#787293 (C++17) No.1611 Minimum Multiple with Double Divisors

提出ソース

結果

問題	No.1611 Minimum Multiple with Double Divisors
ユーザー	haruki_K
提出日時	2022-08-12 07:47:08
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	1,461 ms / 2,000 ms
コード長	13,055 bytes
コンパイル時間	3,868 ms
コンパイル使用メモリ	217,816 KB
実行使用メモリ	4,372 KB
最終ジャッジ日時	2023-10-23 18:23:39
合計ジャッジ時間	22,639 ms
ジャッジサーバーID （参考情報）	judge11 / judge13

このコードへのチャレンジ
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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	1,461 ms 4,348 KB
testcase_01	AC	653 ms 4,348 KB
testcase_02	AC	710 ms 4,348 KB
testcase_03	AC	711 ms 4,348 KB
testcase_04	AC	709 ms 4,348 KB
testcase_05	AC	710 ms 4,348 KB
testcase_06	AC	709 ms 4,348 KB
testcase_07	AC	712 ms 4,372 KB
testcase_08	AC	709 ms 4,372 KB
testcase_09	AC	708 ms 4,372 KB
testcase_10	AC	255 ms 4,372 KB
testcase_11	AC	881 ms 4,372 KB
testcase_12	AC	824 ms 4,372 KB
testcase_13	AC	823 ms 4,372 KB
testcase_14	AC	820 ms 4,372 KB
testcase_15	AC	819 ms 4,372 KB
testcase_16	AC	824 ms 4,372 KB
testcase_17	AC	819 ms 4,372 KB
testcase_18	AC	823 ms 4,372 KB
testcase_19	AC	7 ms 4,372 KB
testcase_20	AC	7 ms 4,372 KB
testcase_21	AC	7 ms 4,372 KB
testcase_22	AC	8 ms 4,372 KB
testcase_23	AC	7 ms 4,372 KB
testcase_24	AC	8 ms 4,372 KB
testcase_25	AC	7 ms 4,372 KB
testcase_26	AC	7 ms 4,372 KB
testcase_27	AC	7 ms 4,372 KB
testcase_28	AC	2 ms 4,372 KB
testcase_29	AC	2 ms 4,372 KB
testcase_30	AC	2 ms 4,372 KB
testcase_31	AC	2 ms 4,372 KB
testcase_32	AC	2 ms 4,372 KB
testcase_33	AC	2 ms 4,372 KB
testcase_34	AC	3 ms 4,372 KB
testcase_35	AC	2 ms 4,372 KB
testcase_36	AC	2 ms 4,372 KB
testcase_37	AC	2 ms 4,372 KB
testcase_38	AC	2 ms 4,372 KB

