結果

問題 No.2438 Double Least Square
コンテスト
ユーザー ebi_fly
提出日時 2023-08-11 23:40:18
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
(最新)
AC  
(最初)
実行時間 -
コード長 7,864 bytes
コンパイル時間 1,734 ms
コンパイル使用メモリ 162,844 KB
最終ジャッジ日時 2025-02-16 02:17:20
ジャッジサーバーID
（参考情報） 		judge5 / judge3
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
sample AC * 1 WA * 2
other AC * 5 WA * 25
権限があれば一括ダウンロードができます

ソースコード

diff # 

#line 1 "template/template.hpp"
#include <algorithm>
#include <bitset>
#include <cassert>
#include <chrono>
#include <climits>
#include <cmath>
#include <complex>
#include <cstddef>
#include <cstdint>
#include <cstdlib>
#include <cstring>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits>
#include <map>
#include <memory>
#include <numeric>
#include <optional>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

#define rep(i, a, n) for (int i = (int)(a); i < (int)(n); i++)
#define rrep(i, a, n) for (int i = ((int)(n)-1); i >= (int)(a); i--)
#define Rep(i, a, n) for (i64 i = (i64)(a); i < (i64)(n); i++)
#define RRep(i, a, n) for (i64 i = ((i64)(n)-i64(1)); i >= (i64)(a); i--)
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()

#line 2 "template/debug_template.hpp"

#line 4 "template/debug_template.hpp"

namespace ebi {

#ifdef LOCAL
#define debug(...)                                                      \
    std::cerr << "LINE: " << __LINE__ << "  [" << #__VA_ARGS__ << "]:", \
        debug_out(__VA_ARGS__)
#else
#define debug(...)
#endif

void debug_out() {
    std::cerr << std::endl;
}

template <typename Head, typename... Tail> void debug_out(Head h, Tail... t) {
    std::cerr << " " << h;
    if (sizeof...(t) > 0) std::cerr << " :";
    debug_out(t...);
}

}
#line 2 "template/int_alias.hpp"

#line 4 "template/int_alias.hpp"

namespace ebi {

using std::size_t;
using i8 = std::int8_t;
using u8 = std::uint8_t;
using i16 = std::int16_t;
using u16 = std::uint16_t;
using i32 = std::int32_t;
using u32 = std::uint32_t;
using i64 = std::int64_t;
using u64 = std::uint64_t;
using i128 = __int128_t;
using u128 = __uint128_t;

}
#line 2 "template/io.hpp"

#line 6 "template/io.hpp"

namespace ebi {

template <typename T1, typename T2>
std::ostream &operator<<(std::ostream &os, const std::pair<T1, T2> &pa) {
    return os << pa.first << " " << pa.second;
}

template <typename T1, typename T2>
std::istream &operator>>(std::istream &os, std::pair<T1, T2> &pa) {
    return os >> pa.first >> pa.second;
}

template <typename T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &vec) {
    for (std::size_t i = 0; i < vec.size(); i++)
        os << vec[i] << (i + 1 == vec.size() ? "" : " ");
    return os;
}

template <typename T>
std::istream &operator>>(std::istream &os, std::vector<T> &vec) {
    for (T &e : vec) std::cin >> e;
    return os;
}

template <typename T>
std::ostream &operator<<(std::ostream &os, const std::optional<T> &opt) {
    if (opt) {
        os << opt.value();
    } else {
        os << "invalid value";
    }
    return os;
}

void fast_io() {
    std::cout << std::fixed << std::setprecision(15);
    std::cin.tie(nullptr);
    std::ios::sync_with_stdio(false);
}

}  // namespace ebi
#line 2 "template/utility.hpp"

#line 5 "template/utility.hpp"

#line 7 "template/utility.hpp"

namespace ebi {

template <class T> inline bool chmin(T &a, T b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}

template <class T> inline bool chmax(T &a, T b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

constexpr i64 LNF = std::numeric_limits<i64>::max() / 4;

constexpr int INF = std::numeric_limits<int>::max() / 2;

const std::vector<int> dy = {1, 0, -1, 0, 1, 1, -1, -1};
const std::vector<int> dx = {0, 1, 0, -1, 1, -1, 1, -1};

}  // namespace ebi
#line 2 "graph/template.hpp"

