#422840 (C++14) No.955 ax^2+bx+c=0

提出ソース

結果

問題	No.955 ax^2+bx+c=0
ユーザー	square1001
提出日時	2020-01-30 20:57:03
言語	C++14 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	4 ms / 2,000 ms
コード長	19,440 bytes
コンパイル時間	2,902 ms
コンパイル使用メモリ	127,104 KB
実行使用メモリ	5,376 KB
最終ジャッジ日時	2024-09-16 03:51:52
合計ジャッジ時間	6,097 ms
ジャッジサーバーID （参考情報）	judge4 / judge3

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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	4 ms 5,248 KB
testcase_01	AC	2 ms 5,376 KB
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ソースコード

raw source code

#ifndef ___CLASS_MODINT
#define ___CLASS_MODINT

#include <vector>
#include <cstdint>

using singlebit = uint32_t;
using doublebit = uint64_t;

static constexpr singlebit find_inv(singlebit n, int d = 5, singlebit x = 1) {
    return d == 0 ? x : find_inv(n, d - 1, x * (2 - x * n));
}
template <singlebit mod, singlebit primroot> class modint {
    // Fast Modulo Integer, Assertion: mod < 2^31
private:
    singlebit n;
    static constexpr int level = 32; // LIMIT OF singlebit
    static constexpr singlebit max_value = -1;
    static constexpr singlebit r2 = (((1ull << level) % mod) << level) % mod;
    static constexpr singlebit inv = singlebit(-1) * find_inv(mod);
    static singlebit reduce(doublebit x) {
        singlebit res = (x + doublebit(singlebit(x) * inv) * mod) >> level;
        return res < mod ? res : res - mod;
    }
public:
    modint() : n(0) {};
    modint(singlebit n_) { n = reduce(doublebit(n_) * r2); };
    modint& operator=(const singlebit x) { n = reduce(doublebit(x) * r2); return *this; }
    bool operator==(const modint& x) const { return n == x.n; }
    bool operator!=(const modint& x) const { return n != x.n; }
    modint& operator+=(const modint& x) { n += x.n; n -= (n < mod ? 0 : mod); return *this; }
    modint& operator-=(const modint& x) { n += mod - x.n; n -= (n < mod ? 0 : mod); return *this; }
    modint& operator*=(const modint& x) { n = reduce(1ull * n * x.n); return *this; }
    modint operator+(const modint& x) const { return modint(*this) += x; }
    modint operator-(const modint& x) const { return modint(*this) -= x; }
    modint operator*(const modint& x) const { return modint(*this) *= x; }
    static singlebit get_mod() { return mod; }
    static singlebit get_primroot() { return primroot; }
    singlebit get() { return reduce(doublebit(n)); }
    modint binpow(singlebit b) {
        modint ans(1), cur(*this);
        while (b > 0) {
            if (b & 1) ans *= cur;
            cur *= cur;
            b >>= 1;
        }
        return ans;
    }
};

template<typename modulo>
std::vector<modulo> get_modvector(std::vector<int> v) {
    std::vector<modulo> ans(v.size());
    for (int i = 0; i < v.size(); ++i) {
        ans[i] = v[i];
    }
    return ans;
}

