Submission #1092871

#	Time	Username	Problem	Language	Result	Execution time	Memory
1092871		Pannda	Naan (JOI19_naan)	C++17	29 / 100	4066 ms	4912 KiB

naan

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

// base and base_digits must be consistent
const long long base = 1e9;
const int base_digits = 9;

struct bigint {
    vector<long long> a;
    int sign;

    bigint() :
        sign(1) {
    }

    bigint(long long v) {
        *this = v;
    }

    bigint(const string &s) {
        read(s);
    }

    void operator=(const bigint &v) {
        sign = v.sign;
        a = v.a;
    }

    void operator=(long long v) {
        sign = 1;
        if (v < 0)
            sign = -1, v = -v;
        for (; v > 0; v = v / base)
            a.push_back(v % base);
    }

    bigint operator+(const bigint &v) const {
        if (sign == v.sign) {
            bigint res = v;

            for (long long i = 0, carry = 0; i < (long long) max(a.size(), v.a.size()) || carry; ++i) {
                if (i == (long long) res.a.size())
                    res.a.push_back(0);
                res.a[i] += carry + (i < (long long) a.size() ? a[i] : 0);
                carry = res.a[i] >= base;
                if (carry)
                    res.a[i] -= base;
            }
            return res;
        }
        return *this - (-v);
    }

    bigint operator-(const bigint &v) const {
        if (sign == v.sign) {
            if (abs() >= v.abs()) {
                bigint res = *this;
                for (long long i = 0, carry = 0; i < (long long) v.a.size() || carry; ++i) {
                    res.a[i] -= carry + (i < (long long) v.a.size() ? v.a[i] : 0);
                    carry = res.a[i] < 0;
                    if (carry)
                        res.a[i] += base;
                }
                res.trim();
                return res;
            }
            return -(v - *this);
        }
        return *this + (-v);
    }

    void operator*=(long long v) {
        if (v < 0)
            sign = -sign, v = -v;
        for (long long i = 0, carry = 0; i < (long long) a.size() || carry; ++i) {
            if (i == (long long) a.size())
                a.push_back(0);
            long long cur = a[i] * (long long) v + carry;
            carry = (long long) (cur / base);
            a[i] = (long long) (cur % base);
            //asm("divl %%ecx" : "=a"(carry), "=d"(a[i]) : "A"(cur), "c"(base));
        }
        trim();
    }

    bigint operator*(long long v) const {
        bigint res = *this;
        res *= v;
        return res;
    }

    friend pair<bigint, bigint> divmod(const bigint &a1, const bigint &b1) {
        long long norm = base / (b1.a.back() + 1);
        bigint a = a1.abs() * norm;
        bigint b = b1.abs() * norm;
        bigint q, r;
        q.a.resize(a.a.size());

        for (long long i = a.a.size() - 1; i >= 0; i--) {
            r *= base;
            r += a.a[i];
            long long s1 = r.a.size() <= b.a.size() ? 0 : r.a[b.a.size()];
            long long s2 = r.a.size() <= b.a.size() - 1 ? 0 : r.a[b.a.size() - 1];
            long long d = ((long long) base * s1 + s2) / b.a.back();
            r -= b * d;
            while (r < 0)
                r += b, --d;
            q.a[i] = d;
        }

        q.sign = a1.sign * b1.sign;
        r.sign = a1.sign;
        q.trim();
        r.trim();
        return make_pair(q, r / norm);
    }

    bigint operator/(const bigint &v) const {
        return divmod(*this, v).first;
    }

    bigint operator%(const bigint &v) const {
        return divmod(*this, v).second;
    }

    void operator/=(long long v) {
        if (v < 0)
            sign = -sign, v = -v;
        for (long long i = (long long) a.size() - 1, rem = 0; i >= 0; --i) {
            long long cur = a[i] + rem * (long long) base;
            a[i] = (long long) (cur / v);
            rem = (long long) (cur % v);
        }
        trim();
    }

    bigint operator/(long long v) const {
        bigint res = *this;
        res /= v;
        return res;
    }

    long long operator%(long long v) const {
        if (v < 0)
            v = -v;
        long long m = 0;
        for (long long i = a.size() - 1; i >= 0; --i)
            m = (a[i] + m * (long long) base) % v;
        return m * sign;
    }

    void operator+=(const bigint &v) {
        *this = *this + v;
    }
    void operator-=(const bigint &v) {
        *this = *this - v;
    }
    void operator*=(const bigint &v) {
        *this = *this * v;
    }
    void operator/=(const bigint &v) {
        *this = *this / v;
    }

