結果
| 問題 | No.1510 Simple Integral |
| ユーザー |
 rniya
|
| 提出日時 | 2021-05-16 14:29:16 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 266 ms / 2,000 ms |
| コード長 | 11,643 bytes |
| コンパイル時間 | 2,638 ms |
| コンパイル使用メモリ | 215,532 KB |
| 最終ジャッジ日時 | 2025-01-21 13:10:31 |
|
ジャッジサーバーID （参考情報） |
judge5 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 43 |
ソースコード
#define LOCAL
#include <bits/stdc++.h>
using namespace std;
#pragma region Macros
typedef long long ll;
typedef __int128_t i128;
typedef unsigned int uint;
typedef unsigned long long ull;
#define ALL(x) (x).begin(), (x).end()
template <typename T> istream& operator>>(istream& is, vector<T>& v) {
for (T& x : v) is >> x;
return is;
}
template <typename T> ostream& operator<<(ostream& os, const vector<T>& v) {
for (int i = 0; i < (int)v.size(); i++) {
os << v[i] << (i + 1 == (int)v.size() ? "" : " ");
}
return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const pair<T, U>& p) {
os << '(' << p.first << ',' << p.second << ')';
return os;
}
template <typename T, typename U, typename V> ostream& operator<<(ostream& os, const tuple<T, U, V>& t) {
os << '(' << get<0>(t) << ',' << get<1>(t) << ',' << get<2>(t) << ')';
return os;
}
template <typename T, typename U, typename V, typename W> ostream& operator<<(ostream& os, const tuple<T, U, V, W>& t) {
os << '(' << get<0>(t) << ',' << get<1>(t) << ',' << get<2>(t) << ',' << get<3>(t) << ')';
return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const map<T, U>& m) {
os << '{';
for (auto itr = m.begin(); itr != m.end();) {
os << '(' << itr->first << ',' << itr->second << ')';
if (++itr != m.end()) os << ',';
}
os << '}';
return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const unordered_map<T, U>& m) {
os << '{';
for (auto itr = m.begin(); itr != m.end();) {
os << '(' << itr->first << ',' << itr->second << ')';
if (++itr != m.end()) os << ',';
}
os << '}';
return os;
}
template <typename T> ostream& operator<<(ostream& os, const set<T>& s) {
os << '{';
for (auto itr = s.begin(); itr != s.end();) {
os << *itr;
if (++itr != s.end()) os << ',';
}
os << '}';
return os;
}
template <typename T> ostream& operator<<(ostream& os, const multiset<T>& s) {
os << '{';
for (auto itr = s.begin(); itr != s.end();) {
os << *itr;
if (++itr != s.end()) os << ',';
}
os << '}';
return os;
}
template <typename T> ostream& operator<<(ostream& os, const unordered_set<T>& s) {
os << '{';
for (auto itr = s.begin(); itr != s.end();) {
os << *itr;
if (++itr != s.end()) os << ',';
}
os << '}';
return os;
}
template <typename T> ostream& operator<<(ostream& os, const deque<T>& v) {
for (int i = 0; i < (int)v.size(); i++) {
os << v[i] << (i + 1 == (int)v.size() ? "" : " ");
}
return os;
}
void debug_out() { cerr << '\n'; }
template <class Head, class... Tail> void debug_out(Head&& head, Tail&&... tail) {
cerr << head;
if (sizeof...(Tail) > 0) cerr << ", ";
debug_out(move(tail)...);
}
#ifdef LOCAL
#define debug(...) \
cerr << " "; \
cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n'; \
cerr << " "; \
debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif
template <typename T> T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; }
template <typename T> T lcm(T x, T y) { return x / gcd(x, y) * y; }
template <class T1, class T2> inline bool chmin(T1& a, T2 b) {
if (a > b) {