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ソースコード

raw source code

// >>> TEMPLATES
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;
#define int ll
using pii = pair<int, int>;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define rep1(i, n) for (int i = 1; i <= (int)(n); i++)
#define repR(i, n) for (int i = (int)(n)-1; i >= 0; i--)
#define rep1R(i, n) for (int i = (int)(n); i >= 1; i--)
#define loop(i, a, B) for (int i = a; i B; i++)
#define loopR(i, a, B) for (int i = a; i B; i--)
#define all(x) begin(x), end(x)
#define allR(x) rbegin(x), rend(x)
#define pb push_back
#define eb emplace_back
#define fst first
#define snd second
template <class Int> auto constexpr inf_ = numeric_limits<Int>::max()/2-1;
auto constexpr INF32 = inf_<int32_t>;
auto constexpr INF64 = inf_<int64_t>;
auto constexpr INF   = inf_<int>;
#ifdef LOCAL
#include "debug.hpp"
#define oj_local(x, y) (y)
#else
#define dump(...) (void)(0)
#define debug if (0)
#define oj_local(x, y) (x)
#endif
template <class T, class Comp> struct pque : priority_queue<T, vector<T>, Comp> { vector<T> &data() { return this->c; } void clear() { this->c.clear(); } };
template <class T> using pque_max = pque<T, less<T>>;
template <class T> using pque_min = pque<T, greater<T>>;
template <class T, class = typename T::iterator, enable_if_t<!is_same<T, string>::value, int> = 0>
ostream& operator<<(ostream& os, T const& a) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; }
template <class T, size_t N, enable_if_t<!is_same<T, char>::value, int> = 0>
ostream& operator<<(ostream& os, const T (&a)[N]) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; }
template <class T, class = decltype(begin(declval<T&>())), class = typename enable_if<!is_same<T, string>::value>::type>
istream& operator>>(istream& is, T &a) { for (auto& x : a) is >> x; return is; }
template <class T, class S> ostream& operator<<(ostream& os, pair<T, S> const& p) { return os << p.first << " " << p.second; }
template <class T, class S> istream& operator>>(istream& is, pair<T, S>& p) { return is >> p.first >> p.second; }
template <class... T> ostream& operator<<(ostream& os, tuple<T...> const& t)
{ bool f = true; apply([&](auto&&... x) { ((os << (f ? f = false, "" : " ") << x), ...); }, t); return os; }
template <class... T> istream& operator>>(istream& is, tuple<T...>& t) { apply([&](auto&&... x) { ((is >> x), ...); }, t); return is; }
struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup;
template <class F> struct FixPoint : private F {
    constexpr FixPoint(F&& f) : F(forward<F>(f)) {}
    template <class... T> constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward<T>(x)...); }
};
struct MakeFixPoint { template <class F> constexpr auto operator|(F&& f) const { return FixPoint<F>(forward<F>(f)); } };
#define def(name, ...) auto name = MakeFixPoint() | [&](auto &&name, __VA_ARGS__)
template <class T, size_t d> struct vec_impl {
    using type = vector<typename vec_impl<T, d-1>::type>;
    template <class... U> static type make_v(size_t n, U&&... x) { return type(n, vec_impl<T, d-1>::make_v(forward<U>(x)...)); }
};
template <class T> struct vec_impl<T, 0> { using type = T; static type make_v(T const& x = {}) { return x; } };
template <class T, size_t d = 1> using vec = typename vec_impl<T, d>::type;
template <class T, size_t d = 1, class... Args> auto make_v(Args&&... args) { return vec_impl<T, d>::make_v(forward<Args>(args)...); }
template <class T> void quit(T const& x) { cout << x << '\n'; exit(0); }
template <class T, class U> constexpr bool chmin(T& x, U const& y) { if (x > (T)y) { x = (T)y; return true; } return false; }
template <class T, class U> constexpr bool chmax(T& x, U const& y) { if (x < (T)y) { x = (T)y; return true; } return false; }
template <class It> constexpr auto sumof(It b, It e) { return accumulate(b, e, typename iterator_traits<It>::value_type{}); }
template <class T, class = decltype(begin(declval<T&>()))> constexpr auto min(T const& a) { return *min_element(begin(a), end(a)); }
template <class T, class = decltype(begin(declval<T&>()))> constexpr auto max(T const& a) { return *max_element(begin(a), end(a)); }
