結果

問題 No.1747 Many Formulae 2
ユーザー NyaanNyaan
提出日時 2021-11-19 23:01:06
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 3 ms / 2,000 ms
コード長 20,169 bytes
コンパイル時間 4,482 ms
コンパイル使用メモリ 284,556 KB
最終ジャッジ日時 2025-01-25 20:50:51
ジャッジサーバーID
(参考情報)
judge2 / judge1
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ファイルパターン 結果
other AC * 19
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/**
* date : 2021-11-19 23:01:09
*/
#define NDEBUG
using namespace std;
// intrinstic
#include <immintrin.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
// utility
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
template <typename T, typename U>
struct P : pair<T, U> {
template <typename... Args>
P(Args... args) : pair<T, U>(args...) {}
using pair<T, U>::first;
using pair<T, U>::second;
T &x() { return first; }
const T &x() const { return first; }
U &y() { return second; }
const U &y() const { return second; }
P &operator+=(const P &r) {
first += r.first;
second += r.second;
return *this;
}
P &operator-=(const P &r) {
first -= r.first;
second -= r.second;
return *this;
}
P &operator*=(const P &r) {
first *= r.first;
second *= r.second;
return *this;
}
P operator+(const P &r) const { return P(*this) += r; }
P operator-(const P &r) const { return P(*this) -= r; }
P operator*(const P &r) const { return P(*this) *= r; }
};
using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;
constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;
template <typename T>
int sz(const T &t) {
return t.size();
}
template <typename T, typename U>
inline bool amin(T &x, U y) {
return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
return (x < y) ? (x = y, true) : false;
}
template <typename T>
inline T Max(const vector<T> &v) {
return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
return accumulate(begin(v), end(v), 0LL);
}
template <typename T>
int lb(const vector<T> &v, const T &a) {
return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
return upper_bound(begin(v), end(v), a) - begin(v);
}
constexpr long long TEN(int n) {
long long ret = 1, x = 10;
for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
return ret;
}
template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
return make_pair(t, u);
}
template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
vector<T> ret(v.size() + 1);
if (rev) {
for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
} else {
for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
}
return ret;
};
template <typename T>
vector<T> mkuni(const vector<T> &v) {
vector<T> ret(v);
sort(ret.begin(), ret.end());
ret.erase(unique(ret.begin(), ret.end()), ret.end());
return ret;
}
template <typename F>
vector<int> mkord(int N, F f) {
vector<int> ord(N);
iota(begin(ord), end(ord), 0);
sort(begin(ord), end(ord), f);
return ord;
}
template <typename T>
vector<int> mkinv(vector<T> &v) {
int max_val = *max_element(begin(v), end(v));
vector<int> inv(max_val + 1, -1);
for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
return inv;
}
} // namespace Nyaan
// bit operation
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
return _mm_popcnt_u64(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
} // namespace Nyaan
// inout
namespace Nyaan {
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>
istream &operator>>(istream &is, pair<T, U> &p) {
is >> p.first >> p.second;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
int s = (int)v.size();
for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (auto &x : v) is >> x;
return is;
}
void in() {}
template <typename T, class... U>
void in(T &t, U &... u) {
cin >> t;
in(u...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &... u) {
cout << t;
if (sizeof...(u)) cout << sep;
out(u...);
}
void outr() {}
template <typename T, class... U, char sep = ' '>
void outr(const T &t, const U &... u) {
cout << t;
outr(u...);
}
struct IoSetupNya {
IoSetupNya() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
