結果

問題 No.2075 GCD Subsequence
ユーザー ei1333333ei1333333
提出日時 2022-09-16 22:02:58
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 516 ms / 4,000 ms
コード長 5,417 bytes
コンパイル時間 2,188 ms
コンパイル使用メモリ 207,220 KB
最終ジャッジ日時 2025-02-07 09:32:23
ジャッジサーバーID
(参考情報)
judge2 / judge1
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 28
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 #
プレゼンテーションモードにする

#include<bits/stdc++.h>
using namespace std;
using int64 = long long;
const int mod = 998244353;
const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;
struct IoSetup {
IoSetup() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(10);
cerr << fixed << setprecision(10);
}
} iosetup;
template< typename T1, typename T2 >
ostream &operator<<(ostream &os, const pair< T1, T2 > &p) {
os << p.first << " " << p.second;
return os;
}
template< typename T1, typename T2 >
istream &operator>>(istream &is, pair< T1, T2 > &p) {
is >> p.first >> p.second;
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 != v.size() ? " " : "");
}
return os;
}
template< typename T >
istream &operator>>(istream &is, vector< T > &v) {
for (T &in: v) is >> in;
return is;
}
template< typename T1, typename T2 >
inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }
template< typename T1, typename T2 >
inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }
template< typename T = int64 >
vector< T > make_v(size_t a) {
return vector< T >(a);
}
template< typename T, typename... Ts >
auto make_v(size_t a, Ts... ts) {
return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...));
}
template< typename T, typename V >
typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) {
t = v;
}
template< typename T, typename V >
typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) {
for (auto &e: t) fill_v(e, v);
}
template< typename F >
struct FixPoint: F {
explicit FixPoint(F &&f): F(forward< F >(f)) {}
template< typename... Args >
decltype(auto) operator()(Args &&... args) const {
return F::operator()(*this, forward< Args >(args)...);
}
};
template< typename F >
inline decltype(auto) MFP(F &&f) {
return FixPoint< F >{forward< F >(f)};
}
#line 1 "math/combinatorics/montgomery-mod-int.hpp"
/**
* @brief Montgomery ModInt
*/
template< uint32_t mod, bool fast = false >
struct MontgomeryModInt {
using mint = MontgomeryModInt;
using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;
static constexpr u32 get_r() {
u32 ret = mod;
for(i32 i = 0; i < 4; i++) ret *= 2 - mod * ret;
return ret;
}
static constexpr u32 r = get_r();
static constexpr u32 n2 = -u64(mod) % mod;
static_assert(r * mod == 1, "invalid, r * mod != 1");
static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
u32 x;
MontgomeryModInt() : x{} {}
MontgomeryModInt(const i64 &a)
: x(reduce(u64(fast ? a : (a % mod + mod)) * n2)) {}
static constexpr u32 reduce(const u64 &b) {
return u32(b >> 32) + mod - u32((u64(u32(b) * r) * mod) >> 32);
}
mint &operator+=(const mint &p) {
if(i32(x += p.x - 2 * mod) < 0) x += 2 * mod;
return *this;
}
mint &operator-=(const mint &p) {
if(i32(x -= p.x) < 0) x += 2 * mod;
return *this;
}
mint &operator*=(const mint &p) {
x = reduce(u64(x) * p.x);
return *this;
}
mint &operator/=(const mint &p) {
*this *= p.inverse();
return *this;
}
mint operator-() const { return mint() - *this; }
mint operator+(const mint &p) const { return mint(*this) += p; }
mint operator-(const mint &p) const { return mint(*this) -= p; }
mint operator*(const mint &p) const { return mint(*this) *= p; }
mint operator/(const mint &p) const { return mint(*this) /= p; }
bool operator==(const mint &p) const { return (x >= mod ? x - mod : x) == (p.x >= mod ? p.x - mod : p.x); }
bool operator!=(const mint &p) const { return (x >= mod ? x - mod : x) != (p.x >= mod ? p.x - mod : p.x); }
u32 get() const {
u32 ret = reduce(x);
return ret >= mod ? ret - mod : ret;
}
mint pow(u64 n) const {
mint ret(1), mul(*this);
while(n > 0) {
if(n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
mint inverse() const {
return pow(mod - 2);
}
friend ostream &operator<<(ostream &os, const mint &p) {
return os << p.get();
}
friend istream &operator>>(istream &is, mint &a) {
i64 t;
is >> t;
a = mint(t);
return is;
}
static u32 get_mod() { return mod; }
};
using modint = MontgomeryModInt< mod >;
const int MAX_A = 1e6;
vector< int > fs[MAX_A + 1];
int main() {
int N;
cin >> N;
vector< int > A(N);
cin >> A;
for(int i = 2; i <= MAX_A; i++) {
if(fs[i].empty()) {
for(int j = i; j <= MAX_A; j += i) {
fs[j].emplace_back(i);
}
}
}
vector< modint > dp(MAX_A + 1);
modint ans = 0;
for(int i = 0; i < N; i++) {
auto& vs = fs[A[i]];
modint ret = 1;
MFP([&](auto calc, int idx, int mul, bool f) -> void {
if(idx == vs.size()) {
if(mul == 1) return;
if(f) ret += dp[mul];
else ret -= dp[mul];
} else {
calc(idx + 1, mul * vs[idx], f ^ 1);
calc(idx + 1, mul, f);
}
}) (0, 1, 0);
ans += ret;
MFP([&](auto calc, int idx, int mul) -> void {
if(idx == vs.size()) {
dp[mul] += ret;
} else {
calc(idx + 1, mul * vs[idx]);
calc(idx + 1, mul);
}
}) (0, 1);
}
cout << ans << endl;
}
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