template <class T> constexpr T min(set<T> const& st) { assert(st.size()); return *st.begin(); }
template <class T> constexpr T max(set<T> const& st) { assert(st.size()); return *prev(st.end()); }
template <class T> constexpr T min(multiset<T> const& st) { assert(st.size()); return *st.begin(); }
template <class T> constexpr T max(multiset<T> const& st) { assert(st.size()); return *prev(st.end()); }
constexpr ll max(signed x, ll y) { return max<ll>(x, y); }
constexpr ll max(ll x, signed y) { return max<ll>(x, y); }
constexpr ll min(signed x, ll y) { return min<ll>(x, y); }
constexpr ll min(ll x, signed y) { return min<ll>(x, y); }
template <class T> int sz(T const& x) { return x.size(); }
template <class C, class T> int lbd(C const& v, T const& x) { return lower_bound(begin(v), end(v), x)-begin(v); }
template <class C, class T> int ubd(C const& v, T const& x) { return upper_bound(begin(v), end(v), x)-begin(v); }
constexpr ll mod(ll x, ll m) { assert(m > 0); return (x %= m) < 0 ? x+m : x; }
constexpr ll div_floor(ll x, ll y) { assert(y != 0); return x/y - ((x^y) < 0 and x%y); }
constexpr ll div_ceil(ll x, ll y) { assert(y != 0); return x/y + ((x^y) > 0 and x%y); }
constexpr int dx[] = { 1, 0, -1, 0, 1, -1, -1, 1 };
constexpr int dy[] = { 0, 1, 0, -1, 1, 1, -1, -1 };
auto four_nbd(int n, int m) {
    static vector<pair<int, int>> v;
    return [n, m](int i, int j) {
        const int dx[] = { 1, 0, -1, 0 }, dy[] = { 0, 1, 0, -1 };
        v.clear();
        rep (dir, 4) {
            int ni = i+dx[dir], nj = j+dy[dir];
            if (0 <= ni and ni < n and 0 <= nj and nj < m) {
                v.emplace_back(ni, nj);
            }
        }
        return v;
    };
};
template <class Comp> vector<int> iota(int n, Comp comp) {
    vector<int> idx(n);
    iota(begin(idx), end(idx), 0);
    stable_sort(begin(idx), end(idx), comp);
    return idx;
}
constexpr int popcnt(ll x) { return __builtin_popcountll(x); }
mt19937_64 seed_{random_device{}()};
template <class Int> Int rand(Int a, Int b) { return uniform_int_distribution<Int>(a, b)(seed_); }
i64 irand(i64 a, i64 b) { return rand<i64>(a, b); } // [a, b]
u64 urand(u64 a, u64 b) { return rand<u64>(a, b); } //
template <class It> void shuffle(It l, It r) { shuffle(l, r, seed_); }
template <class V> V &operator--(V &v) { for (auto &x : v) --x; return v; }
template <class V> V &operator++(V &v) { for (auto &x : v) ++x; return v; }
bool next_product(vector<int> &v, int m) {
    repR (i, v.size()) if (++v[i] < m) return true; else v[i] = 0;
    return false;
}
bool next_product(vector<int> &v, vector<int> const& s) {
    repR (i, v.size()) if (++v[i] < s[i]) return true; else v[i] = 0;
    return false;
}
template <class vec> int sort_unique(vec &v) {
    sort(begin(v), end(v));
    v.erase(unique(begin(v), end(v)), end(v));
    return v.size();
}
template <class It> auto prefix_sum(It l, It r) {
    vector<typename It::value_type> s = { 0 };
    while (l != r) s.emplace_back(s.back() + *l++);
    return s;
}
template <class It> auto suffix_sum(It l, It r) {
    vector<typename It::value_type> s = { 0 };
    while (l != r) s.emplace_back(*--r + s.back());
    reverse(s.begin(), s.end());
    return s;
}
template <class T> T pop(vector<T> &a) { auto x = a.back(); a.pop_back(); return x; }
template <class T> T pop_back(vector<T> &a) { auto x = a.back(); a.pop_back(); return x; }
template <class T, class V, class C> T pop(priority_queue<T, V, C> &a) { auto x = a.top(); a.pop(); return x; }
template <class T> T pop(queue<T> &a) { auto x = a.front(); a.pop(); return x; }
template <class T> T pop_front(deque<T> &a) { auto x = a.front(); a.pop_front(); return x; }
template <class T> T pop_back(deque<T> &a) { auto x = a.back(); a.pop_back(); return x; }
template <class T> T pop_front(set<T> &a) { auto x = *a.begin(); a.erase(a.begin()); return x; }
template <class T> T pop_back(set<T> &a) { auto it = prev(a.end()); auto x = *it; a.erase(it); return x; }
template <class T> T pop_front(multiset<T> &a) { auto it = a.begin(); auto x = *it; a.erase(it); return x; }
template <class T> T pop_back(multiset<T> &a) { auto it = prev(a.end()); auto x = *it; a.erase(it); return x; }
// <<<
// >>> is_prime, factor
namespace internal {