cerr << fixed << setprecision(7);
}
} iosetupnya;
} // namespace Nyaan
// debug
namespace DebugImpl {
template <typename U, typename = void>
struct is_specialize : false_type {};
template <typename U>
struct is_specialize<
U, typename conditional<false, typename U::iterator, void>::type>
: true_type {};
template <typename U>
struct is_specialize<
U, typename conditional<false, decltype(U::first), void>::type>
: true_type {};
template <typename U>
struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type {
};
void dump(const char& t) { cerr << t; }
void dump(const string& t) { cerr << t; }
void dump(const bool& t) { cerr << (t ? "true" : "false"); }
template <typename U,
enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr>
void dump(const U& t) {
cerr << t;
}
template <typename T>
void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) {
string res;
if (t == Nyaan::inf) res = "inf";
if constexpr (is_signed<T>::value) {
if (t == -Nyaan::inf) res = "-inf";
}
if constexpr (sizeof(T) == 8) {
if (t == Nyaan::infLL) res = "inf";
if constexpr (is_signed<T>::value) {
if (t == -Nyaan::infLL) res = "-inf";
}
}
if (res.empty()) res = to_string(t);
cerr << res;
}
template <typename T, typename U>
void dump(const pair<T, U>&);
template <typename T>
void dump(const pair<T*, int>&);
template <typename T>
void dump(const T& t,
enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) {
cerr << "[ ";
for (auto it = t.begin(); it != t.end();) {
dump(*it);
cerr << (++it == t.end() ? "" : ", ");
}
cerr << " ]";
}
template <typename T, typename U>
void dump(const pair<T, U>& t) {
cerr << "( ";
dump(t.first);
cerr << ", ";
dump(t.second);
cerr << " )";
}
template <typename T>
void dump(const pair<T*, int>& t) {
cerr << "[ ";
for (int i = 0; i < t.second; i++) {
dump(t.first[i]);
cerr << (i == t.second - 1 ? "" : ", ");
}
cerr << " ]";
}
void trace() { cerr << endl; }
template <typename Head, typename... Tail>
void trace(Head&& head, Tail&&... tail) {
cerr << " ";
dump(head);
if (sizeof...(tail) != 0) cerr << ",";
trace(forward<Tail>(tail)...);
}
} // namespace DebugImpl
#ifdef NyaanDebug
#define trc(...) \
do { \
cerr << "## " << #__VA_ARGS__ << " = "; \
DebugImpl::trace(__VA_ARGS__); \
} while (0)
#else
#define trc(...) (void(0))
#endif
// macro
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...) \
int __VA_ARGS__; \
in(__VA_ARGS__)
#define inl(...) \
long long __VA_ARGS__; \
in(__VA_ARGS__)
#define ins(...) \
string __VA_ARGS__; \
in(__VA_ARGS__)
#define in2(s, t) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i]); \
}
#define in3(s, t, u) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i]); \
}
#define in4(s, t, u, v) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i], v[i]); \
}
#define die(...) \
do { \
Nyaan::out(__VA_ARGS__); \
return; \
} while (0)
namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }
//
namespace inner {
using i32 = int32_t;
using u32 = uint32_t;
using i64 = int64_t;
using u64 = uint64_t;
template <typename T>
T gcd(T a, T b) {
while (b) swap(a %= b, b);
return a;
}
template <typename T>
T inv(T a, T p) {
T b = p, x = 1, y = 0;
while (a) {
T q = b / a;
swap(a, b %= a);
swap(x, y -= q * x);
}
assert(b == 1);
return y < 0 ? y + p : y;
}
template <typename T, typename U>
T modpow(T a, U n, T p) {
T ret = 1 % p;
for (; n; n >>= 1, a = U(a) * a % p)
if (n & 1) ret = U(ret) * a % p;
return ret;
}
} // namespace inner
namespace my_rand {
// [0, 2^64 - 1)
uint64_t rng() {
static uint64_t x_ =
uint64_t(chrono::duration_cast<chrono::nanoseconds>(
chrono::high_resolution_clock::now().time_since_epoch())
.count()) *
10150724397891781847ULL;
x_ ^= x_ << 7;
return x_ ^= x_ >> 9;
}
// [l, r)
int64_t randint(int64_t l, int64_t r) {
assert(l < r);
return l + rng() % (r - l);
}
// choose n numbers from [l, r) without overlapping
vector<int64_t> randset(int64_t l, int64_t r, int64_t n) {
assert(l <= r && n <= r - l);
unordered_set<int64_t> s;