    bool operator<(const bigint &v) const {
        if (sign != v.sign)
            return sign < v.sign;
        if (a.size() != v.a.size())
            return a.size() * sign < v.a.size() * v.sign;
        for (long long i = a.size() - 1; i >= 0; i--)
            if (a[i] != v.a[i])
                return a[i] * sign < v.a[i] * sign;
        return false;
    }

    bool operator>(const bigint &v) const {
        return v < *this;
    }
    bool operator<=(const bigint &v) const {
        return !(v < *this);
    }
    bool operator>=(const bigint &v) const {
        return !(*this < v);
    }
    bool operator==(const bigint &v) const {
        return !(*this < v) && !(v < *this);
    }
    bool operator!=(const bigint &v) const {
        return *this < v || v < *this;
    }

    void trim() {
        while (!a.empty() && !a.back())
            a.pop_back();
        if (a.empty())
            sign = 1;
    }

    bool isZero() const {
        return a.empty() || (a.size() == 1 && !a[0]);
    }

    bigint operator-() const {
        bigint res = *this;
        res.sign = -sign;
        return res;
    }

    bigint abs() const {
        bigint res = *this;
        res.sign *= res.sign;
        return res;
    }

    long long longValue() const {
        long long res = 0;
        for (long long i = a.size() - 1; i >= 0; i--)
            res = res * base + a[i];
        return res * sign;
    }

    friend bigint gcd(const bigint &a, const bigint &b) {
        return b.isZero() ? a : gcd(b, a % b);
    }
    friend bigint lcm(const bigint &a, const bigint &b) {
        return a / gcd(a, b) * b;
    }

    void read(const string &s) {
        sign = 1;
        a.clear();
        long long pos = 0;
        while (pos < (long long) s.size() && (s[pos] == '-' || s[pos] == '+')) {
            if (s[pos] == '-')
                sign = -sign;
            ++pos;
        }
        for (long long i = s.size() - 1; i >= pos; i -= base_digits) {
            long long x = 0;
            for (long long j = max(pos, i - base_digits + 1); j <= i; j++)
                x = x * 10 + s[j] - '0';
            a.push_back(x);
        }
        trim();
    }

    friend istream& operator>>(istream &stream, bigint &v) {
        string s;
        stream >> s;
        v.read(s);
        return stream;
    }

    friend ostream& operator<<(ostream &stream, const bigint &v) {
        if (v.sign == -1)
            stream << '-';
        stream << (v.a.empty() ? 0 : v.a.back());
        for (long long i = (long long) v.a.size() - 2; i >= 0; --i)
            stream << setw(base_digits) << setfill('0') << v.a[i];
        return stream;
    }

    static vector<long long> convert_base(const vector<long long> &a, long long old_digits, long long new_digits) {
        vector<long long> p(max(old_digits, new_digits) + 1);
        p[0] = 1;
        for (long long i = 1; i < (long long) p.size(); i++)
            p[i] = p[i - 1] * 10;
        vector<long long> res;
        long long cur = 0;
        long long cur_digits = 0;
        for (long long i = 0; i < (long long) a.size(); i++) {
            cur += a[i] * p[cur_digits];
            cur_digits += old_digits;
            while (cur_digits >= new_digits) {
                res.push_back((long long)(cur % p[new_digits]));
                cur /= p[new_digits];
                cur_digits -= new_digits;
            }
        }
        res.push_back((long long) cur);
        while (!res.empty() && !res.back())
            res.pop_back();
        return res;
    }

    typedef vector<long long> vll;

    static vll karatsubaMultiply(const vll &a, const vll &b) {
        long long n = a.size();
        vll res(n + n);
        if (n <= 32) {
            for (long long i = 0; i < n; i++)
                for (long long j = 0; j < n; j++)
                    res[i + j] += a[i] * b[j];
            return res;
        }

        long long k = n >> 1;
        vll a1(a.begin(), a.begin() + k);
        vll a2(a.begin() + k, a.end());
        vll b1(b.begin(), b.begin() + k);
        vll b2(b.begin() + k, b.end());

        vll a1b1 = karatsubaMultiply(a1, b1);
        vll a2b2 = karatsubaMultiply(a2, b2);

        for (long long i = 0; i < k; i++)
            a2[i] += a1[i];
        for (long long i = 0; i < k; i++)
            b2[i] += b1[i];

        vll r = karatsubaMultiply(a2, b2);
        for (long long i = 0; i < (long long) a1b1.size(); i++)
            r[i] -= a1b1[i];
        for (long long i = 0; i < (long long) a2b2.size(); i++)
            r[i] -= a2b2[i];

        for (long long i = 0; i < (long long) r.size(); i++)
            res[i + k] += r[i];
        for (long long i = 0; i < (long long) a1b1.size(); i++)
            res[i] += a1b1[i];
        for (long long i = 0; i < (long long) a2b2.size(); i++)
            res[i + n] += a2b2[i];
        return res;
    }

