#1025306 (C++23) No.2953 Maximum Right Triangle

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結果

問題	No.2953 Maximum Right Triangle
コンテスト
ユーザー	nono00
提出日時	2024-11-08 22:30:57
言語	C++23 (gcc 13.3.0 + boost 1.87.0)
結果	RE
実行時間	-
コード長	11,412 bytes
コンパイル時間	4,183 ms
コンパイル使用メモリ	266,808 KB
実行使用メモリ	6,824 KB
最終ジャッジ日時	2024-11-08 22:31:19
合計ジャッジ時間	4,691 ms
ジャッジサーバーID （参考情報）	judge3 / judge2
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
other	AC * 3 RE * 3
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ソースコード

raw source code
#include <algorithm>
#include <limits>
#include <queue>
#include <utility>
#include <vector>

#include <ranges>
#include <utility>
#include <vector>

namespace nono {

template <class T>
class CSRArray {
    using iterator = std::vector<T>::iterator;
    using const_iterator = std::vector<T>::const_iterator;
    using subrange = std::ranges::subrange<iterator, iterator>;
    using const_subrange = std::ranges::subrange<const_iterator, const_iterator>;

  public:
    CSRArray() = default;

    CSRArray(int row_size, const std::vector<std::pair<int, T>>& data)
        : row_size_(row_size),
          indptr_(row_size_ + 1),
          data_(data.size()) {
        for (auto key: data | std::views::keys) {
            indptr_[key + 1]++;
        }
        for (int i = 0; i < row_size_; i++) {
            indptr_[i + 1] += indptr_[i];
        }
        auto index = indptr_;
        for (const auto& [key, value]: data) {
            data_[index[key]++] = value;
        }
    }

    CSRArray(int row_size, const std::vector<int>& row, const std::vector<T>& data)
        : row_size_(row_size),
          indptr_(row_size_ + 1),
          data_(data.size()) {
        for (auto key: row) {
            indptr_[key + 1]++;
        }
        for (int i = 0; i < row_size_; i++) {
            indptr_[i + 1] += indptr_[i];
        }
        auto index = indptr_;
        for (int i = 0; i < (int)data.size(); i++) {
            data_[index[row[i]]++] = data[i];
        }
    }

    subrange operator[](int i) {
        return std::ranges::subrange(data_.begin() + indptr_[i], data_.begin() + indptr_[i + 1]);
    }

    const_subrange operator[](int i) const {
        return std::ranges::subrange(data_.begin() + indptr_[i], data_.begin() + indptr_[i + 1]);
    }

    int all_size() const {
        return data_.size();
    }

    int size() const {
        return row_size_;
    }

  private:
    int row_size_;
    std::vector<int> indptr_;
    std::vector<T> data_;
};

}  //  namespace nono

#include <iterator>
#include <ranges>
#include <vector>

namespace nono {

template <class T>
struct EdgeBase {
    int from;
    int to;
    T weight;
    EdgeBase() {}
    EdgeBase(int from, int to, T weight = 1): from(from), to(to), weight(weight) {}
};

using Edge = EdgeBase<int>;
template <class T>
using WeightedEdge = EdgeBase<T>;

template <class T>
class Graph {
    struct Edge_ {
        int to;
        T weight;
        int id;
    };

    using iterator = std::vector<Edge_>::iterator;
    using const_iterator = std::vector<Edge_>::const_iterator;
    using subrange = std::ranges::subrange<iterator, iterator>;
    using const_subrange = std::ranges::subrange<const_iterator, const_iterator>;

  public:
    template <class U>
    friend Graph<U> to_undirected_graph(int n, const std::vector<EdgeBase<U>>& edges);
    template <class U>
    friend Graph<U> to_directed_graph(int n, const std::vector<EdgeBase<U>>& edges);

    subrange operator[](int i) {
        return std::ranges::subrange(edges_.begin() + indptr_[i], edges_.begin() + indptr_[i + 1]);
    }
    const_subrange operator[](int i) const {
        return std::ranges::subrange(edges_.begin() + indptr_[i], edges_.begin() + indptr_[i + 1]);
    }

    int size() const {
        return n_;
    }
    int edge_size() const {
        return m_;
    }
    bool is_directed() const {
        return directed_;
    }
    bool is_undirected() const {
        return !is_directed();
    }

