結果

問題 No.1339 循環小数
ユーザー Gosu_Hiroo
提出日時 2021-01-15 22:15:20
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 17,401 bytes
コンパイル時間 2,154 ms
コンパイル使用メモリ 204,724 KB
最終ジャッジ日時 2025-01-17 19:36:37
ジャッジサーバーID
(参考情報)
judge5 / judge4
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 1
other AC * 3 WA * 33
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

/**
* code generated by JHelper
* More info: https://github.com/AlexeyDmitriev/JHelper
* @author
*/
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
template<typename T, typename U = T>
using P = pair<T, U>;
template<typename T>
using V = vector<T>;
using VI = vector<int>;
using VL = vector<long long>;
//#pragma GCC optimize("O3")
//#pragma GCC target("avx2")
//#pragma GCC target("avx512f")
//#pragma GCC optimize("unroll-loops")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
//#pragma GCC optimize("Ofast")
#define G(size_1) vector<vector<int>>(size_1, vector<int>())
#define SZ(x) ((long long)(x).size())
#define READ ({long long t;cin >> t;t;})
#define FOR(i, __begin, __end) for (auto i = (__begin) - ((__begin) > (__end)); i != (__end) - ((__begin) > (__end)); i += 1 - 2 * ((__begin) >
    (__end)))
#define REP(i, __end) for (auto i = decltype(__end){0}; i < (__end); ++i)
#define ALL(x) (x).begin(),(x).end()
#define RALL(x) (x).rbegin(),(x).rend()
#define F first
#define S second
#define y0 y3487465
#define y1 y8687969
#define j0 j1347829
#define j1 j234892
#define BIT(n) (1LL<<(n))
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() )
#define EB emplace_back
#define PB push_back
#define fcout cout << fixed << setprecision(12)
#define fcerr cerr << fixed << setprecision(12)
#define print(x) cout << (x) << '\n'
#define printE(x) cout << (x) << endl;
#define fprint(x) cout << fixed << setprecision(12) << (x) << '\n'
# define BYE(a) do { cout << (a) << endl; return ; } while (false)
#define LB lower_bound
#define UB upper_bound
#define LBI(c, x) distance((c).begin(), lower_bound((c).begin(), (c).end(), (x)))
#define UBI(c, x) distance((c).begin(), upper_bound((c).begin(), (c).end(), (x)))
#ifdef DEBUG
#define DBG(args...) { string _s = #args; replace(_s.begin(), _s.end(), ',', ' '); stringstream _ss(_s); istream_iterator<string> _it(_ss); _err(cerr
    ,_it, args); }
#define ERR(args...) { string _s = #args; replace(_s.begin(), _s.end(), ',', ' '); stringstream _ss(_s); istream_iterator<string> _it(_ss); _err(std
    ::cerr,_it, args); }
#else
#define DBG(args...) {};
#define ERR(args...) {};
#endif
void _err(std::ostream& cerr, istream_iterator<string> it){cerr << endl;}
template<typename T, typename... Args>
void _err(std::ostream& cerr, istream_iterator<string> it, T a, Args... args){
cerr << *it << " = " << a << " ";
_err(cerr, ++it, args...);
}
namespace aux{
template<std::size_t...>
struct seq{
};
template<std::size_t N, std::size_t... Is>
struct gen_seq : gen_seq<N - 1, N - 1, Is...>{
};
template<std::size_t... Is>
struct gen_seq<0, Is...> : seq<Is...>{
};
template<class Ch, class Tr, class Tuple, std::size_t... Is>
void print_tuple(std::basic_ostream<Ch, Tr>& os, Tuple const& t, seq<Is...>){
using swallow = int[];
(void) swallow{0, (void(os << (Is == 0 ? "" : ",") << std::get<Is>(t)), 0)...};
}
template<class Ch, class Tr, class Tuple, std::size_t... Is>
void read_tuple(std::basic_istream<Ch, Tr>& os, Tuple& t, seq<Is...>){
using swallow = int[];
(void) swallow{0, (void(os >> std::get<Is>(t)), 0)...};
}
} // aux::
template<class Ch, class Tr, class... Args>
