#682712 (C++17) No.1626 三角形の構築

• 問題: No.1626 三角形の構築
• ユーザー: maine_honzuki
• 提出日時: 2021-07-23 22:07:12
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: TLE
• 実行時間: -
• コード長: 6,140 bytes
• コンパイル時間: 2,417 ms
• コンパイル使用メモリ: 224,512 KB
• 最終ジャッジ日時: 2025-01-23 08:02:26
• ジャッジサーバーID （参考情報）: judge3 / judge3

ファイルパターン	結果
sample	AC * 1
other	AC * 23 TLE * 3

ソースコード

#include <bits/stdc++.h>
using namespace std;
using ll = long long;

namespace FastPrimeFactorization {
template <typename word, typename dword, typename sword>
struct UnsafeMod {
    UnsafeMod() : x(0) {}
    UnsafeMod(word _x) : x(init(_x)) {}
    bool operator==(const UnsafeMod& rhs) const { return x == rhs.x; }
    bool operator!=(const UnsafeMod& rhs) const { return x != rhs.x; }
    UnsafeMod& operator+=(const UnsafeMod& rhs) {
        if ((x += rhs.x) >= mod)
            x -= mod;
        return *this;
    }
    UnsafeMod& operator-=(const UnsafeMod& rhs) {
        if (sword(x -= rhs.x) < 0)
            x += mod;
        return *this;
    }
    UnsafeMod& operator*=(const UnsafeMod& rhs) {
        x = reduce(dword(x) * rhs.x);
        return *this;
    }
    UnsafeMod operator+(const UnsafeMod& rhs) const { return UnsafeMod(*this) += rhs; }
    UnsafeMod operator-(const UnsafeMod& rhs) const { return UnsafeMod(*this) -= rhs; }
    UnsafeMod operator*(const UnsafeMod& rhs) const { return UnsafeMod(*this) *= rhs; }
    UnsafeMod pow(uint64_t e) const {
        UnsafeMod ret(1);
        for (UnsafeMod base = *this; e; e >>= 1, base *= base) {
            if (e & 1)
                ret *= base;
        }
        return ret;
    }
    word get() const { return reduce(x); }
    static constexpr int word_bits = sizeof(word) * 8;
    static word modulus() { return mod; }
    static word init(word w) { return reduce(dword(w) * r2); }
    static void set_mod(word m) {
        mod = m;
        inv = mul_inv(mod);
        r2 = -dword(mod) % mod;
    }
    static word reduce(dword x) {
        word y = word(x >> word_bits) - word((dword(word(x) * inv) * mod) >> word_bits);
        return sword(y) < 0 ? y + mod : y;
    }
    static word mul_inv(word n, int e = 6, word x = 1) { return !e ? x : mul_inv(n, e - 1, x * (2 - x * n)); }
    static word mod, inv, r2;
    word x;
};
using uint128_t = __uint128_t;
using Mod64 = UnsafeMod<uint64_t, uint128_t, int64_t>;
template <>
uint64_t Mod64::mod = 0;
template <>
uint64_t Mod64::inv = 0;
template <>
uint64_t Mod64::r2 = 0;
using Mod32 = UnsafeMod<uint32_t, uint64_t, int32_t>;
template <>
uint32_t Mod32::mod = 0;
template <>
uint32_t Mod32::inv = 0;
template <>
uint32_t Mod32::r2 = 0;
bool miller_rabin_primality_test_uint64(uint64_t n) {
    Mod64::set_mod(n);
    uint64_t d = n - 1;
    while (d % 2 == 0)
        d /= 2;
    Mod64 e{1}, rev{n - 1};
    // http://miller-rabin.appspot.com/  < 2^64
    for (uint64_t a : {2, 325, 9375, 28178, 450775, 9780504, 1795265022}) {
        if (n <= a)
            break;
        uint64_t t = d;
        Mod64 y = Mod64(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 miller_rabin_primality_test_uint32(uint32_t n) {
    Mod32::set_mod(n);
    uint32_t d = n - 1;
    while (d % 2 == 0)
        d /= 2;
    Mod32 e{1}, rev{n - 1};
    for (uint32_t a : {2, 7, 61}) {
        if (n <= a)
            break;
        uint32_t t = d;
        Mod32 y = Mod32(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(uint64_t n) {
    if (n == 2)
        return true;
    if (n == 1 || n % 2 == 0)
        return false;
    if (n < uint64_t(1) << 31)
        return miller_rabin_primality_test_uint32(n);
    return miller_rabin_primality_test_uint64(n);
}
uint64_t pollard_rho(uint64_t n) {
    if (is_prime(n))
        return n;
    if (n % 2 == 0)
        return 2;
    Mod64::set_mod(n);
    uint64_t d;
    Mod64 one{1};
    for (Mod64 c{one};; c += one) {
        Mod64 x{2}, y{2};
        do {
            x = x * x + c;
            y = y * y + c;
            y = y * y + c;
            d = __gcd((x - y).get(), n);
        } while (d == 1);
        if (d < n)
            return d;
    }
    assert(0);
}
vector<uint64_t> prime_factor(uint64_t n) {
    if (n <= 1)
        return {};
    uint64_t p = pollard_rho(n);
    if (p == n)
        return {p};
    auto l = prime_factor(p);
    auto r = prime_factor(n / p);
    copy(begin(r), end(r), back_inserter(l));
    return l;
}
};  // namespace FastPrimeFactorization

vector<pair<ll, ll>> prime_factorize(ll n) {
    auto V = FastPrimeFactorization::prime_factor(n);
    map<ll, ll> mp;
    for (auto&& e : V) {
        mp[e]++;
    }
    vector<pair<ll, ll>> ret;
    for (auto p : mp) {
        ret.emplace_back(p);
    }
    return ret;
}

ll S, T;
vector<pair<ll, ll>> V;
vector<vector<ll>> Pow;
set<vector<ll>> ans;

void maine(vector<ll> Len, int idx) {
    if (idx == V.size()) {
        for (auto&& l : Len) {
            l = T - l;
            if (l % 2 == 1 || l <= 0)
                return;
            l /= 2;
        }
        sort(begin(Len), end(Len));
        if (Len[0] + Len[1] > Len[2] && Len[1] + Len[2] > Len[0] && Len[2] + Len[0] > Len[1] && Len[0] + Len[1] + Len[2] == T)
            ans.insert(Len);
    } else {
        auto [n, m] = V[idx];
        for (int i = 0; i <= m; i++) {
            for (int j = 0; j <= m - i; j++) {
                int k = m - i - j;
                auto nxt = Len;
                nxt[0] *= Pow[idx][i];
                nxt[1] *= Pow[idx][j];
                nxt[2] *= Pow[idx][k];
                maine(nxt, idx + 1);
            }
        }
    }
}

void solve() {
    ans.clear();
    Pow.clear();
    cin >> S >> T;
    if ((16 * S * S) % T) {
        cout << 0 << endl;
        return;
    }
    V = prime_factorize(16 * S * S / T);
    for (auto&& [n, m] : V) {
        vector<ll> book(1, 1);
        for (int i = 0; i < m; i++) {
            book.emplace_back(n * book.back());
        }
        Pow.emplace_back(book);
    }
    maine({1, 1, 1}, 0);
    cout << ans.size() << endl;
    for (auto&& e : ans) {
        for (int i = 0; i < 3; i++) {
            cout << e[i] << " \n"[i == 2];
        }
    }
}

int main() {
    int t;
    cin >> t;
    while (t--) {
        solve();
    }
}