結果
| 問題 |
No.1648 Sum of Powers
|
| コンテスト | |
| ユーザー |
 tomo0608
|
| 提出日時 | 2023-10-07 16:52:43 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 54 ms / 2,000 ms |
| コード長 | 14,706 bytes |
| コンパイル時間 | 2,815 ms |
| コンパイル使用メモリ | 237,140 KB |
| 最終ジャッジ日時 | 2025-02-17 06:09:46 |
|
ジャッジサーバーID （参考情報） |
judge4 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 56 |
ソースコード
#pragma region competitive_programming
#ifdef __LOCAL
#define _GLIBCXX_DEBUG
#endif
#pragma GCC optimize("Ofast")
#include<bits/stdc++.h>
//#include "modint_plus.hpp"
//typedef atcoder::modint1000000007 mint;
//typedef atcoder::modint998244353 mint;
//#include<atcoder/convolution>
//#include "Formal_Power_Series.hpp"
//typedef tomo0608::Formal_Power_Series<mint> fps;
#include<atcoder/math>
namespace tomo0608 {
#define is_prime(n) atcoder::internal::is_prime_constexpr(n)
std::map<long long, int> prime_factorization(long long n) {
std::map<long long, int> res;
n = abs(n);
assert(n > 1);
for (long long i = 2; i * i <= n; i++) {
if (n % i == 0) {
int num = 0;
while (n % i == 0) {
num++;
n /= i;
}
res[i] = num;
}
}
if (n != 1)res[n] = 1;
return res;
}
class Osa_k {
public:
const int MAX_N;
std::vector<int> min_prime;
Osa_k(int size) : MAX_N(size), min_prime(size + 1) {
if (MAX_N < 2)return;
std::vector<int> primes{ 2, 3 };
for (int i = 2; i <= MAX_N; i += 2)min_prime[i] = 2;
for (int i = 3; i <= MAX_N; i += 6)min_prime[i] = 3;
for (int i = 5, d = 4; i <= MAX_N; i += d = 6 - d) {
if (!min_prime[i]) {
min_prime[i] = i;
primes.emplace_back(i);
}
for (int j = 2; j < (int)primes.size() && i * primes[j] <= MAX_N; j++) {
min_prime[i * primes[j]] = primes[j];
if (primes[j] == min_prime[i])break;
}
}
}
std::vector<std::pair<int, int>> factorization(int n) {
assert(0 < n && n <= MAX_N);
std::vector<std::pair<int, int>> res;
while (n > 1) {
int p = min_prime[n];
int num = 0;
while (min_prime[n] == p) {
num++;
n /= p;
}
res.emplace_back(p, num);
}
return res;
}
};
std::vector<int> prime_enumerate(int N) {
std::vector<bool> sieve(N / 3 + 1, 1);
for (int p = 5, d = 4, i = 1, sqn = std::sqrt(N); p <= sqn; p += d = 6 - d, i++) {
if (!sieve[i]) continue;
for (int q = p * p / 3, r = d * p / 3 + (d * p % 3 == 2), s = 2 * p, qe = sieve.size();q < qe; q += r = s - r)sieve[q] = 0;
}
std::vector<int> ret{ 2, 3 };
for (int p = 5, d = 4, i = 1; p <= N; p += d = 6 - d, i++)
if (sieve[i]) ret.push_back(p);
while (!ret.empty() && ret.back() > N) ret.pop_back();
return ret;
}
template<class T>
void div_zeta(std::vector<T>& a) {
std::vector<int> sieve = prime_enumerate((int)a.size() - 1);
for (auto& p : sieve)for (int i = 1; i * p < a.size(); i++)a[i * p] += a[i];
}
template<class T>
void div_mobius(std::vector<T>& a) {
std::vector<int> sieve = prime_enumerate((int)a.size() - 1);
for (auto& p : sieve)for (int i = ((int)a.size() - 1) / p; i > 0; i--)a[i * p] -= a[i];
}
template<class T>
void mul_zeta(std::vector<T>& a) {
std::vector<int> sieve = prime_enumerate((int)a.size() - 1);
for (auto& p : sieve)for (int i = ((int)a.size() - 1) / p; i > 0; i--)a[i] += a[i * p];
}
template<class T>
void mul_mobius(std::vector<T>& a) {
std::vector<int> sieve = prime_enumerate((int)a.size() - 1);
