結果

問題 No.2597 Yet Another Topological Problem
コンテスト
ユーザー hitonanode
提出日時 2023-12-25 02:16:30
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 27 ms / 2,000 ms
コード長 13,620 bytes
コンパイル時間 2,284 ms
コンパイル使用メモリ 185,108 KB
実行使用メモリ 6,948 KB
最終ジャッジ日時 2024-09-27 14:03:37
合計ジャッジ時間 4,856 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge1
このコードへのチャレンジ
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ファイルパターン 結果
other AC * 55
権限があれば一括ダウンロードができます
コンパイルメッセージ
main.cpp: In function 'bool validate(std::vector<std::pair<int, int> >)':
main.cpp:192:1: warning: control reaches end of non-void function [-Wreturn-type]
  192 | }
      | ^

ソースコード

diff # 

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <numeric>
#include <optional>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
const std::vector<std::pair<int, int>> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }
template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r.first, l.second + r.second); }
template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r.first, l.second - r.second); }
template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <class T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <class T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }

template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);

template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; }
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl
#define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr)
#else
#define dbg(x) ((void)0)
#define dbgif(cond, x) ((void)0)
#endif

#include <limits>

// Rational number + {infinity(1 / 0), -infiity(-1 / 0), nan(0 / 0)} （有理数）
// Do not compare any number with nan
// Verified: Yandex Cup 2022 Final E https://contest.yandex.com/contest/42710/problems/K
template <class Int, bool AlwaysReduce = false> struct Rational {
    Int num, den;
    static constexpr Int my_gcd(Int a, Int b) {
        // return __gcd(a, b);
        if (a < 0) a = -a;
        if (b < 0) b = -b;
        while (a and b) {
            if (a > b)
                a %= b;
            else
                b %= a;
        }
        return a + b;
    }
    constexpr Rational(Int num = 0, Int den = 1) : num(num), den(den) { normalize(); }
    constexpr void normalize() noexcept {
        if constexpr (AlwaysReduce) { // reduction
            Int g = my_gcd(num, den);
            if (g) num /= g, den /= g;
        } else {
            if (den == 0) {
                if (num > 1) num = 1;
                if (num < -1) num = -1;
            }
        }
        if (den < 0) num = -num, den = -den; // denominator >= 0
    }
    constexpr Rational operator+(const Rational &r) const noexcept {
        if (!den and !r.den) return Rational(num + r.num, den);
        return Rational(num * r.den + den * r.num, den * r.den);
    }
    constexpr Rational operator-(const Rational &r) const noexcept {
        if (!den and !r.den) return Rational(num - r.num, den);
        return Rational(num * r.den - den * r.num, den * r.den);
    }
    constexpr Rational operator*(const Rational &r) const noexcept {
        return Rational(num * r.num, den * r.den);
    }
    constexpr Rational operator/(const Rational &r) const noexcept {
        return Rational(num * r.den, den * r.num);
    }
    constexpr Rational &operator+=(const Rational &r) noexcept { return *this = *this + r; }
    constexpr Rational &operator-=(const Rational &r) noexcept { return *this = *this - r; }
    constexpr Rational &operator*=(const Rational &r) noexcept { return *this = *this * r; }
    constexpr Rational &operator/=(const Rational &r) noexcept { return *this = *this / r; }
    constexpr Rational operator-() const noexcept { return Rational(-num, den); }
    constexpr Rational abs() const noexcept { return Rational(num > 0 ? num : -num, den); }
    constexpr bool operator==(const Rational &r) const noexcept {
        if constexpr (AlwaysReduce) {
            return num == r.num and den == r.den;
        } else {
            return num * r.den == r.num * den;
        }
    }
    constexpr bool operator!=(const Rational &r) const noexcept { return !(*this == r); }
    constexpr bool operator<(const Rational &r) const noexcept {
        if (den == 0 and r.den == 0)
            return num < r.num;
        else if (den == 0)
            return num < 0;
        else if (r.den == 0)
            return r.num > 0;
        else
            return num * r.den < den * r.num;
    }
    constexpr bool operator<=(const Rational &r) const noexcept {
        return (*this == r) or (*this < r);
    }
    constexpr bool operator>(const Rational &r) const noexcept { return r < *this; }
    constexpr bool operator>=(const Rational &r) const noexcept {
        return (r == *this) or (r < *this);
    }
    constexpr explicit operator double() const noexcept { return (double)num / (double)den; }
    constexpr explicit operator long double() const noexcept {
        return (long double)num / (long double)den;
    }
    template <class OStream> constexpr friend OStream &operator<<(OStream &os, const Rational &x) {
        return os << x.num << '/' << x.den;
    }
};