auto operator<<(std::basic_ostream<Ch, Tr>& os, std::tuple<Args...> const& t)
-> std::basic_ostream<Ch, Tr>&{
os << "(";
aux::print_tuple(os, t, aux::gen_seq<sizeof...(Args)>());
return os << ")";
}
template<class Ch, class Tr, class... Args>
auto operator>>(std::basic_istream<Ch, Tr>& os, std::tuple<Args...>& t)
-> std::basic_istream<Ch, Tr>&{
aux::read_tuple(os, t, aux::gen_seq<sizeof...(Args)>());
return os;
}
template<class T>
inline bool chmax(T& a, const T& b){
if(a < b){
a = b;
return 1;
}
return 0;
}
template<class T>
inline bool chmin(T& a, const T& b){
if(b < a){
a = b;
return 1;
}
return 0;
}
template<typename T, typename U>
istream& operator>>(istream& is, pair<T, U>& V){
is >> V.F >> V.S;
return is;
}
template<typename T>
istream& operator>>(istream& is, vector<T>& V){
for(auto&& ele : V)is >> ele;
return is;
}
template<typename T>
ostream& operator<<(ostream& os, const vector<T> V){
os << "[";
int cnt = 0;
T curr;
if(!V.empty()){
for(int i = 0; i < V.size() - 1; ++i){
if(V[i] == curr)cnt++;
else cnt = 0;
if(cnt == 4)os << "... ";
if(cnt < 4)
os << i << ":" << V[i] << " ";
curr = V[i];
}
os << V.size() - 1 << ":" << V.back();
}
os << "]\n";
return os;
}
template<typename T, typename U>
ostream& operator<<(ostream& os, const pair<T, U> P){
os << "(";
os << P.first << "," << P.second;
os << ")";
return os;
}
template<typename T, typename U>
ostream& operator<<(ostream& os, const set<T, U> V){
os << "{";
if(!V.empty()){
auto it = V.begin();
for(int i = 0; i < V.size() - 1; ++i){
os << *it << " ";
it++;
}
os << *it;
}
os << "}\n";
return os;
}
template<typename K, typename H, typename P>
ostream& operator<<(ostream& os, const unordered_set<K, H, P> V){
os << "{";
if(!V.empty()){
auto it = V.begin();
for(int i = 0; i < V.size() - 1; ++i){
os << *it << " ";
it++;
}
os << *it;
}
os << "}\n";
return os;
}
template<typename K, typename C>
ostream& operator<<(ostream& os, const multiset<K, C> V){
os << "{";
if(!V.empty()){
auto it = V.begin();
for(int i = 0; i < V.size() - 1; ++i){
os << *it << " ";
it++;
}
os << *it;
}
os << "}";
return os;
}
template<typename K, typename T, typename C>
ostream& operator<<(ostream& os, const map<K, T, C> V){
os << "{";
if(!V.empty()){
auto it = V.begin();
for(int i = 0; i < V.size() - 1; ++i){
os << "(";
os << it->first << "," << it->second;
os << ") ";
it++;
}
os << "(";
os << it->first << "," << it->second;
os << ")";
}
os << "}\n";
return os;
}
template<typename K, typename T, typename C>
ostream& operator<<(ostream& os, const unordered_map<K, T, C> V){
os << "{";
if(!V.empty()){
auto it = V.begin();
for(int i = 0; i < V.size() - 1; ++i){
os << "(";
os << it->first << "," << it->second;
os << ") ";
it++;
}
os << "(";
os << it->first << "," << it->second;
os << ")";
}
os << "}\n";
return os;
}
template<typename T>
ostream& operator<<(ostream& os, const deque<T> V){
os << "[";
if(!V.empty()){
for(int i = 0; i < V.size() - 1; ++i){
os << V[i] << "->";
}
if(!V.empty())os << V.back();
}
os << "]\n";
return os;
};
template<typename T, typename Cont, typename Comp>
ostream& operator<<(ostream& os, const priority_queue<T, Cont, Comp> V){
priority_queue<T, Cont, Comp> _V = V;
os << "[";
if(!_V.empty()){
while(_V.size() > 1){
os << _V.top() << "->";
_V.pop();
}
os << _V.top();
}
os << "]\n";
return os;
};
template<class F>
struct y_combinator{
F f; // the lambda will be stored here
// a forwarding operator():
template<class... Args>
decltype(auto) operator()(Args&& ... args) const{
// we pass ourselves to f, then the arguments.