for (auto& p : sieve)for (int i = 1; i * p < a.size(); i++)a[i] -= a[i * p];
}
template<class T>
std::vector<T> gcd_convolution(std::vector<T> a, std::vector<T> b){
mul_zeta(a);
mul_zeta(b);
for(int i = 0; i < a.size(); i++)a[i] *= b[i];
mul_mobius(a);
return a;
}
template<class T>
std::vector<T> lcm_convolution(std::vector<T> a, std::vector<T> b){
div_zeta(a);
div_zeta(b);
for(int i = 0; i < a.size(); i++)a[i] *= b[i];
div_mobius(a);
return a;
}
long long euler_phi(long long n) {
long long res = n;
for (long long i = 2; i * i <= n; i++) {
if (n % i == 0) {
res -= res / i;
while (n % i == 0)n /= i;
}
}
if (n > 1)res -= res / n;
return res;
}
#if __cplusplus >= 201703L
template<class Set,
class Monoid,
auto action,
auto composition,
auto id>
long long discrete_logarithm(Monoid f, Set s, Set t, long long MAX_N) {// return the smallest integer n lower than MAX_N such that f^n s = t if exists, otherwise -1
static_assert(std::is_convertible_v<decltype(action),
std::function<Set(Monoid, Set)>>, "action must work as Set(Monoid, Set)");
static_assert(std::is_convertible_v<decltype(composition),
std::function<Monoid(Monoid, Monoid)>>, "composition must work as Monoid(Monoid, Monoid)");
static_assert(std::is_convertible_v<decltype(id),
std::function<Monoid()>>, "id must work as Monoid()");
#else
template<class Set,
class Monoid,
Set(*action)(Monoid, Set),
Monoid(*composition)(Monoid, Monoid),
Monoid(*id)()>
long long discrete_logarithm(Monoid f, Set s, Set t, long long MAX_N) {
#endif
if (s == t)return 0;
long long SQRT_N = sqrt(MAX_N) + 1;
std::set<Set> T;
Set f_t = t;
for (int i = 1; i <= SQRT_N; i++) {
f_t = action(f, f_t);
T.emplace(f_t);
}
Monoid f_m = id();
{
long long n = SQRT_N;
Monoid _f = f;
while(n > 0){
if(n&1)f_m = composition(f_m, _f);
_f = composition(_f, _f);
n >>= 1;
}
}
int num_of_failures = 0;
Set pre_s = s;
for (int k = 1; k <= SQRT_N; k++) {
Set now_s = action(f_m, pre_s);
if (T.count(now_s)) {
Set lhs = pre_s;
for (int i = 0; i < SQRT_N; i++, lhs = action(f, lhs)) {
if (lhs == t)return (k - 1) * SQRT_N + i;
}
num_of_failures++;
if (num_of_failures == 2)return -1;
}
std::swap(pre_s, now_s);
}
return -1;
};
}
namespace tomo0608 {
typedef long long ll;
typedef long double ld;
template <class T> using V = std::vector<T>;
template <class T> using VV = V<V<T>>;
template <class T> using VVV = V<VV<T>>;
typedef std::pair<int, int> pii;
typedef std::pair<long long, long long> pll;
template<class... T>void input(T&... a) { (std::cin >> ... >> a); };
#define INT(...) int __VA_ARGS__; IN(__VA_ARGS__)
#define LL(...) long long __VA_ARGS__; IN(__VA_ARGS__)
#define CHAR(...) char __VA_ARGS__; IN(__VA_ARGS__)
#define STR(...) string __VA_ARGS__; IN(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__; IN(__VA_ARGS__)
#define VEC(type, name, size) std::vector<type> name(size);IN(name)
#define VECVEC(type, name, h, w) std::vector<std::vector<type>> name(h, std::vector<type>(w));IN(name)
template<class T1, class T2> std::istream& operator>>(std::istream& is, std::pair<T1, T2>& p) { is >> p.first >> p.second; return is; }
template<class T1, class T2> std::ostream& operator<<(std::ostream& os, const std::pair<T1, T2>& p) { os << '(' << p.first << ", " << p.second << ')'; return os; }