#endif

#ifndef ___CLASS_NTT
#define ___CLASS_NTT

#include <vector>

template<typename modulo>
class ntt {
    // Number Theoretic Transform
private:
    int depth;
    std::vector<modulo> roots;
    std::vector<modulo> powinv;
public:
    ntt() {
        depth = 0;
        uint32_t div_number = modulo::get_mod() - 1;
        while (div_number % 2 == 0) div_number >>= 1, ++depth;
        modulo b = modulo::get_primroot();
        for (int i = 0; i < depth; ++i) b *= b;
        modulo baseroot = modulo::get_primroot(), bb = b;
        while (bb != 1) bb *= b, baseroot *= modulo::get_primroot();
        roots = std::vector<modulo>(depth + 1, 0);
        powinv = std::vector<modulo>(depth + 1, 0);
        powinv[1] = (modulo::get_mod() + 1) / 2;
        for (int i = 2; i <= depth; ++i) powinv[i] = powinv[i - 1] * powinv[1];
        roots[depth] = 1;
        for (int i = 0; i < modulo::get_mod() - 1; i += 1 << depth) roots[depth] *= baseroot;
        for (int i = depth - 1; i >= 1; --i) roots[i] = roots[i + 1] * roots[i + 1];
    }
    void fourier_transform(std::vector<modulo>& v, bool inverse) {
        int s = v.size();
        for (int i = 0, j = 1; j < s - 1; ++j) {
            for (int k = s >> 1; k > (i ^= k); k >>= 1);
            if (i < j) std::swap(v[i], v[j]);
        }
        int sc = 0, sz = 1;
        while (sz < s) sz *= 2, ++sc;
        std::vector<modulo> pw(s + 1); pw[0] = 1;
        for (int i = 1; i <= s; i++) pw[i] = pw[i - 1] * roots[sc];
        int qs = s;
        for (int b = 1; b < s; b <<= 1) {
            qs >>= 1;
            for (int i = 0; i < s; i += b * 2) {
                for (int j = i; j < i + b; ++j) {
                    modulo delta = pw[(inverse ? b * 2 - j + i : j - i) * qs] * v[j + b];
                    v[j + b] = v[j] - delta;
                    v[j] += delta;
                }
            }
        }
        if (inverse) {
            for (int i = 0; i < s; ++i) v[i] *= powinv[sc];
        }
    }
    std::vector<modulo> convolve(std::vector<modulo> v1, std::vector<modulo> v2) {
        const int threshold = 16;
        if (v1.size() < v2.size()) swap(v1, v2);
        int s1 = 1; while (s1 < v1.size()) s1 <<= 1; v1.resize(s1);
        int s2 = 1; while (s2 < v2.size()) s2 <<= 1; v2.resize(s2 * 2);
        std::vector<modulo> ans(s1 + s2);
        if (s2 <= threshold) {
            for (int i = 0; i < s1; ++i) {
                for (int j = 0; j < s2; ++j) {
                    ans[i + j] += v1[i] * v2[j];
                }
            }
        }
        else {
            fourier_transform(v2, false);
            for (int i = 0; i < s1; i += s2) {
                std::vector<modulo> v(v1.begin() + i, v1.begin() + i + s2);
                v.resize(s2 * 2);
                fourier_transform(v, false);
                for (int j = 0; j < v.size(); ++j) v[j] *= v2[j];
                fourier_transform(v, true);
                for (int j = 0; j < s2 * 2; ++j) {
                    ans[i + j] += v[j];
                }
            }
        }
        return ans;
    }
};

#endif

#ifndef __CLASS_BASICINTEGER
#define __CLASS_BASICINTEGER

#include <vector>
#include <algorithm>

using modulo1 = modint<469762049, 3>; ntt<modulo1> ntt_base1;
using modulo2 = modint<167772161, 3>; ntt<modulo2> ntt_base2;

const modulo1 magic_inv = modulo1(modulo2::get_mod()).binpow(modulo1::get_mod() - 2);

