結果

問題 No.551 夏休みの思い出（２）
コンテスト
ユーザー tottoripaper
提出日時 2017-08-02 13:35:06
言語 C++14
(gcc 13.3.0 + boost 1.89.0)
結果
TLE  
実行時間 -
コード長 5,491 bytes
記録
コンパイル時間 2,180 ms
コンパイル使用メモリ 198,424 KB
実行使用メモリ 10,404 KB
最終ジャッジ日時 2024-10-11 12:56:28
合計ジャッジ時間 8,956 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge5
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ファイルパターン 結果
sample -- * 2
other AC * 27 TLE * 1 -- * 19
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ソースコード

diff #
raw source code 

#include <bits/stdc++.h>

using namespace std;

#define fst(t) std::get<0>(t)
#define snd(t) std::get<1>(t)
#define thd(t) std::get<2>(t)

using ll = long long;

template <typename T>
T expt(T a, T n, T mod = std::numeric_limits<T>::max());
template <typename T>
T inverse(T n, T mod);
std::tuple<ll,ll,ll> extgcd(ll a, ll b);

ll P, R;
map<ll,ll> inv_map, bsgs_map;
ll n, alpha;
ll table[100000];
vector<tuple<ll,ll,ll>> P1_factors;

struct llMod{
    llMod() = default;
    llMod(ll n) : n(n) {}
    llMod(const llMod&) = default;
    llMod& operator=(const llMod&) = default;
    operator long long(){return n;}
    llMod operator+(const llMod& m) const{
        return (n + m.n) % P;
    }
    llMod operator-() const{
        return (P - n) % P;
    }
    llMod operator*(const llMod& m) const{
        return n * m.n % P;
    }
    llMod operator/(const llMod& m) const{
        return n * inverse(m.n, P) % P;
    }
    llMod operator^(const ll m) const{
        return expt(n, m, P);
    }
    ll n;
};

const int dx[8] = {-1, 1, 0, 0, -1, -1, 1, 1}, dy[8] = {0, 0, -1, 1, -1, 1, -1, 1};

void init();
ll babyStepGiantStep(ll a, ll b, ll p);
ll PohligHellmanPrime(llMod h, llMod generator, ll p, ll e);
ll PohligHellman(llMod h, llMod generator, std::vector<std::tuple<ll,ll,ll>>& factors);

int main(){
    std::cin.tie(nullptr);
    std::ios::sync_with_stdio(false);

    std::cin >> P >> R;
    
    init();
    
    ll g, s;
    tie(g, s, ignore) = extgcd(2ll, P-1);
    
    int Q;
    std::cin >> Q;
        
    for(int i=0;i<Q;++i){
        ll a, b, c;
        std::cin >> a >> b >> c;

        ll D = (b * b - 4ll * a * c) % P;
        D = D >= 0 ? D : D + P;
        
        ll sq;

        if(D == 0){
            sq = 0;
        }else{
            if(bsgs_map.find(D) == bsgs_map.end()){
                bsgs_map[D] = PohligHellman((llMod)D, (llMod)R, P1_factors);
            }
            ll m = bsgs_map[D];
            
            if(m % g != 0){
                std::cout << -1ll << std::endl;
                continue;
            }
            
            ll t = s * (m / g) % (P - 1);
            t = t >= 0 ? t : t + (P - 1);
            
            sq = expt(R, t, P);
        }

        ll den = 2ll * a % P;
        if(inv_map.find(den) == inv_map.end()){
            inv_map[den] = inverse(den, P);
        }
        den = inv_map[den];
        
        ll x0 = (-b - sq) * den % P,
            x1 = (-b + sq) * den % P;
        x0 = x0 >= 0 ? x0 : x0 + P;
        x1 = x1 >= 0 ? x1 : x1 + P;

        if(x0 > x1){swap(x0, x1);}
        if(x0 == x1){
            std::cout << x0 << std::endl;
        }else{
            std::cout << x0 << " " << x1 << std::endl;
        }
    }
}

void init(){
    ll _p = P - 1;
    for(ll i=2;i*i<=_p;++i){
        ll e = 0, pe = 1ll;
        while(_p % i == 0){
            ++e;
            pe *= i;
            _p /= i;
        }

        if(e > 0){P1_factors.emplace_back(i, e, pe);}
    }

    if(_p > 1){P1_factors.emplace_back(_p, 1, _p);}
}

// solve a^n = b (in F_p)
ll babyStepGiantStep(ll a, ll b, ll p){
    ll n = std::floor(std::sqrt(p)), alpha = expt(a, n, p);

    std::vector<std::tuple<ll,int>> expos(n);
    for(int i=0;i<n;++i){
        expos[i] = std::make_tuple(expt(a, 1ll * i, p), i);
    }

    std::sort(expos.begin(), expos.end());
    
    for(int i=0;n*i<p;++i){
        ll v = b * inverse(expt(alpha, 1ll * i, p), p) % p;
        
        auto it = std::lower_bound(expos.begin(), expos.end(), std::make_tuple(v, 0), [](const auto& lhs, const auto& rhs){return std::get<0>(lhs) < std::get<0>(rhs);});
        
        if(it != expos.end() && std::get<0>(*it) == v){
            ll c = n * i + std::get<1>(*it);
            return c;
        }
    }

    return -1ll;
}

std::tuple<ll,ll,ll> extgcd(ll a, ll b){
    if(b == 0){
        return std::make_tuple(a, 1ll, 0ll);
    }
    auto s = extgcd(b, a % b);

    return std::make_tuple(fst(s), thd(s), snd(s)-(a/b)*thd(s));
}

template <typename T>
T expt(T a, T n, T mod){
    T res = 1;
    while(n){
        if(n & 1){res = res * a % mod;}
        a = a * a % mod;
        n >>= 1;
    }
    return res;
}

template <typename T>
inline T inverse(T n, T mod){
    return expt(n, mod-2, mod);
}

// solve generator^x \equiv h
ll PohligHellmanPrime(llMod h, llMod generator, ll p, ll e){
    ll x = 0ll;
    llMod gamma = generator ^ expt(p, e-1);
    
    for(ll k=0;k<e;++k){
        ll _h = ((llMod)1 / (generator ^ x) * h) ^ expt(p, e-1-k);
        
        ll d = babyStepGiantStep(gamma, _h, P);
        x = x + expt(p, k) * d;
    }
    return x;
}

// solve x \equiv ak (mod nk) (k = 1, 2)
// (when gcd(n1, n2) = 1)
tuple<ll,ll> chineseRemainder(ll a1, ll n1, ll a2, ll n2){
    ll s, t;
    tie(ignore, s, t) = extgcd(n1, n2);

    ll pr = n1 * n2, solution = (a2 * s % pr * n1 % pr + a1 * t % pr * n2 % pr) % pr;
    if(solution < 0){solution += pr;}

    return std::make_tuple(solution, pr);
}

ll PohligHellman(llMod h, llMod generator, std::vector<std::tuple<ll,ll,ll>>& factors){
    ll n = P - 1;
    ll x = -1ll, modulo = -1ll;
    
    for(const auto& f : factors){
        ll q, e, qe;
        tie(q, e, qe) = f;
        
        llMod g = generator ^ (n / qe),
            _h = h ^ (n / qe);    
        
        ll a = PohligHellmanPrime(_h, g, q, e);
        
        if(x == -1ll){x = a; modulo = qe;}
        else{
            tie(x, modulo) = chineseRemainder(x, modulo, a, qe);
        }
    }

    return x;
}
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