  private:
    Graph(int n, const std::vector<EdgeBase<T>>& edges, bool directed)
        : n_(n),
          m_(edges.size()),
          indptr_(n_ + 1),
          edges_(directed ? edges.size() : 2 * edges.size()),
          directed_(directed) {
        for (const auto& e: edges) {
            indptr_[e.from + 1]++;
            if (!directed_) indptr_[e.to + 1]++;
        }
        for (int i = 0; i < n_; i++) {
            indptr_[i + 1] += indptr_[i];
        }
        auto index = indptr_;
        for (int i = 0; i < std::ssize(edges); i++) {
            const auto& e = edges[i];
            edges_[index[e.from]++] = Edge_(e.to, e.weight, i);
            if (!directed_) edges_[index[e.to]++] = Edge_(e.from, e.weight, i);
        }
    }

    int n_;
    int m_;
    std::vector<int> indptr_;
    std::vector<Edge_> edges_;
    bool directed_;
};

template <class T>
Graph<T> to_undirected_graph(int n, const std::vector<EdgeBase<T>>& edges) {
    return Graph<T>(n, edges, false);
}

template <class T>
Graph<T> to_directed_graph(int n, const std::vector<EdgeBase<T>>& edges) {
    return Graph<T>(n, edges, true);
}

}  //  namespace nono

#include <vector>

namespace nono {

template <class T>
bool is_bipartite(const Graph<T>& graph) {
    int n = graph.size();
    std::vector<short> color(n, -1);
    auto dfs = [&](auto&& self, int u) -> bool {
        for (auto e: graph[u]) {
            if (color[e.to] == -1) {
                color[e.to] = color[u] ^ 1;
                if (!self(self, e.to)) return false;
            } else if (color[e.to] == color[u]) {
                return false;
            }
        }
        return true;
    };
    for (int i = 0; i < n; i++) {
        if (color[i] == -1) {
            color[i] = 0;
            if (!dfs(dfs, i)) return false;
        }
    }
    return true;
}

}  //  namespace nono

namespace nono {

std::vector<int> bipartite_matching(int left, int right, std::vector<std::pair<int, int>> edges) {
    int m = edges.size();
    for (auto& [u, v]: edges) {
        v += left;
    }
    const CSRArray graph(left, edges);
    const int inf = std::numeric_limits<int>::max();
    std::vector<int> adj(left + right, -1);
    std::vector<int> dist(left + right, inf);
    std::queue<int> que;
    while (true) {
        std::fill(dist.begin(), dist.end(), inf);
        for (int i = 0; i < left; i++) {
            if (adj[i] == -1) {
                dist[i] = 0;
                que.push(i);
            }
        }
        while (!que.empty()) {
            int u = que.front();
            que.pop();
            for (auto v: graph[u]) {
                if (dist[v] == inf && adj[u] != v) {
                    dist[v] = dist[u] + 1;
                    if (adj[v] != -1) {
                        dist[adj[v]] = dist[v] + 1;
                        que.push(adj[v]);
                    }
                }
            }
        }
        bool reached = false;
        for (int i = left; i < left + right; i++) {
            reached |= dist[i] != inf && adj[i] == -1;
        }
        if (!reached) break;
        auto dfs = [&](auto&& self, int u) -> bool {
            for (auto v: graph[u]) {
                if (dist[u] + 1 == dist[v]) {
                    dist[v] = inf;
                    if (adj[v] == -1 || self(self, adj[v])) {
                        adj[u] = v;
                        adj[v] = u;
                        return true;
                    }
                }
            }
            return false;
        };
        for (int i = 0; i < left; i++) {
            if (adj[i] == -1) {
                dfs(dfs, i);
            }
        }
    }
    std::vector<int> result;
    for (int i = 0; i < m; i++) {
        auto [u, v] = edges[i];
        if (adj[u] == v) {
            result.push_back(i);
            adj[u] = -1;
        }
    }
    return result;
}