// the lambda should take the first argument as `auto&& recurse` or similar.
return f(*this, std::forward<Args>(args)...);
}
};
// helper function that deduces the type of the lambda:
template<class F>
y_combinator<std::decay_t<F>> recursive(F&& f){
return {std::forward<F>(f)};
}
struct hash_pair{
template<class T1, class T2>
size_t operator()(const pair<T1, T2>& p) const{
auto hash1 = hash<T1>{}(p.first);
auto hash2 = hash<T2>{}(p.second);
return hash1^hash2;
}
};
template<typename U>
auto vec(int n, U v){
return std::vector(n, v);
}
template<typename... Args>
auto vec(int n, Args... args){
auto val = vec(std::forward<Args>(args)...);
return std::vector<decltype(val)>(n, std::move(val));
}
const double PI = 2*acos(.0);
const int INF = 0x3f3f3f3f;
template<class T>
inline T ceil(T a, T b){return (a + b - 1)/b;}
inline long long popcount(ll x){return __builtin_popcountll(x);}
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;
}
#ifndef ATCODER_MATH_HPP
#define ATCODER_MATH_HPP 1
#include <algorithm>
#include <cassert>
#include <tuple>
#include <vector>
#ifndef ATCODER_INTERNAL_MATH_HPP
#define ATCODER_INTERNAL_MATH_HPP 1
#include <utility>
namespace atcoder {
namespace internal {
// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
// Fast moduler by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
unsigned int _m;
unsigned long long im;
// @param m `1 <= m`
barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
// @return m
unsigned int umod() const { return _m; }
// @param a `0 <= a < m`
// @param b `0 <= b < m`
// @return `a * b % m`
unsigned int mul(unsigned int a, unsigned int b) const {
// [1] m = 1
// a = b = im = 0, so okay
// [2] m >= 2
// im = ceil(2^64 / m)
// -> im * m = 2^64 + r (0 <= r < m)
// let z = a*b = c*m + d (0 <= c, d < m)
// a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
// c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
// ((ab * im) >> 64) == c or c + 1
unsigned long long z = a;
z *= b;
#ifdef _MSC_VER
unsigned long long x;
_umul128(z, im, &x);
#else
unsigned long long x =
(unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned int v = (unsigned int)(z - x * _m);
if (_m <= v) v += _m;
return v;
}
};
// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
long long d = n - 1;
while (d % 2 == 0) d /= 2;
for (long long a : {2, 7, 61}) {
long long t = d;
long long y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) {
return false;
}
}
return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);
// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
a = safe_mod(a, b);
if (a == 0) return {b, 0};
// Contracts:
// [1] s - m0 * a = 0 (mod b)
// [2] t - m1 * a = 0 (mod b)
// [3] s * |m1| + t * |m0| <= b
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while (t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b
// [3]:
// (s - t * u) * |m1| + t * |m0 - m1 * u|
// <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
// = s * |m1| + t * |m0| <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
// by [3]: |m0| <= b/g
// by g != b: |m0| < b/g
