#604393 (C++17) No.1339 循環小数

• 問題: No.1339 循環小数
• ユーザー: Gosu_Hiroo
• 提出日時: 2021-01-15 22:24:18
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 558 ms / 2,000 ms
• コード長: 17,428 bytes
• コンパイル時間: 2,183 ms
• コンパイル使用メモリ: 212,972 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-05-05 00:24:48
• 合計ジャッジ時間: 9,409 ms
• ジャッジサーバーID （参考情報）: judge5 / judge2

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 5,248 KB
testcase_01	AC	2 ms; 5,376 KB
testcase_02	AC	2 ms; 5,376 KB
testcase_03	AC	2 ms; 5,376 KB
testcase_04	AC	2 ms; 5,376 KB
testcase_05	AC	2 ms; 5,376 KB
testcase_06	AC	2 ms; 5,376 KB
testcase_07	AC	1 ms; 5,376 KB
testcase_08	AC	2 ms; 5,376 KB
testcase_09	AC	2 ms; 5,376 KB
testcase_10	AC	2 ms; 5,376 KB
testcase_11	AC	4 ms; 5,376 KB
testcase_12	AC	4 ms; 5,376 KB
testcase_13	AC	3 ms; 5,376 KB
testcase_14	AC	4 ms; 5,376 KB
testcase_15	AC	4 ms; 5,376 KB
testcase_16	AC	4 ms; 5,376 KB
testcase_17	AC	4 ms; 5,376 KB
testcase_18	AC	4 ms; 5,376 KB
testcase_19	AC	4 ms; 5,376 KB
testcase_20	AC	4 ms; 5,376 KB
testcase_21	AC	306 ms; 5,376 KB
testcase_22	AC	360 ms; 5,376 KB
testcase_23	AC	336 ms; 5,376 KB
testcase_24	AC	313 ms; 5,376 KB
testcase_25	AC	334 ms; 5,376 KB
testcase_26	AC	344 ms; 5,376 KB
testcase_27	AC	342 ms; 5,376 KB
testcase_28	AC	344 ms; 5,376 KB
testcase_29	AC	290 ms; 5,376 KB
testcase_30	AC	311 ms; 5,376 KB
testcase_31	AC	499 ms; 5,376 KB
testcase_32	AC	540 ms; 5,376 KB
testcase_33	AC	387 ms; 5,376 KB
testcase_34	AC	208 ms; 5,376 KB
testcase_35	AC	558 ms; 5,376 KB
testcase_36	AC	332 ms; 5,376 KB

ソースコード

/**
 * 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;
        while(N%2==0)N/=2;
        while(N%5==0)N/=5;
//        ll g = gcd(10, N);
//        ll t = atcoder::inv_mod(10/gcd(10,N), N/gcd(10,N));
        if(ll x = mod_log(10, inv_mod(10, 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;
}