#line 4 "graph/template.hpp"

namespace ebi {

template <class T> struct Edge {
    int to;
    T cost;
    Edge(int _to, T _cost = 1) : to(_to), cost(_cost) {}
};

template <class T> struct Graph : std::vector<std::vector<Edge<T>>> {
    using std::vector<std::vector<Edge<T>>>::vector;
    void add_edge(int u, int v, T w, bool directed = false) {
        (*this)[u].emplace_back(v, w);
        if (directed) return;
        (*this)[v].emplace_back(u, w);
    }
};

struct graph : std::vector<std::vector<int>> {
    using std::vector<std::vector<int>>::vector;
    void add_edge(int u, int v, bool directed = false) {
        (*this)[u].emplace_back(v);
        if (directed) return;
        (*this)[v].emplace_back(u);
    }
};

}  // namespace ebi
#line 3 "a.cpp"

namespace ebi {

template <class T> void arg_sort_ll(std::vector<std::pair<T, T>> &a) {
    using Point = std::pair<T, T>;
    int n = a.size();
    std::vector ps(4, std::vector<Point>());
    auto idx = [](Point v) -> int {
        if (v.second >= 0)
            return (v.first >= 0) ? 0 : 1;
        else
            return (v.first >= 0) ? 3 : 2;
    };
    for (auto p : a) {
        assert(!(p.first == 0 && p.second == 0));
        ps[idx(p)].emplace_back(p);
    }
    a.clear();
    a.reserve(n);
    for (int j = 0; j < 4; j++) {
        int i = (3 + j) % 4;
        std::sort(ps[i].begin(), ps[i].end(), [](Point &p1, Point &p2) -> bool {
            T flag = p1.first * p2.second - p2.first * p1.second;
            return flag == 0 ? (p1.first * p1.first + p1.second * p1.second <
                                p2.first * p2.first + p2.second * p2.second)
                             : flag > 0;
        });
        for (auto &p : ps[i]) a.emplace_back(p);
    }
    return;
}

struct random_number_generator {
    std::random_device rnd;
    std::mt19937_64 mt;

    int get(int a, int b) {
        std::uniform_int_distribution<int> dist(a, b-1);
        return dist(mt);
    }
};

void main_() {
    int n;
    i64 w, h;
    std::cin >> n >> w >> h;
    std::vector<std::pair<i64,i64>> ps(n);
    std::vector<i64> xs;
    for(auto &[x, y]: ps) {
        std::cin >> x >> y;
        xs.emplace_back(x);
    }
    std::sort(all(xs));
    xs.erase(std::unique(all(xs)), xs.end());
    std::vector<int> arg_ord;
    {
        std::vector<std::pair<i64,i64>> ret;
        std::map<std::pair<i64, i64>, int> map;
        rep(i,0,n) {
            auto [x, y] = ps[i];
            ret.emplace_back(2 * x, 2 * y - h);
            map[{2 * x, 2 * y - h}] = i;
        }
        arg_sort_ll(ret);
        for(auto [x, y]: ret) {
            arg_ord.emplace_back(map[{x, y}]);
        }
    }
    using ld = long double;
    ld ans = std::numeric_limits<ld>::max();
    auto calc_score = [](const std::vector<i64> &a) -> ld {
        if(a[2] == 0) return 0;
        return ld(a[0]) - ld(a[1] * a[1]) / ld(4 * a[2]);
    };
    random_number_generator rnd;
    for(auto tx: xs) {
        std::vector<i64> u(3, 0), d(3, 0);
        for(auto [x, y]: ps) {
            if(x < tx) {
                u[0] += (y - h) * (y - h);
                u[1] += -2 * (y - h) * x;
                u[2] += x * x;
            }
            else {
                d[0] += y * y;
                d[1] += -2 * x * y;
                d[2] += x * x;
            }
        }
        if(rnd.get(0, 100)) chmin(ans, calc_score(u) + calc_score(d));
        for(auto i: arg_ord) {
            auto [x, y] = ps[i];
            if(x < tx) {
                u[0] -= (y - h) * (y - h);
                u[1] -= -2 * (y - h) * x;
                u[2] -= x * x;

                d[0] += y * y;
                d[1] += -2 * x * y;
                d[2] += x * x;
            }
            else {
                d[0] -= y * y;
                d[1] -= -2 * x * y;
                d[2] -= x * x;

                u[0] += (y - h) * (y - h);
                u[1] += -2 * (y - h) * x;
                u[2] += x * x;
            }
            if(rnd.get(0, 100)) chmin(ans, calc_score(u) + calc_score(d));
        }
    }
    std::cout << ans << '\n';
}

}  // namespace ebi

int main() {
    ebi::fast_io();
    int t = 1;
    // std::cin >> t;
    while (t--) {
        ebi::main_();
    }
    return 0;
}
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