1);},
				[&](int j){return sum_dp[j]*invfac[2*j+1] * (mint(j) * mint(j) + mint(j));},
				[&](int ij){return fac[ij-1];});
		apply(sum_dp,
				[&](int i){return mint(-2*i);},
				[&](int j){return sum_dp[j]*invfac[2*j+1]*mint(j);},
				[&](int ij){return fac[ij-1];});
	};

	auto solve = [&](auto const& solve, int l, int r) ->void{
		if(l + 1 == r) return;
		int m = l + (r - l) / 2;
		solve(solve, l, m);
		induce(l, m, r);
		solve(solve, m, r);
	};
	solve(solve, 0, N + 1);

	mint default_ans(1);
	for(int i = N * 2 - 1;i >= 1; i -= 2)
		default_ans *= mint(i);
	
#ifdef LOCAL
	for(int i = 0;i <= N; ++i)
		printf("%d -- %d\n", dp[i], sum_dp[i]);
#endif
	printf("%d\n", (int)(default_ans - dp[N]));
	return 0;
}

Compilation message (stderr)

festival2.cpp: In function 'std::vector<mint> multiply(std::vector<mint>&&, std::vector<mint>&&)':
festival2.cpp:68:19: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<mint>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   68 |   for(int i = 0;i < a.size(); ++i)
      |                 ~~^~~~~~~~~~
festival2.cpp:69:20: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<mint>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   69 |    for(int j = 0;j < b.size(); ++j)
      |                  ~~^~~~~~~~~~
festival2.cpp:88:23: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<mint>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   88 |   for(int i = 0;i + m < a.size(); ++i) a[i] += a[i+m], b[i] += b[i+m];
      |                 ~~~~~~^~~~~~~~~~
festival2.cpp:94:19: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<mint>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   94 |   for(int i = 0;i < M.size(); ++i)
      |                 ~~^~~~~~~~~~
festival2.cpp:97:9: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<mint>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   97 |    if(i < H.size()) M[i] -= H[i];
      |       ~~^~~~~~~~~~
festival2.cpp:102:19: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<mint>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  102 |   for(int i = 0;i < M.size() && i + m < fin_sz; ++i) ans[i+m] += M[i];
      |                 ~~^~~~~~~~~~
festival2.cpp:102:39: warning: comparison of integer expressions of different signedness: 'int' and 'size_t' {aka 'long unsigned int'} [-Wsign-compare]
  102 |   for(int i = 0;i < M.size() && i + m < fin_sz; ++i) ans[i+m] += M[i];
      |                                 ~~~~~~^~~~~~~~
festival2.cpp:103:19: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<mint>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  103 |   for(int i = 0;i < H.size() && i + 2*m < fin_sz; ++i) ans[i+2*m] += H[i];
      |                 ~~^~~~~~~~~~
festival2.cpp:103:41: warning: comparison of integer expressions of different signedness: 'int' and 'size_t' {aka 'long unsigned int'} [-Wsign-compare]
  103 |   for(int i = 0;i < H.size() && i + 2*m < fin_sz; ++i) ans[i+2*m] += H[i];
      |                                 ~~~~~~~~^~~~~~~~

• Subtask 1: 5 / 5
• Subtask 2: 5 / 5
• Subtask 3: 27 / 27
• Subtask 4: 14 / 14
• Subtask 5: 36 / 36
• Subtask 6: 13 / 13