template <class T>
std::vector<int> bipartite_matching(const Graph<T>& graph) {
    int n = graph.size();
    int m = graph.edge_size();
    std::vector<int> mapping(n, -1);
    std::vector<bool> is_lefts(n);
    int left = 0, right = 0;
    auto dfs = [&](auto&& self, int u, bool is_left = true) -> void {
        is_lefts[u] = is_left;
        if (is_left) {
            mapping[u] = left++;
        } else {
            mapping[u] = right++;
        }
        for (auto e: graph[u]) {
            if (mapping[e.to] == -1) {
                self(self, e.to, is_left ^ true);
            }
        }
    };
    for (int i = 0; i < n; i++) {
        if (mapping[i] == -1) {
            dfs(dfs, i);
        }
    }
    std::vector<std::pair<int, int>> edges(m);
    for (int u = 0; u < n; u++) {
        if (!is_lefts[u]) continue;
        for (auto e: graph[u]) {
            edges[e.id] = {mapping[u], mapping[e.to]};
        }
    }
    return bipartite_matching(left, right, edges);
}

}  //  namespace nono

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using ull = unsigned long long;
template <class T>
using max_heap = priority_queue<T>;
template <class T>
using min_heap = priority_queue<T, vector<T>, greater<T>>;
#define rep(i, l, r) for (ll i = (l); i < (r); i++)
#define rrep(i, r, l) for (ll i = (r); i-- > (l);)
#define all(x) begin(x), end(x)
template <class T>
bool chmin(T& lhs, T rhs) {
    return lhs > rhs ? (lhs = rhs, true) : false;
}
template <class T>
bool chmax(T& lhs, T rhs) {
    return lhs < rhs ? (lhs = rhs, true) : false;
}
struct IOIO {
    IOIO() {
        cin.tie(0)->sync_with_stdio(0);
    }
} ioio;
template <class S, class T>
ostream& operator<<(ostream& os, const pair<S, T>& p) {
    os << '(' << p.first << ", " << p.second << ')';
    return os;
}
template <class T>
ostream& operator<<(ostream& os, const vector<T>& vs) {
    os << '{';
    rep(i, 0, (int)vs.size()) os << vs[i] << (i + 1 == (int)vs.size() ? "" : ", ");
    os << '}';
    return os;
}
template <class T>
ostream& operator<<(ostream& os, const set<T>& vs) {
    os << '{';
    for (auto it = vs.begin(); it != vs.end(); it++) {
        if (it != vs.begin()) {
            os << ", ";
        }
        os << *it;
    }
    os << '}';
    return os;
}
template <class T, class U>
ostream& operator<<(ostream& os, const map<T, U>& vs) {
    os << '{';
    for (auto it = vs.begin(); it != vs.end(); it++) {
        if (it != vs.begin()) {
            os << ", ";
        }
        os << *it;
    }
    os << '}';
    return os;
}
#ifdef DEBUG
void dump_func() {
    cerr << endl;
}
template <class Head, class... Tail>
void dump_func(Head&& head, Tail&&... tail) {
    cerr << head;
    if (sizeof...(Tail) > 0) {
        cerr << ", ";
    }
    dump_func(std::move(tail)...);
}
#define dump(...) cerr << "[" + string(#__VA_ARGS__) + "] ", dump_func(__VA_ARGS__)
#else
#define dump(...) static_cast<int>(0)
#endif

void solve() {
    ll d, x, y;
    cin >> d >> x >> y;
    ll ans = 0;
    auto F = [&](ll a) {
        return -((x * (a - x)) / y) + y;
    };
    auto area = [&](ll x1, ll y1, ll x2, ll y2) {
        return abs((x1 * y2) - (x2 * y1));
    };
    auto in = [&](ll v) {
        return 0 <= v && v <= d;
    };
    {
        ll g = y / gcd(y, x);
        ll ok = 0;
        ll ng = (d + g) / g;
        while (ng - ok > 1) {
            ll key = (ok + ng) / 2;
            if (in(g * key + x) && in(F(g * key + x)))
                ok = key;
            else
                ng = key;
        }
        chmax(ans, area(x, y, g * ok + x, F(g * ok + x)));
    }
    {
        ll g = y / gcd(y, x);
        ll ok = 0;
        ll ng = -((x + g) / g);
        while (ok - ng > 1) {
            ll key = (ok + ng) / 2;
            if (in(g * key + x) && in(F(g * key + x)))
                ok = key;
            else
                ng = key;
        }
        chmax(ans, area(x, y, g * ok + x, F(g * ok + x)));
    }
    cout << ans << '\n';
}

int main() {
    int t;
    cin >> t;
    while (t--) solve();
}
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結果

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