template <class Int> struct std::numeric_limits<Rational<Int, false>> {
    static constexpr Rational<Int, false> max() noexcept {
        return std::numeric_limits<Int>::max();
    }
    static constexpr Rational<Int, false> min() noexcept {
        return std::numeric_limits<Int>::min();
    }
    static constexpr Rational<Int, false> lowest() noexcept {
        return std::numeric_limits<Int>::lowest();
    }
};

using Rat = Rational<lint>;

bool validate(vector<pint> vec) {
    assert(vec.size() > 1);
    assert(vec.size() <= 250001);
}

vector<pint> build(const int p, const int q, const int pe_short, const int pe_long, const int i1, const int W) {
    constexpr int UB = 250000;

    vector<pint> ret;
    ret.emplace_back(0, 0);

    auto addp = [&](int x, int y) {
        if (ret.back().first == x) {
            int u = ret.back().second;
            while (u != y) {
                u += (u < y ? 1 : -1);
                ret.emplace_back(x, u);
            }
        } else if (ret.back().second == y) {
            int u = ret.back().first;
            while (u != x) {
                u += (u < x ? 1 : -1);
                ret.emplace_back(u, y);
            }
        } else {
            assert(false);
        }
    };

    for (int loop = 0;; ++loop) {
        const int ylo = -i1 + loop;
        const int yhi = loop + 1;

        int nxtx = min(W, pe_short * (loop + 1));

        if (nxtx == W) {
            if (loop != i1) {
                dbg(make_tuple(p, q, pe_short, pe_long, i1, W, loop));
            }
            assert(loop == i1);
            addp(pe_long * loop, 0);
            addp(W, 0);
            break;
        }
        addp(pe_long * loop, ylo);
        addp(pe_short * (loop + 1), ylo);
        addp(pe_short * (loop + 1), yhi);
        addp(pe_long * (loop + 1), yhi);
    }
    return ret;
}

// p / q
vector<pint> solve(int p, int q) {
    if (p == 1) return {};

    const Rat r(p, q);
    if (r > Rat(1, 2)) return {};

    for (int W = 501; W > 0; ++W) {
        auto p0 = r * W;

        const int pe_long = (p0.num / p0.den + 1);
        int i1 = W / pe_long;

        const int pe_short = (p0.num + p0.den - 1) / p0.den - 1;

        if (pe_short + 1 != pe_long) continue;

        assert(pe_short + 1 == pe_long or pe_short + 2 == pe_long);

        int i2 = (W + pe_short - 1) / pe_short;
        if (i1 + 1 == i2) {
            // assert(W == 250000);
            // dbg(make_tuple(p, q, W, i1, i2));
            dbgif(W > 36000, make_tuple(p, q, W, i1, i2));
            return build(p, q, pe_short, pe_long, i1, W);
        }
    }
    assert(false);
}

int main() {
    // FOR(p, 1, 501) {
    //     FOR(q, p + 1, 501) {
    //         if (gcd(p, q) != 1) continue;
    //         auto ret = solve(p, q);
    //     }
    // }
    lint p, q;
    cin >> p >> q;
    const Rat r(p, q);
    dbg(r);

    if (p == 1) {
        puts("Impossible");
        return 0;
    } else if (r > Rat(1, 2)) {
        puts("Possible");
        puts("6");
        puts("0 0");
        puts("0 -1");
        puts("1 -1");
        puts("1 0");
        puts("1 1");
        puts("2 1");
        puts("2 0");
    } else {
        // puts("Possible");
        auto ret = solve(p, q);
        cout << "Possible\n";
        cout << ret.size() - 1 << '\n';
        for (auto [x, y] : ret) {
            cout << x << ' ' << y << '\n';
        }
        // exit(1);
    }
}
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