for (int64_t i = n; i; --i) {
int64_t m = randint(l, r + 1 - i);
if (s.find(m) != s.end()) m = r - i;
s.insert(m);
}
vector<int64_t> ret;
for (auto& x : s) ret.push_back(x);
return ret;
}
// [0.0, 1.0)
double rnd() {
union raw_cast {
double t;
uint64_t u;
};
constexpr uint64_t p = uint64_t(1023 - 64) << 52;
return rng() * ((raw_cast*)(&p))->t;
}
template <typename T>
void randshf(vector<T>& v) {
int n = v.size();
for (int loop = 0; loop < 2; loop++)
for (int i = 0; i < n; i++) swap(v[i], v[randint(0, n)]);
}
} // namespace my_rand
using my_rand::randint;
using my_rand::randset;
using my_rand::randshf;
using my_rand::rnd;
using my_rand::rng;
struct ArbitraryLazyMontgomeryModInt {
using mint = ArbitraryLazyMontgomeryModInt;
using i32 = int32_t;
using u32 = uint32_t;
using u64 = uint64_t;
static u32 mod;
static u32 r;
static u32 n2;
static u32 get_r() {
u32 ret = mod;
for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
return ret;
}
static void set_mod(u32 m) {
assert(m < (1 << 30));
assert((m & 1) == 1);
mod = m;
n2 = -u64(m) % m;
r = get_r();
assert(r * mod == 1);
}
u32 a;
ArbitraryLazyMontgomeryModInt() : a(0) {}
ArbitraryLazyMontgomeryModInt(const int64_t &b)
: a(reduce(u64(b % mod + mod) * n2)){};
static u32 reduce(const u64 &b) {
return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
}
mint &operator+=(const mint &b) {
if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
return *this;
}
mint &operator-=(const mint &b) {
if (i32(a -= b.a) < 0) a += 2 * mod;
return *this;
}
mint &operator*=(const mint &b) {
a = reduce(u64(a) * b.a);
return *this;
}
mint &operator/=(const mint &b) {
*this *= b.inverse();
return *this;
}
mint operator+(const mint &b) const { return mint(*this) += b; }
mint operator-(const mint &b) const { return mint(*this) -= b; }
mint operator*(const mint &b) const { return mint(*this) *= b; }
mint operator/(const mint &b) const { return mint(*this) /= b; }
bool operator==(const mint &b) const {
return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
}
bool operator!=(const mint &b) const {
return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
}
mint operator-() const { return mint() - mint(*this); }
mint pow(u64 n) const {
mint ret(1), mul(*this);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
friend ostream &operator<<(ostream &os, const mint &b) {
return os << b.get();
}
friend istream &operator>>(istream &is, mint &b) {
int64_t t;
is >> t;
b = ArbitraryLazyMontgomeryModInt(t);
return (is);
}
mint inverse() const { return pow(mod - 2); }
u32 get() const {
u32 ret = reduce(a);
return ret >= mod ? ret - mod : ret;
}
static u32 get_mod() { return mod; }
};
typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::mod;
typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::r;
typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::n2;
struct montgomery64 {
using mint = montgomery64;
using i64 = int64_t;
using u64 = uint64_t;
using u128 = __uint128_t;
static u64 mod;
static u64 r;
static u64 n2;
static u64 get_r() {
u64 ret = mod;
for (i64 i = 0; i < 5; ++i) ret *= 2 - mod * ret;
return ret;
}
static void set_mod(u64 m) {
assert(m < (1LL << 62));
assert((m & 1) == 1);
mod = m;
n2 = -u128(m) % m;
r = get_r();
assert(r * mod == 1);
}
u64 a;
montgomery64() : a(0) {}
montgomery64(const int64_t &b) : a(reduce((u128(b) + mod) * n2)){};
static u64 reduce(const u128 &b) {
return (b + u128(u64(b) * u64(-r)) * mod) >> 64;
}
mint &operator+=(const mint &b) {
if (i64(a += b.a - 2 * mod) < 0) a += 2 * mod;
return *this;
}
mint &operator-=(const mint &b) {
if (i64(a -= b.a) < 0) a += 2 * mod;
return *this;
}
mint &operator*=(const mint &b) {
a = reduce(u128(a) * b.a);
return *this;
}
mint &operator/=(const mint &b) {
*this *= b.inverse();
return *this;
}
mint operator+(const mint &b) const { return mint(*this) += b; }
mint operator-(const mint &b) const { return mint(*this) -= b; }
mint operator*(const mint &b) const { return mint(*this) *= b; }