template<class T> std::istream& operator>>(std::istream& is, std::vector<T>& v) { for (auto& e : v) is >> e; return is; }
template<class T> std::ostream& operator<<(std::ostream& os, const std::vector<T>& v) { for (auto& e : v) os << e << ' '; return os; }
template<typename T> std::ostream& operator << (std::ostream& os, std::set<T>& set_var) { os << "{"; for (auto itr = set_var.begin(); itr != set_var.end(); itr++) { os << *itr;++itr;if (itr != set_var.end()) os << ", ";itr--; }os << "}";return os; }
template <typename T, typename U> std::ostream& operator<<(std::ostream& os, std::map<T, U>& map_var) { os << "{";for (auto itr = map_var.begin(); itr != map_var.end(); itr++) { os << *itr;itr++;if (itr != map_var.end()) os << ", ";itr--; }os << "}";return os; }
template<int i, class T> void print_tuple(std::ostream&, const T&) {}
template<int i, class T, class H, class ...Args> void print_tuple(std::ostream& os, const T& t) {
if (i){os << ", ";} os << std::get<i>(t); print_tuple<i + 1, T, Args...>(os, t);
}
template<class ...Args> std::ostream& operator<<(std::ostream& os, const std::tuple<Args...>& t) {
os << "{"; print_tuple<0, std::tuple<Args...>, Args...>(os, t); return os << "}";
}
void IN() {}
template <class Head, class... Tail> void IN(Head& head, Tail &...tail) {
std::cin >> head;
IN(tail...);
}
void print() { std::cout << '\n'; }
template<class T, class... Ts>void print(const T& a, const Ts&... b) { std::cout << a; (std::cout << ... << (std::cout << ' ', b)); std::cout << '\n'; }
void drop() { std::cout << '\n';exit(0); }
template<class T, class... Ts>void drop(const T& a, const Ts&... b) { std::cout << a; (std::cout << ... << (std::cout << ' ', b)); std::cout << '\n';exit(0); }
#ifdef __LOCAL
void debug_out() { std::cerr << std::endl; }
template < class Head, class... Tail> void debug_out(Head H, Tail... T) { std::cerr << ' ' << H; debug_out(T...); }
#define debug(...) std::cerr << 'L' << __LINE__ << " [" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#define dump(x) std::cerr << 'L' << __LINE__ << " " << #x << " = " << (x) << std::endl
#else
#define debug(...) (void(0))
#define dump(x) (void(0))
#endif
#define rep1(a) for(long long i = 0; i < (a); i++)
#define rep2(i, a) for(long long i = 0; i < (a); i++)
#define rep3(i, a, b) for(long long i = (a); i < (b); i++)
#define rep4(i, a, b, c) for(long long i = (a); i < (b); i += (c))
#define drep1(a) for(long long i = (a)-1; i >= 0; i--)
#define drep2(i, a) for(long long i = (a)-1; i >= 0; i--)
#define drep3(i, a, b) for(long long i = (a)-1; i >= (b); i--)
#define drep4(i, a, b, c) for(long long i = (a)-1; i >= (b); i -= (c))
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define drep(...) overload4(__VA_ARGS__, drep4, drep3, drep2, drep1)(__VA_ARGS__)
#define endl '\n'
struct io_setup {
io_setup() {
std::cin.tie(0);
std::ios_base::sync_with_stdio(false);
std::cout << std::setprecision(20);
}
}io_setup;
} // namespace tomo0608
namespace tomo0608 {
#define ALL(x) x.begin(),x.end()
template <class T = long long, class S> T SUM(const S& v) { return accumulate(ALL(v), T(0)); }
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define SORT(v) sort(ALL(v))