a = b;
return true;
}
return false;
}
template <class T1, class T2> inline bool chmax(T1& a, T2 b) {
if (a < b) {
a = b;
return true;
}
return false;
}
#pragma endregion
/**
* @brief modint
* @docs docs/modulo/modint.md
*/
template <uint32_t mod> class modint {
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;
public:
u32 v;
constexpr modint(const i64 x = 0) noexcept : v(x < 0 ? mod - 1 - (-(x + 1) % mod) : x % mod) {}
constexpr u32& value() noexcept { return v; }
constexpr const u32& value() const noexcept { return v; }
constexpr modint operator+(const modint& rhs) const noexcept { return modint(*this) += rhs; }
constexpr modint operator-(const modint& rhs) const noexcept { return modint(*this) -= rhs; }
constexpr modint operator*(const modint& rhs) const noexcept { return modint(*this) *= rhs; }
constexpr modint operator/(const modint& rhs) const noexcept { return modint(*this) /= rhs; }
constexpr modint& operator+=(const modint& rhs) noexcept {
v += rhs.v;
if (v >= mod) v -= mod;
return *this;
}
constexpr modint& operator-=(const modint& rhs) noexcept {
if (v < rhs.v) v += mod;
v -= rhs.v;
return *this;
}
constexpr modint& operator*=(const modint& rhs) noexcept {
v = (u64)v * rhs.v % mod;
return *this;
}
constexpr modint& operator/=(const modint& rhs) noexcept { return *this *= rhs.pow(mod - 2); }
constexpr modint pow(u64 exp) const noexcept {
modint self(*this), res(1);
while (exp > 0) {
if (exp & 1) res *= self;
self *= self;
exp >>= 1;
}
return res;
}
constexpr modint& operator++() noexcept {
if (++v == mod) v = 0;
return *this;
}
constexpr modint& operator--() noexcept {
if (v == 0) v = mod;
return --v, *this;
}
constexpr modint operator++(int) noexcept {
modint t = *this;
return ++*this, t;
}
constexpr modint operator--(int) noexcept {
modint t = *this;
return --*this, t;
}
constexpr modint operator-() const noexcept { return modint(mod - v); }
template <class T> friend constexpr modint operator+(T x, modint y) noexcept { return modint(x) + y; }
template <class T> friend constexpr modint operator-(T x, modint y) noexcept { return modint(x) - y; }
template <class T> friend constexpr modint operator*(T x, modint y) noexcept { return modint(x) * y; }
template <class T> friend constexpr modint operator/(T x, modint y) noexcept { return modint(x) / y; }
constexpr bool operator==(const modint& rhs) const noexcept { return v == rhs.v; }
constexpr bool operator!=(const modint& rhs) const noexcept { return v != rhs.v; }
constexpr bool operator!() const noexcept { return !v; }
friend istream& operator>>(istream& s, modint& rhs) noexcept {
i64 v;
rhs = modint{(s >> v, v)};
return s;
}
friend ostream& operator<<(ostream& s, const modint& rhs) noexcept { return s << rhs.v; }
};
/**
* @brief Number Theoretic Transform
* @docs docs/convolution/NumberTheoreticTransform.md
*/
template <int mod> struct NumberTheoreticTransform {
using Mint = modint<mod>;
vector<Mint> roots;
vector<int> rev;
int base, max_base;
Mint root;
NumberTheoreticTransform() : base(1), rev{0, 1}, roots{Mint(0), Mint(1)} {
int tmp = mod - 1;
for (max_base = 0; tmp % 2 == 0; max_base++) tmp >>= 1;
root = 2;
while (root.pow((mod - 1) >> 1) == 1) root++;
root = root.pow((mod - 1) >> max_base);
}
void ensure_base(int nbase) {
if (nbase <= base) return;
rev.resize(1 << nbase);
