結果

問題 No.1145 Sums of Powers
ユーザー heno239heno239
提出日時 2020-08-28 21:08:04
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 721 ms / 2,000 ms
コード長 6,761 bytes
コンパイル時間 1,858 ms
コンパイル使用メモリ 131,048 KB
実行使用メモリ 21,776 KB
最終ジャッジ日時 2024-04-26 12:32:18
合計ジャッジ時間 4,602 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge1
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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 2 ms
5,248 KB
testcase_01 AC 1 ms
5,376 KB
testcase_02 AC 5 ms
5,376 KB
testcase_03 AC 709 ms
21,772 KB
testcase_04 AC 713 ms
21,776 KB
testcase_05 AC 721 ms
20,620 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<utility>
#include<cassert>
#include<complex>
#include<numeric>
#include<array>
using namespace std;

//#define int long long
typedef long long ll;

typedef unsigned long long ul;
typedef unsigned int ui;
constexpr ll mod = 998244353;
const ll INF = mod * mod;
typedef pair<int, int>P;
#define stop char nyaa;cin>>nyaa;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
#define all(v) (v).begin(),(v).end()
typedef pair<ll, ll> LP;
typedef long double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-12;
const ld pi = acosl(-1.0);

ll mod_pow(ll x, ll n, ll m=mod) {
	ll res = 1;
	while (n) {
		if (n & 1)res = res * x % m;
		x = x * x % m; n >>= 1;
	}
	return res;
}
struct modint {
	ll n;
	modint() :n(0) { ; }
	modint(ll m) :n(m) {
		if (n >= mod)n %= mod;
		else if (n < 0)n = (n % mod + mod) % mod;
	}
	operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; }
modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; }
modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; }
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, ll n) {
	if (n == 0)return modint(1);
	modint res = (a * a) ^ (n / 2);
	if (n % 2)res = res * a;
	return res;
}

ll inv(ll a, ll p) {
	return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }

const int max_n = 1 << 1;
modint fact[max_n], factinv[max_n];
void init_f() {
	fact[0] = modint(1);
	for (int i = 0; i < max_n - 1; i++) {
		fact[i + 1] = fact[i] * modint(i + 1);
	}
	factinv[max_n - 1] = modint(1) / fact[max_n - 1];
	for (int i = max_n - 2; i >= 0; i--) {
		factinv[i] = factinv[i + 1] * modint(i + 1);
	}
}
modint comb(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[b] * factinv[a - b];
}


modint mod_inverse(modint a) {
	return mod_pow(a, mod - 2);
}
modint root[24], invroot[24];
void init() {
	rep(i, 24) {
		int n = (1 << i);
		root[i] = mod_pow(3, (mod - 1) / n);
		invroot[i] = mod_inverse(root[i]);
	}
}
typedef vector <modint> poly;
void dft(poly &f, bool inverse = false) {
	int n = f.size(); if (n == 1)return;
	
	static poly w{ 1 }, iw{ 1 };
	for (int m = w.size(); m < n / 2; m *= 2) {
		modint dw = mod_pow(3,(mod-1)/(4*m)), dwinv = (modint)1 / dw;
		w.resize(m * 2); iw.resize(m * 2);
		for (int i = 0; i < m; i++)w[m + i] = w[i] * dw, iw[m + i] = iw[i] * dwinv;
	}
	if (!inverse) {
		for (int m = n; m >>= 1;) {
			for (int s = 0, k = 0; s < n; s += 2 * m, k++) {
				for (int i = s; i < s + m; i++) {
					modint x = f[i], y = f[i + m] * w[k];
					f[i] = x + y, f[i + m] = x - y;
				}
			}
		}
	}
	else {
		for (int m = 1; m < n; m *= 2) {
			for (int s = 0, k = 0; s < n; s += 2 * m, k++) {
				for (int i = s; i < s + m; i++) {
					modint x = f[i], y = f[i + m];
					f[i] = x + y, f[i + m] = (x - y) * iw[k];
				}
			}
		}
		modint n_inv = (modint)1 / (modint)n;
		for (modint& v : f)v *= n_inv;
	}
}
poly multiply(poly g, poly h) {
	int n = 1;
	int pi = 0, qi = 0;
	rep(i, g.size())if (g[i])pi = i;
	rep(i, h.size())if (h[i])qi = i;
	int sz = pi + qi + 2;
	while (n < sz)n *= 2;
	g.resize(n); h.resize(n);
	dft(g); dft(h);
	rep(i, n) {
		g[i] *= h[i];
	}
	dft(g, true);
	return g;
}