using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;
using u128 = __uint128_t;

mt19937_64 mt{random_device{}()};
u64 rnd(u64 n) { return uniform_int_distribution<u64>(0, n-1)(mt); }

// >>> montgomery (64bit)
struct m64 {
    using i64 = int64_t;
    using u64 = uint64_t;
    using u128 = __uint128_t;

    inline static u64 m, r, n2; // r * m = -1 (mod 1<<64), n2 = 1<<128 (mod m)
    static void set_mod(u64 m) {
        assert(m < (1ull << 62));
        assert((m & 1) == 1);
        m64::m = m;
        n2 = -u128(m) % m;
        r = m;
        rep (_, 5) r *= 2 - m*r;
        r = -r;
        assert(r * m == -1ull);
    }
    static u64 reduce(u128 b) { return (b + u128(u64(b) * r) * m) >> 64; }

    u64 x;
    m64() : x(0) {}
    m64(u64 x) : x(reduce(u128(x) * n2)){};
    u64 val() const { u64 y = reduce(x); return y >= m ? y-m : y; }
    m64 &operator+=(m64 y) {
        x += y.x - (m << 1);
        x = (i64(x) < 0 ? x + (m << 1) : x);
        return *this;
    }
    m64 &operator-=(m64 y) {
        x -= y.x;
        x = (i64(x) < 0 ? x + (m << 1) : x);
        return *this;
    }
    m64 &operator*=(m64 y) { x = reduce(u128(x) * y.x); return *this; }
    m64 operator+(m64 y) const { return m64(*this) += y; }
    m64 operator-(m64 y) const { return m64(*this) -= y; }
    m64 operator*(m64 y) const { return m64(*this) *= y; }
    bool operator==(m64 y) const { return (x >= m ? x-m : x) == (y.x >= m ? y.x-m : y.x); }
    bool operator!=(m64 y) const { return not operator==(y); }
    m64 pow(u64 n) const {
        m64 y = 1, z = *this;
        for ( ; n; n >>= 1, z *= z) if (n & 1) y *= z;
        return y;
    }
};
// <<<

// >>> is_prime (Miller-Rabin)
bool is_prime(const uint64_t x) {
    if (x == 2 or x == 3 or x == 5 or x == 7) return true;
    if (x % 2 == 0 or x % 3 == 0 or x % 5 == 0 or x % 7 == 0) return false;
    if (x < 121) return x > 1;
    const u64 d = (x-1) >> __builtin_ctzll(x-1);
    m64::set_mod(x);
    const m64 one(1), minus_one(x-1);
    auto ok = [&](u64 a) {
        auto y = m64(a).pow(d);
        u64 t = d;
        while (y != one and y != minus_one and t != x-1) y *= y, t <<= 1;
        if (y != minus_one and t % 2 == 0) return false;
        return true;
    };
    if (x < (1ull << 32)) {
        for (u64 a : { 2, 7, 61 }) if (not ok(a)) return false;
    } else {
        for (u64 a : { 2, 325, 9375, 28178, 450775, 9780504, 1795265022 }) {
            if (x <= a) return true;
            if (not ok(a)) return false;
        }
    }
    return true;
}
// <<<

// >>> factor (Pollard rho)

u64 rho(u64 n, u64 c) {
    m64::set_mod(n);
    assert(n > 1);
    const m64 cc(c);
    auto f = [&](m64 x) { return x*x + cc; };
    m64 x = 1, y = 2, z = 1, q = 1;
    u64 g = 1;
    const u64 m = 1LL<<(__lg(n)/5); // ?
    for (u64 r = 1; g == 1; r <<= 1) {
        x = y;
        rep (_, r) y = f(y);
        for (u64 k = 0; k < r and g == 1; k += m) {
            z = y;
            rep (_, min(m, r-k)) y = f(y), q *= x-y;
            g = gcd(q.val(), n);
        }
    }
    if (g == n) do { z = f(z); g = gcd((x-z).val(), n); } while (g == 1);
    return g;
}

u64 find_prime_factor(u64 n) {
    assert(n > 1);
    if (is_prime(n)) return n;
    rep (_, 100) {
        u64 m = rho(n, rnd(n));
        if (is_prime(m)) return m;
        n = m;
    }
    cerr << "failed" << endl;
    assert(false);
    return -1;
}

vector<pair<u64, u32>> factor(u64 n) {
    static vector<pair<u64, u32>> v;
    v.clear();
    for (u64 i = 2; i <= 100 and i*i <= n; ++i) {
        if (n % i == 0) {
            u32 cnt = 0;
            do ++cnt, n /= i; while (n % i == 0);
            v.emplace_back(i, cnt);
        }
    }
    while (n > 1) {
        auto p = find_prime_factor(n);
        u32 cnt = 0;
        do ++cnt, n /= p; while (n % p == 0);
        v.emplace_back(p, cnt);
    }
    sort(v.begin(), v.end());
    return v;
}

// <<<

}
using ::internal::is_prime;
using ::internal::factor;
// <<<

int divisors_num(int x) {
    int ans = 1;
    for (auto [_, k] : factor(x)) {
        ans *= k+1;
    }
    return ans;
}

auto solve() {
    int x; cin >> x;
    int n = divisors_num(x);
    for (int y = 2*x; ; y += x) {
        if (divisors_num(y) == 2*n) {
            cout << y << '\n';
            break;
        }
    }
}

int32_t main() {
    int t; cin >> t;
    while (t--) {
        solve();
//        cout << (solve() ? "YES" : "NO") << '\n';
        debug { cerr << endl; }
    }
}

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結果

テストケース

ソースコード