結果
問題 | No.1510 Simple Integral |
ユーザー |
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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 |
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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 Macrostypedef 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#endiftemplate <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.htmlint64_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;}