#define REVERSE(v) reverse(ALL(v))
#define RSORT(v) sort(ALL(v)); reverse(ALL(v))
#define UNIQUE(x) SORT(x), x.erase(unique(ALL(x)), x.end())
#define lb(c, x) distance((c).begin(), lower_bound(ALL(c), (x)))
#define ub(c, x) distance((c).begin(), upper_bound(ALL(c), (x)))
template <typename T> void zip(std::vector<T>& x) { std::vector<T> y = x;UNIQUE(y);for (int i = 0; i < x.size(); ++i) { x[i] = lb(y, x[i]); } }
template<class T> using priority_queue_rev = std::priority_queue<T, std::vector<T>, std::greater<T>>;
template<class T, class U> inline bool chmax(T& a, const U& b) { if (a < b) { a = b; return 1; } return 0; }
template<class T, class U> inline bool chmin(T& a, const U& b) { if (a > b) { a = b; return 1; } return 0; }
template<class T> inline int count_between(std::vector<T>& a, T l, T r) { return lower_bound(ALL(a), r) - lower_bound(ALL(a), l); } // [l, r)
template<typename T> int bittest(T n, int k) { return (n >> k) & 1; }
int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
int topbit(long long t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
int lowbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); }
int lowbit(long long a) { return a == 0 ? 64 : __builtin_ctzll(a); }
#define perm(v) for(bool permrepflag = true; (permrepflag ? exchange(permrepflag, false) : next_permutation(ALL(v)));)
template <typename T, typename S> T ceil(T x, S y) {
assert(y);
return (y < 0 ? ceil(-x, -y) : (x > 0 ? (x + y - 1) / y : x / y));
}
template <typename T, typename S> T floor(T x, S y) {
assert(y);
return (y < 0 ? floor(-x, -y) : (x > 0 ? x / y : x / y - (x % y == 0 ? 0 : 1)));
}
template <typename T> std::vector<int> id_sort(const std::vector<T>& v, bool greater = false) {
int n = v.size();
std::vector<int> ret(n);
std::iota(ALL(ret), 0);
std::sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; });
return ret;
}
}
//using namespace atcoder;
using namespace std;
using namespace tomo0608;
int dx[8] = { 1, 0, -1, 0, 1, 1, -1, -1 };
int dy[8] = { 0, 1, 0, -1, 1, -1, -1, 1 };
// インタラクティブ問題のときは出力するたびにcout.flush();を忘れない!!!!!
void solve();
int main() {
int codeforces = 1;
//cin >> codeforces;
while (codeforces--) {
solve();
}
return 0;
}
#pragma endregion
typedef array<ll,2> Set;
typedef array<ll, 4> Monoid;
const ll MOD = 998244353;
Set action(Monoid M, Set s){
Set res;
res[0] = M[0] * s[0] + M[1] * s[1];
res[1] = M[2] * s[0] + M[3] * s[1];
res[0] = (res[0] + MOD)%MOD;
res[1] = (res[1] + MOD)%MOD;
return res;
};
Monoid composition(Monoid M_1, Monoid M_2){
Monoid res;
res[0] = M_1[0] * M_2[0] + M_1[1] * M_2[2];
res[1] = M_1[0] * M_2[1] + M_1[1] * M_2[3];
res[2] = M_1[2] * M_2[0] + M_1[3] * M_2[2];
res[3] = M_1[2] * M_2[1] + M_1[3] * M_2[3];
res[0] = (res[0] + MOD)%MOD;
res[1] = (res[1] + MOD)%MOD;
res[2] = (res[2] + MOD)%MOD;
res[3] = (res[3] + MOD)%MOD;
return res;
};
Monoid id(){
Monoid e;
e[0] = 1;
e[1] = 0;
e[2] = 0;
e[3] = 1;
return e;
};
void solve() {
LL(a, b, p, q);
Monoid f;
f[0] = a;
f[1] = MOD-b;
f[2] = 1;
f[3] = 0;
Set s, t;
s[0] = (a*a-2*b+MOD)%MOD;
s[1] = a;
t[0] = p;
t[1] = q;
ll MAX_N = 10000000001;
print(discrete_logarithm<Set, Monoid, action, composition, id>(f, s, t, MAX_N)+2);
}