template<int base>
class basic_integer {
protected:
    std::vector<int> a;
public:
    basic_integer() : a(std::vector<int>({ 0 })) {};
    basic_integer(const std::vector<int>& a_) : a(a_) {};
    int size() const { return a.size(); }
    int nth_digit(int n) const { return a[n]; }
    basic_integer& resize() {
        int lim = 1;
        for (int i = 0; i < a.size(); ++i) {
            if (a[i] != 0) lim = i + 1;
        }
        a.resize(lim);
        return *this;
    }
    basic_integer& shift() {
        for (int i = 0; i < int(a.size()) - 1; ++i) {
            if (a[i] >= 0) {
                a[i + 1] += a[i] / base;
                a[i] %= base;
            }
            else {
                int x = (-a[i] + base - 1) / base;
                a[i] += x * base;
                a[i + 1] -= x;
            }
        }
        while (a.back() >= base) {
            a.push_back(a.back() / base);
            a[a.size() - 2] %= base;
        }
        return *this;
    }
    bool operator==(const basic_integer& b) const { return a == b.a; }
    bool operator!=(const basic_integer& b) const { return a != b.a; }
    bool operator<(const basic_integer& b) const {
        if (a.size() != b.a.size()) return a.size() < b.a.size();
        for (int i = a.size() - 1; i >= 0; --i) {
            if (a[i] != b.a[i]) return a[i] < b.a[i];
        }
        return false;
    }
    bool operator>(const basic_integer& b) const { return b < (*this); }
    bool operator<=(const basic_integer& b) const { return !((*this) > b); }
    bool operator>=(const basic_integer& b) const { return !((*this) < b); }
    basic_integer& operator<<=(const uint32_t x) {
        if (a.back() >= 1 || a.size() >= 2) {
            std::vector<int> v(x, 0);
            a.insert(a.begin(), v.begin(), v.end());
        }
        return (*this);
    }
    basic_integer& operator>>=(const uint32_t x) {
        if (x == 0) return *this;
        if (x > a.size()) a = { 0 };
        else a = std::vector<int>(a.begin() + x, a.end());
        return (*this);
    }
    basic_integer& operator+=(const basic_integer& b) {
        if (a.size() < b.a.size()) a.resize(b.a.size(), 0);
        for (int i = 0; i < b.a.size(); ++i) a[i] += b.a[i];
        return (*this).shift();
    }
    basic_integer& operator-=(const basic_integer& b) {
        for (int i = 0; i < b.a.size(); ++i) a[i] -= b.a[i];
        return (*this).shift().resize();
    }
    basic_integer& operator*=(const basic_integer& b) {
        std::vector<modulo1> mul_base1 = ntt_base1.convolve(get_modvector<modulo1>(a), get_modvector<modulo1>(b.a));
        std::vector<modulo2> mul_base2 = ntt_base2.convolve(get_modvector<modulo2>(a), get_modvector<modulo2>(b.a));
        const int margin = 20;
        a = std::vector<int>(mul_base1.size() + margin);
        for (int i = 0; i < a.size() - margin; ++i) {
            // s * p1 + a1 = val = t * p2 + a2's solution is t = (a1 - a2) / p2 (mod p1)
            long long val = (long long)(((mul_base1[i] - modulo1(mul_base2[i].get())) * magic_inv).get()) * modulo2::get_mod() + mul_base2[i].get();
            for (int j = i; val > 0 && j < a.size(); ++j) {
                a[j] += val % base;
                if (a[j] >= base) {
                    a[j] -= base;
                    a[j + 1] += 1;
                }
                val /= base;
            }
        }
        return (*this).resize();
    }
    basic_integer& operator/=(const basic_integer& b) {
        int preci = a.size() - b.a.size();
        basic_integer t({ 1 });
        basic_integer two = basic_integer({ 2 }) << b.a.size();
        basic_integer pre;
        int lim = std::min(preci, 3);
        int blim = std::min(int(b.a.size()), 6);
        t <<= lim;
        while (pre != t) {
            basic_integer rb = b >> (b.a.size() - blim);
            if (blim != b.a.size()) rb += basic_integer({ 1 });
            pre = t;
            t *= (basic_integer({ 2 }) << (blim + lim)) - rb * t;
            t.a = std::vector<int>(t.a.begin() + lim + blim, t.a.end());
        }
        if (lim != preci) {
            pre = basic_integer();
            while (pre != t) {
                basic_integer rb = b >> (b.a.size() - blim);
                if (blim != b.a.size()) rb += basic_integer({ 1 });
                pre = t;
                t *= (basic_integer({ 2 }) << (blim + lim)) - rb * t;
                t.a = std::vector<int>(t.a.begin() + lim + blim, t.a.end());
                int next_lim = std::min(lim * 2 + 1, preci);
                if (next_lim != lim) t <<= next_lim - lim;
                int next_blim = std::min(blim * 2 + 1, int(b.a.size()));
                lim = next_lim;
                blim = next_blim;
            }
        }
        basic_integer ans = (*this) * t;
        ans.a = std::vector<int>(ans.a.begin() + a.size(), ans.a.end());
        while ((ans + basic_integer({ 1 })) * b <= (*this)) {
            ans += basic_integer({ 1 });
        }
        (*this) = ans.resize();
        return *this;
    }
    basic_integer& divide_by_2() {
        for (int i = a.size() - 1; i >= 0; --i) {
            int carry = a[i] % 2;
            a[i] /= 2;
            if (i != 0) a[i - 1] += carry * base;
        }
        if (a.size() >= 2 && a.back() == 0) a.pop_back();
        return *this;
    }
    basic_integer operator<<(int x) const { return basic_integer(*this) <<= x; }
    basic_integer operator >> (int x) const { return basic_integer(*this) >>= x; }
    basic_integer operator+(const basic_integer& b) const { return basic_integer(*this) += b; }
    basic_integer operator-(const basic_integer& b) const { return basic_integer(*this) -= b; }
    basic_integer operator*(const basic_integer& b) const { return basic_integer(*this) *= b; }
    basic_integer operator/(const basic_integer& b) const { return basic_integer(*this) /= b; }
};