for (int i = 0; i < (1 << nbase); i++) {
rev[i] = (rev[i >> 1] >> 1) | ((i & 1) << (nbase - 1));
}
roots.resize(1 << nbase);
for (; base < nbase; base++) {
Mint z = root.pow(1 << (max_base - 1 - base));
for (int i = 1 << (base - 1); i < (1 << base); i++) {
roots[i << 1] = roots[i];
roots[i << 1 | 1] = roots[i] * z;
}
}
}
void ntt(vector<Mint>& a) {
const int n = a.size();
int zeros = __builtin_ctz(n);
ensure_base(zeros);
int shift = base - zeros;
for (int i = 0; i < n; i++) {
if (i < (rev[i] >> shift)) {
swap(a[i], a[rev[i] >> shift]);
}
}
for (int k = 1; k < n; k <<= 1) {
for (int i = 0; i < n; i += (k << 1)) {
for (int j = 0; j < k; j++) {
Mint z = a[i + j + k] * roots[j + k];
a[i + j + k] = a[i + j] - z;
a[i + j] = a[i + j] + z;
}
}
}
}
vector<Mint> multiply(vector<Mint> a, vector<Mint> b) {
int need = a.size() + b.size() - 1;
int nbase = 1;
while ((1 << nbase) < need) nbase++;
ensure_base(nbase);
int sz = 1 << nbase;
a.resize(sz, Mint(0));
b.resize(sz, Mint(0));
ntt(a);
ntt(b);
Mint inv_sz = 1 / Mint(sz);
for (int i = 0; i < sz; i++) a[i] *= b[i] * inv_sz;
reverse(a.begin() + 1, a.end());
ntt(a);
a.resize(need);
return a;
}
vector<int> multiply(vector<int> a, vector<int> b) {
vector<Mint> A(a.size()), B(b.size());
for (int i = 0; i < a.size(); i++) A[i] = Mint(a[i]);
for (int i = 0; i < b.size(); i++) B[i] = Mint(b[i]);
vector<Mint> C = multiply(A, B);
vector<int> res(C.size());
for (int i = 0; i < C.size(); i++) res[i] = C[i].v;
return res;
}
};
const int INF = 1e9;
const long long IINF = 1e18;
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const char dir[4] = {'D', 'R', 'U', 'L'};
// const long long MOD = 1000000007;
const long long MOD = 998244353;
// https://ei1333.github.io/luzhiled/snippets/math/mod-log.html
int64_t mod_log(int64_t a, int64_t b, int64_t p) {
int64_t g = 1;
for (int64_t i = p; i; i /= 2) (g *= a) %= p;
g = __gcd(g, p);
int64_t t = 1, c = 0;
for (; t % g; c++) {
if (t == b) return c;
(t *= a) %= p;
}
if (b % g) return -1;
t /= g;
b /= g;
int64_t n = p / g, h = 0, gs = 1;
for (; h * h < n; h++) (gs *= a) %= n;
unordered_map<int64_t, int64_t> bs;
for (int64_t s = 0, e = b; s < h; bs[e] = ++s) {
(e *= a) %= n;
}
for (int64_t s = 0, e = t; s < n;) {
(e *= gs) %= n;
s += h;
if (bs.count(e)) return c + s - bs[e];
}
return -1;
}
/**
* @brief 繰り返し2乗法
*/
long long modpow(long long x, long long n, long long mod) {
long long res = 1;
while (n > 0) {
if (n & 1LL) res = res * x % mod;
x = x * x % mod;
n >>= 1LL;
}
return res;
}
long long modinv(long long x, long long p) { return modpow(x, p - 2, p); }
using mint = modint<MOD>;
const int root = 3, MAX_A = 1000010;
int main() {
cin.tie(0);
ios::sync_with_stdio(false);
mint iroot = modpow(root, mod_log(root, MOD - 1, MOD) / 2, MOD);
int N;
cin >> N;
vector<int> A(N), cnt(MAX_A, 0);
for (int& x : A) {
cin >> x;
cnt[x]++;
}
for (int i = 0; i < N; i++) A.emplace_back(-A[i]);
NumberTheoreticTransform<MOD> NTT;
mint ans = 0;
for (int i = 0; i < MAX_A; i++) {
if (!cnt[i]) continue;
vector<mint> f(N + 1, 0);
f[0] = 1;
for (int& z : A) {
if (z == i) continue;
mint inv = mint(1) / (iroot * (z - i));
vector<mint> g(N + 1);
g[0] = -inv;
for (int i = 1; i <= N; i++) g[i] = g[i - 1] * inv;
f = NTT.multiply(f, g);
while (f.size() > N + 1) f.pop_back();
}
ans += f[cnt[i] - 1] * 2 * iroot;
}
cout << ans << '\n';
return 0;
}