    bigint operator*(const bigint &v) const {
        vector<long long> a6 = convert_base(this->a, base_digits, 6);
        vector<long long> b6 = convert_base(v.a, base_digits, 6);
        vll a(a6.begin(), a6.end());
        vll b(b6.begin(), b6.end());
        while (a.size() < b.size())
            a.push_back(0);
        while (b.size() < a.size())
            b.push_back(0);
        while (a.size() & (a.size() - 1))
            a.push_back(0), b.push_back(0);
        vll c = karatsubaMultiply(a, b);
        bigint res;
        res.sign = sign * v.sign;
        for (long long i = 0, carry = 0; i < (long long) c.size(); i++) {
            long long cur = c[i] + carry;
            res.a.push_back((long long) (cur % 1000000));
            carry = (long long) (cur / 1000000);
        }
        res.a = convert_base(res.a, 6, base_digits);
        res.trim();
        return res;
    }
};

bigint mygcd(bigint a, bigint b) {
    if (b == 0) return a;
    return mygcd(b, a % b);
}

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

    struct Fraction {
        bigint a = 0, b = 1;
        bool operator<(const Fraction &other) const & {
            return a * other.b < other.a * b;
        }
        bool operator<=(const Fraction &other) const & {
            return !(other < *this);
        }
        Fraction operator*(const Fraction &other) const & {
            bigint A = a * other.a;
            bigint B = b * other.b;
            return {A, B};
//            bigint G = __gcd(A, B);
//            return {A / G, B / G};
        }
        Fraction operator+(const Fraction &other) const & {
            bigint B = b * other.b;
            bigint A = a * other.b + other.a * b;
            return {A, B};
//            bigint G = abs(__gcd(A, B));
//            return {A / G, B / G};
        }
        Fraction operator-(Fraction other) {
            other.a *= -1;
            return (*this) + other;
        }
    };

    int n, m;
    cin >> n >> m;

    vector<vector<int>> v(n, vector<int>(m));
    vector<vector<int>> f(n, vector<int>(m + 1, 0));
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < m; j++) {
            int x;
            cin >> x;
            v[i][j] = x;
            f[i][j + 1] = f[i][j] + x;
        }
    }

    vector<Fraction> key;
    vector<int> perm;

    vector<bool> chosen(n, false);
    Fraction cur = {0, 1};
    vector<int> ptr(n, 0); // possible cut for i is in [ptr[i], ptr[i] + 1)

    for (int t = 0; t < n - 1; t++) {
//        cout << "Yo!" << endl;
        vector<pair<Fraction, int>> get = [&]() -> vector<pair<Fraction, int>> {
            vector<pair<Fraction, int>> res;
            for (int i = 0; i < n; i++) {
                if (chosen[i]) continue;
//                cout << "Ya!" << endl;
                Fraction nxt = [&]() -> Fraction {
                    auto F = [&](Fraction x) -> Fraction {
                        bigint get = x.a / x.b;
                        int j = get.a.size() == 0 ? 0 : get.a[0];
                        if (j < m) return Fraction{f[i][j], 1} + Fraction{v[i][j], 1} * Fraction{x.a % x.b, x.b};
                        return Fraction{f[i][m], 1};
                    };
                    Fraction req = F(Fraction{m, 1}) * Fraction{1, n};
                    while (true) {
                        if (F(Fraction{ptr[i] + 1, 1}) - F(cur) <= req) { // then is not enough
                            ptr[i]++;
                            continue;
                        }
                        Fraction rem = req + F(cur) - F(Fraction{ptr[i], 1});
                        return Fraction{ptr[i], 1} + rem * Fraction{1, v[i][ptr[i]]};
                    }
                }();
//                cout << "Ye!" << endl;
                res.push_back({nxt, i});
            }
            return res;
        }();
        auto [nxt, i] = *min_element(get.begin(), get.end());
        key.push_back(nxt);
        perm.push_back(i);
        cur = nxt;
        chosen[i] = true;
//        cout << nxt.a << ' ' << nxt.b << endl;
    }

    for (int i = 0; i < n; i++) {
        if (!chosen[i]) perm.push_back(i);
    }

    for (Fraction frac : key) {
        bigint g = gcd(frac.a, frac.b);
        cout << frac.a / g << ' ' << frac.b / g << '\n';
//        cout << frac.a << ' ' << frac.b << '\n';
    }
    for (int i : perm) {
        cout << i + 1 << ' ';
    }
    cout << '\n';
}

• Subtask 1: 5 / 5
• Subtask 2: 24 / 24
• Subtask 3: 0 / 71