#endif

#ifndef ___CLASS_NEWBIGINT
#define ___CLASS_NEWBIGINT

#include <string>
#include <iostream>
#include <algorithm>

const int digit = 4;
const int digit_base = 10000;

class bigint : public basic_integer<digit_base> {
public:
    bigint() { a = std::vector<int>({ 0 }); };
    bigint(long long x) {
        a.clear();
        for (int i = 0; x > 0; ++i) {
            a.push_back(x % digit_base);
            x /= digit_base;
        }
        if (a.size() == 0) a = { 0 };
    }
    bigint(const std::string& s) {
        a.clear();
        for (int i = 0; digit * i < s.size(); ++i) {
            a.push_back(std::stoi(s.substr(std::max(int(s.size()) - i * digit - digit, 0), digit - std::max(digit + i * digit - int(s.size()), 0))));
        }
        if (a.size() == 0) a = { 0 };
    }
    std::string to_string() const {
        std::string ret;
        bool flag = false;
        for (int i = a.size() - 1; i >= 0; --i) {
            if (a[i] > 0 && !flag) {
                ret += std::to_string(a[i]);
                flag = true;
            }
            else if (flag) {
                std::string sub = std::to_string(a[i]);
                ret += std::string(digit - sub.size(), '0') + sub;
            }
        }
        return ret.empty() ? "0" : ret;
    }
    int convert_int() const { return std::stoi((*this).to_string()); }
    long long convert_ll() const { return std::stoll((*this).to_string()); }
    bigint& operator<<=(int x) { return reinterpret_cast<bigint&>(reinterpret_cast<basic_integer&>(a) <<= x); }
    bigint& operator>>=(int x) { return reinterpret_cast<bigint&>(reinterpret_cast<basic_integer&>(a) >>= x); }
    bigint& operator+=(const bigint& b) { return reinterpret_cast<bigint&>(reinterpret_cast<basic_integer&>(a) += basic_integer(b)); }
    bigint& operator-=(const bigint& b) { return reinterpret_cast<bigint&>(reinterpret_cast<basic_integer&>(a) -= basic_integer(b)); }
    bigint& operator*=(const bigint& b) { return reinterpret_cast<bigint&>(reinterpret_cast<basic_integer&>(a) *= basic_integer(b)); }
    bigint& operator/=(const bigint& b) { return reinterpret_cast<bigint&>(reinterpret_cast<basic_integer&>(a) /= basic_integer(b)); }
    bigint& divide_by_2() { return reinterpret_cast<bigint&>(reinterpret_cast<basic_integer&>(a).divide_by_2()); }
    bigint operator<<(int x) const { return bigint(*this) <<= x; }
    bigint operator >> (int x) const { return bigint(*this) >>= x; }
    bigint operator+(const bigint& b) const { return bigint(*this) += b; }
    bigint operator-(const bigint& b) const { return bigint(*this) -= b; }
    bigint operator*(const bigint& b) const { return bigint(*this) *= b; }
    bigint operator/(const bigint& b) const { return bigint(*this) /= b; }
    friend std::istream& operator >> (std::istream& is, bigint& x) { std::string s; is >> s; x = bigint(s); return is; }
    friend std::ostream& operator<<(std::ostream& os, const bigint& x) { os << x.to_string(); return os; }
};