if (m0 < 0) m0 += b / s;
return {s, m0};
}
// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0) x /= 2;
for (int i = 3; (long long)(i)*i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) {
x /= i;
}
}
}
if (x > 1) {
divs[cnt++] = x;
}
for (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
} // namespace internal
} // namespace atcoder
#endif // ATCODER_INTERNAL_MATH_HPP
namespace atcoder {
long long pow_mod(long long x, long long n, int m) {
assert(0 <= n && 1 <= m);
if (m == 1) return 0;
internal::barrett bt((unsigned int)(m));
unsigned int r = 1, y = (unsigned int)(internal::safe_mod(x, m));
while (n) {
if (n & 1) r = bt.mul(r, y);
y = bt.mul(y, y);
n >>= 1;
}
return r;
}
long long inv_mod(long long x, long long m) {
assert(1 <= m);
auto z = internal::inv_gcd(x, m);
assert(z.first == 1);
return z.second;
}
// (rem, mod)
std::pair<long long, long long> crt(const std::vector<long long>& r,
const std::vector<long long>& m) {
assert(r.size() == m.size());
int n = int(r.size());
// Contracts: 0 <= r0 < m0
long long r0 = 0, m0 = 1;
for (int i = 0; i < n; i++) {
assert(1 <= m[i]);
long long r1 = internal::safe_mod(r[i], m[i]), m1 = m[i];
if (m0 < m1) {
std::swap(r0, r1);
std::swap(m0, m1);
}
if (m0 % m1 == 0) {
if (r0 % m1 != r1) return {0, 0};
continue;
}
// assume: m0 > m1, lcm(m0, m1) >= 2 * max(m0, m1)
// (r0, m0), (r1, m1) -> (r2, m2 = lcm(m0, m1));
// r2 % m0 = r0
// r2 % m1 = r1
// -> (r0 + x*m0) % m1 = r1
// -> x*u0*g % (u1*g) = (r1 - r0) (u0*g = m0, u1*g = m1)
// -> x = (r1 - r0) / g * inv(u0) (mod u1)
// im = inv(u0) (mod u1) (0 <= im < u1)
long long g, im;
std::tie(g, im) = internal::inv_gcd(m0, m1);
long long u1 = (m1 / g);
// |r1 - r0| < (m0 + m1) <= lcm(m0, m1)
if ((r1 - r0) % g) return {0, 0};
// u1 * u1 <= m1 * m1 / g / g <= m0 * m1 / g = lcm(m0, m1)
long long x = (r1 - r0) / g % u1 * im % u1;
// |r0| + |m0 * x|
// < m0 + m0 * (u1 - 1)
// = m0 + m0 * m1 / g - m0
// = lcm(m0, m1)
r0 += x * m0;
m0 *= u1; // -> lcm(m0, m1)
if (r0 < 0) r0 += m0;
}
return {r0, m0};
}
long long floor_sum(long long n, long long m, long long a, long long b) {
long long ans = 0;
if (a >= m) {
ans += (n - 1) * n * (a / m) / 2;
a %= m;
}
if (b >= m) {
ans += n * (b / m);
b %= m;
}
long long y_max = (a * n + b) / m, x_max = (y_max * m - b);
if (y_max == 0) return ans;
ans += (n - (x_max + a - 1) / a) * y_max;
ans += floor_sum(y_max, a, m, (a - x_max % a) % a);
return ans;
}
} // namespace atcoder
#endif // ATCODER_MATH_HPP
using namespace atcoder;
void solve(std::istream& cin, std::ostream& cout, std::ostream& cerr){
auto solve = [&](){
ll N;
cin >> N;
N = N/gcd(10,N);
ll g = gcd(10, N);
// ll t = atcoder::inv_mod(10/gcd(10,N), N/gcd(10,N));
if(ll x = mod_log(10/g, inv_mod(10/g, N), N);x)print(x + 1);
else
print(1);
};
int testcases;
cin >> testcases;
for(int case_num = 1; case_num <= testcases; case_num++){
solve();
}
}
#undef int
int main() {
istream& in(cin);
ostream& out(cout);
ostringstream err;
in.tie(0); ios::sync_with_stdio(0);
solve(in, out, err);
return 0;
}
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