mint operator/(const mint &b) const { return mint(*this) /= b; }
bool operator==(const mint &b) const {
return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
}
bool operator!=(const mint &b) const {
return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
}
mint operator-() const { return mint() - mint(*this); }
mint pow(u128 n) const {
mint ret(1), mul(*this);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
friend ostream &operator<<(ostream &os, const mint &b) {
return os << b.get();
}
friend istream &operator>>(istream &is, mint &b) {
int64_t t;
is >> t;
b = montgomery64(t);
return (is);
}
mint inverse() const { return pow(mod - 2); }
u64 get() const {
u64 ret = reduce(a);
return ret >= mod ? ret - mod : ret;
}
static u64 get_mod() { return mod; }
};
typename montgomery64::u64 montgomery64::mod, montgomery64::r, montgomery64::n2;
namespace fast_factorize {
using u64 = uint64_t;
template <typename mint>
bool miller_rabin(u64 n, vector<u64> as) {
if (mint::get_mod() != n) mint::set_mod(n);
u64 d = n - 1;
while (~d & 1) d >>= 1;
mint e{1}, rev{int64_t(n - 1)};
for (u64 a : as) {
if (n <= a) break;
u64 t = d;
mint y = mint(a).pow(t);
while (t != n - 1 && y != e && y != rev) {
y *= y;
t *= 2;
}
if (y != rev && t % 2 == 0) return false;
}
return true;
}
bool is_prime(u64 n) {
if (~n & 1) return n == 2;
if (n <= 1) return false;
if (n < (1LL << 30))
return miller_rabin<ArbitraryLazyMontgomeryModInt>(n, {2, 7, 61});
else
return miller_rabin<montgomery64>(
n, {2, 325, 9375, 28178, 450775, 9780504, 1795265022});
}
template <typename mint, typename T>
T pollard_rho(T n) {
if (~n & 1) return 2;
if (is_prime(n)) return n;
if (mint::get_mod() != n) mint::set_mod(n);
mint R, one = 1;
auto f = [&](mint x) { return x * x + R; };
auto rnd_ = [&]() { return rng() % (n - 2) + 2; };
while (1) {
mint x, y, ys, q = one;
R = rnd_(), y = rnd_();
T g = 1;
constexpr int m = 128;
for (int r = 1; g == 1; r <<= 1) {
x = y;
for (int i = 0; i < r; ++i) y = f(y);
for (int k = 0; g == 1 && k < r; k += m) {
ys = y;
for (int i = 0; i < m && i < r - k; ++i) q *= x - (y = f(y));
g = inner::gcd<T>(q.get(), n);
}
}
if (g == n) do
g = inner::gcd<T>((x - (ys = f(ys))).get(), n);
while (g == 1);
if (g != n) return g;
}
exit(1);
}
using i64 = long long;
vector<i64> inner_factorize(u64 n) {
if (n <= 1) return {};
u64 p;
if (n <= (1LL << 30))
p = pollard_rho<ArbitraryLazyMontgomeryModInt, uint32_t>(n);
else
p = pollard_rho<montgomery64, uint64_t>(n);
if (p == n) return {i64(p)};
auto l = inner_factorize(p);
auto r = inner_factorize(n / p);
copy(begin(r), end(r), back_inserter(l));
return l;
}
vector<i64> factorize(u64 n) {
auto ret = inner_factorize(n);
sort(begin(ret), end(ret));
return ret;
}
map<i64, i64> factor_count(u64 n) {
map<i64, i64> mp;
for (auto &x : factorize(n)) mp[x]++;
return mp;
}
vector<i64> divisors(u64 n) {
if (n == 0) return {};
vector<pair<i64, i64>> v;
for (auto &p : factorize(n)) {
if (v.empty() || v.back().first != p) {
v.emplace_back(p, 1);
} else {
v.back().second++;
}
}
vector<i64> ret;
auto f = [&](auto rc, int i, i64 x) -> void {
if (i == (int)v.size()) {
ret.push_back(x);
return;
}
for (int j = v[i].second;; --j) {
rc(rc, i + 1, x);
if (j == 0) break;
x *= v[i].first;
}
};
f(f, 0, 1);
sort(begin(ret), end(ret));
return ret;
}
} // namespace fast_factorize
using fast_factorize::divisors;
using fast_factorize::factor_count;
using fast_factorize::factorize;
using fast_factorize::is_prime;
/**
* @brief (Miller Rabin/Pollard's Rho)
* @docs docs/prime/fast-factorize.md
*/
using namespace Nyaan;
vp eval(string S) {
if (sz(S) == 1) {
vp v{pl(0, S[0] - '0')};
return v;
}
ll bc = S.back() - '0';
S.pop_back();
auto v = eval(S);
vp res;
each2(sm, b, v) {
res.emplace_back(sm, b * 10 + bc);
res.emplace_back(sm + b, bc);
}
return res;
}
void Nyaan::solve() {
ins(S);
trc(eval(S));
ll ans = 0;
each2(u, v, eval(S)) {
if (is_prime(u + v)) ans++;
}
out(ans);
}
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