struct FormalPowerSeries :vector<modint> {
	using vector<modint>::vector;
	using fps = FormalPowerSeries;
	void shrink() {
		while (this->size() && this->back() == (modint)0)this->pop_back();
	}

	fps operator+(const fps& r)const { return fps(*this) += r; }
	fps operator+(const modint& v)const { return fps(*this) += v; }
	fps operator-(const fps& r)const { return fps(*this) -= r; }
	fps operator-(const modint& v)const { return fps(*this) -= v; }
	fps operator*(const fps& r)const { return fps(*this) *= r; }
	fps operator*(const modint& v)const { return fps(*this) *= v; }


	fps& operator+=(const fps& r) {
		if (r.size() > this->size())this->resize(r.size());
		rep(i, r.size())(*this)[i] += r[i];
		shrink();
		return *this;
	}
	fps& operator+=(const modint& v) {
		if (this->empty())this->resize(1);
		(*this)[0] += v;
		shrink();
		return *this;
	}
	fps& operator-=(const fps& r) {
		if (r.size() > this->size())this->resize(r.size());
		rep(i, r.size())(*this)[i] -= r[i];
		shrink();
		return *this;
	}
	fps& operator-=(const modint& v) {
		if (this->empty())this->resize(1);
		(*this)[0] -= v;
		shrink();
		return *this;
	}
	fps& operator*=(const fps& r) {
		if (this->empty() || r.empty())this->clear();
		else {
			poly ret = multiply(*this, r);
			*this = fps(all(ret));
		}
		return *this;
	}
	fps& operator*=(const modint& v) {
		for (auto& x : (*this))x *= v;
		shrink();
		return *this;
	}
	fps operator-()const {
		fps ret = *this;
		for (auto& v : ret)v = -v;
		return ret;
	}
	
	fps pre(int sz)const {
		fps ret(this->begin(), this->begin() + min((int)this->size(), sz));
		ret.shrink();
		return ret;
	}
	fps inv(int deg) {
		const int n = this->size();
		if (deg == -1)deg = n;
		fps ret({ (modint)1 / (*this)[0] });
		for (int i = 1; i < deg; i <<= 1) {
			ret = (ret + ret - ret * ret * pre(i<<1)).pre(i << 1);
		}
		ret = ret.pre(deg);
		ret.shrink();
		return ret;
	}
};
using fps = FormalPowerSeries;

struct pfps {
	fps a,b;
};

pfps operator+(const pfps& a, const pfps& b) {
	return { a.a * b.b + a.b * b.a,a.b * b.b };
}
void solve() {
	int n; cin >> n;
	int m; cin >> m;
	vector<pfps> v(n);
	rep(i, n) {
		int a; cin >> a;
		v[i] = { {1},{1,-a} };
	}
	while (v.size() > 1) {
		vector<pfps> nex;
		int len = v.size();
		rep(j, len / 2) {
			pfps to = v[2 * j] + v[2 * j + 1];
			if (to.a.size() > m + 1)to.a.resize(m + 1);
			if (to.b.size() > m + 1)to.b.resize(m + 1);
			nex.push_back(to);
		}
		if (len % 2)nex.push_back(v.back());
		swap(nex, v);
	}
	fps ans = v[0].a * (v[0].b).inv(m + 1);
	rep1(i, m) {
		if (i>1)cout << " ";
		cout << ans[i];
	}
	cout << "\n";
}

signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	//cout << fixed << setprecision(15);
	//init_f(); 
	init();
	//expr();
	//int t; cin >> t; rep(i, t)
	solve();
	return 0;
}
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