#endif

#ifndef ___CLASS_NEWBIGFLOAT
#define ___CLASS_NEWBIGFLOAT

class bigfloat {
private:
    bigint b;
    int scale; // b * D^scale (b is represented as D-ary number)
public:
    bigfloat() : b(0), scale(0) {};
    bigfloat(const bigint& b_) : b(b_), scale(0) {};
    bigfloat(const bigint& b_, int scale_) : b(b_), scale(scale_) {};
    int get_scale() const { return scale; }
    bigint get_number() const { return b; }
    bigfloat& set_scale(int scale_) {
        if (scale < scale_) b >>= (scale_ - scale);
        else b <<= (scale - scale_);
        scale = scale_;
        return *this;
    }
    bigfloat& operator<<=(int x) { scale += x; return *this; }
    bigfloat& operator>>=(int x) { scale -= x; return *this; }
    bigfloat& operator+=(const bigfloat& f) {
        if (scale > f.scale) (*this).set_scale(f.scale), (*this).b += f.b;
        else {
            bigint delta = f.b << (f.scale - scale);
            (*this).b += delta;
        }
        return *this;
    }
    bigfloat& operator-=(const bigfloat& f) {
        if (scale > f.scale) (*this).set_scale(f.scale), (*this).b -= f.b;
        else (*this).b -= (f.b << (f.scale - scale));
        return *this;
    }
    bigfloat& operator*=(const bigfloat& f) {
        b *= f.b;
        scale += f.scale;
        return *this;
    }
    bigfloat& operator/=(const bigfloat& f) {
        b /= f.b;
        scale -= f.scale;
        return *this;
    }
    bigfloat& divide_by_2() {
        b.divide_by_2();
        return *this;
    }
    bool operator==(const bigfloat& f) { return b == f.b && scale == f.scale; }
    bool operator!=(const bigfloat& f) { return b != f.b || scale != f.scale; }
    bigfloat operator<<(int x) const { return bigfloat(*this) <<= x; }
    bigfloat operator >> (int x) const { return bigfloat(*this) >>= x; }
    bigfloat operator+(const bigfloat& f) const { return bigfloat(*this) += f; }
    bigfloat operator-(const bigfloat& f) const { return bigfloat(*this) -= f; }
    bigfloat operator*(const bigfloat& f) const { return bigfloat(*this) *= f; }
    bigfloat operator/(const bigfloat& f) const { return bigfloat(*this) /= f; }
    std::string to_string() const {
        std::string s = b.to_string();
        if (scale * digit > 0) s += std::string(scale, '0');
        else if (1 <= -scale * digit && -scale * digit < s.size()) {
            s = s.substr(0, s.size() + scale * digit) + "." + s.substr(s.size() + scale * digit);
        }
        else if (-scale * digit >= s.size()) {
            s = "0." + std::string(-scale * digit - s.size(), '0') + s;
        }
        return s;
    }
    bigint to_bigint() const {
        if (scale < 0) return b >> (-scale);
        return b << scale;
    }
    friend std::ostream& operator<<(std::ostream& os, const bigfloat& f) { os << f.to_string(); return os; }
};

#endif

bigint sqrt(bigint x) {
    if (x == bigint(0)) return bigint(0);
    int max_scale = (x.size() + 1) / 2;
    int scale = std::min(4, max_scale);
    bigint a = bigint(1) << (scale - 1), pre;
    while (pre != a) {
        pre = a;
        bigint xd = x;
        if (x.size() > 2 * scale) xd >>= (x.size() - 2 * scale + x.size() % 2);
        bigint b = xd / a;
        a = (a + b).divide_by_2();
    }
    pre = bigint();
    while (pre != a) {
        pre = a;
        bigint xd = x;
        if (x.size() > 2 * scale) xd >>= (x.size() - 2 * scale + x.size() % 2);
        bigint b = xd / a;
        a = (a + b).divide_by_2();
        int next_scale = std::min(max_scale, scale * 2);
        a <<= next_scale - scale;
        scale = next_scale;
    }
    return a;
}
bigfloat sqrt(bigfloat x, int final_scale) {
    x <<= 2 * final_scale;
    bigint b = x.to_bigint();
    b = sqrt(b);
    bigfloat ans = b;
    ans >>= final_scale;
    return ans;
}

#include <cmath>
#include <iostream>
using namespace std;
int main() {
	long long a, b, c;
	cin >> a >> b >> c;
	cout.precision(15);
	if (a == 0 && b == 0 && c == 0) {
		cout << -1 << endl;
	}
	else if (a == 0 && b == 0) {
		cout << 0 << endl;
	}
	else if (a == 0) {
		cout << 1 << endl;
		cout << fixed << -(long double)(c) / b << endl;
	}
	else {
		long long d = b * b - 4 * a * c;
		if (d < 0) {
			cout << 0 << endl;
		}
		else if (d == 0) {
			cout << 1 << endl;
			cout << fixed << -(long double)(b) / (2 * a) << endl;
		}
		else {
			cout << 2 << endl;
            if (a < 0) a *= -1, b *= -1, c *= -1;
            bigfloat sd = sqrt(bigfloat(d), 50);
            bigfloat ans1 = (b <= 0 && b * b >= d ? bigfloat(-b) - sd : (b <= 0 ? sd - bigfloat(-b) : sd + bigfloat(b))) / bigfloat(2 * a);
            bigfloat ans2 = (b <= 0 || b * b <= d ? (b <= 0 ? sd + bigfloat(-b) : sd - bigfloat(b)) : bigfloat(b) - sd) / bigfloat(2 * a);
            string s1 = ans1.to_string(); if (!(b <= 0 && b * b >= d)) s1 = "-" + s1;
            string s2 = ans2.to_string(); if (!(b <= 0 || b * b <= d)) s2 = "-" + s2;
			cout << s1 << endl;
			cout << s2 << endl;
		}
	}
	return 0;
}

yukicoder

結果

テストケース

ソースコード